ISA Transactions ∎ (∎∎∎∎) ∎∎∎–∎∎∎
Contents lists available at ScienceDirect
ISA Transactions journal homepage: www.elsevier.com/locate/isatrans
Anti-disturbance control theory for systems with multiple disturbances: A survey$ Lei Guo a,n, Songyin Cao a,b a b
National Key Laboratory on Aircraft Control Technology, Beihang University, Beijing 100191, PR China Department of Automation, College of Information Engineering, Yangzhou University, Yangzhou 225127, PR China
art ic l e i nf o
a b s t r a c t
Article history: Received 31 May 2013 Received in revised form 9 October 2013 Accepted 17 October 2013 This paper was recommended for publication by Dr. Jeff Pieper
The problem of anti-disturbance control has been an eternal topic along with the development of the control theory. However, most methodologies can only deal with systems subject to a single equivalent disturbance which was merged by various types of uncertainties. In this paper, a review on antidisturbance control is presented for systems with multiple disturbances. First, the classical control methods are briefly reviewed for disturbance attenuation or rejection problems. Then, recent advances in disturbance observer based control (DOBC) theory are introduced and especially, the composite hierarchical anti-disturbance control (CHADC) is firstly addressed. A comparison of different approaches is briefly carried out. Finally, focuses in the field on the current research are also addressed with emphasis on the practical application of the techniques. & 2013 ISA. Published by Elsevier Ltd. All rights reserved.
Keywords: Multiple disturbances Robust control Disturbance observer based control Disturbance rejection and attenuation Anti-disturbance control Composite hierarchical anti-disturbance control
1. Introduction The general purpose of a controller is to monitor and correct the actions of a given dynamical system. Along with the development of control theory, many significant approaches have been presented for different plants. A proportional integral derivative (PID) controller is a generic control loop feedback mechanism widely used in industrial control systems. However, it is difficult to adjust the controller parameters and cannot be used in complex plants. Internal model control has been developed by leaps and bounds since the 1960s [1]. Since disturbances exist in all practical processes, the problem of disturbance attenuation or rejection has been a hot topic in control fields. Stochastic control [2,3] and robust control [4], two branches of the modern control theory, are inherent with anti-disturbance capability. Gaussian control theory, such as Kalman filter and minimum variance control, is presented
☆ This work is partially supported by the National 973 Program of China (Grant no. 2012CB720003), National Natural Science Foundation of China (Grant nos. 61203195 and 61127007), China Postdoctoral Science Foundation (Grant no. 2013M530508) and Universities Natural Science Foundation of Jiangsu Province (Grant no. 12KJB510033). n Corresponding author. Tel.: þ 86 10 82339103; fax: þ 86 10 82316813. E-mail addresses: [email protected] (L. Guo), [email protected], [email protected] (S. Cao).
to control output variance for optimizing the system performance, where the disturbance is supposed to be a Gaussian noise. The performance of Gaussian control approaches could be degraded when the considered system is with model uncertainties, nonGaussian noises and other types of disturbances. Based on probability density function or statistical information set, a class of stochastic distribution control methodologies was addressed for non-Gaussian stochastic control problem (see [3] and references therein). The stochastic control theory assumes that the statistical properties of the noises are known, which is often not satisfied in practical processes. In order to overcome the drawbacks, robust control problems have been studied in the past decade. No statistical property assumptions concerning the noises are required for the robust control, where the norm bounded disturbance and uncertainty can be dealt with. Among the robust control methods, H 1 and H2 control are widely used to attenuate the influences from disturbances to reference output in a desired level (see [4–6], and references therein). However, robust control methods have a large conservativeness for disturbances described by a norm bounded variable. The control approaches can be mainly divided into disturbance attenuation methods (such as stochastic control theory and robust control theory) and disturbance rejection schemes. The typical disturbance rejection approaches include internal model control, output regulation theory, active disturbance rejection control
0019-0578/$ - see front matter & 2013 ISA. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.isatra.2013.10.005
Please cite this article as: Guo L, Cao S. Anti-disturbance control theory for systems with multiple disturbances: A survey. ISA Transactions (2014), http://dx.doi.org/10.1016/j.isatra.2013.10.005i
L. Guo, S. Cao / ISA Transactions ∎ (∎∎∎∎) ∎∎∎–∎∎∎
2
(ADRC), embedded model control [7] and disturbance observer based control (DOBC). For linear systems, internal model control can be used to compensate the disturbance input with neutral stability conditions. The classical output regulation theory is applicable to the disturbance described with exogenous model [8–10]. The feasible disturbance compensation methods or output regulation results are difficult to achieve when the model or parameter of exogenous model is unknown. For a nonlinear system with uncertainties, an adaptive internal model control method was proposed, where adaptive control technology was applied to the output regulation problem [11–13]. Furthermore, disturbance rejection methods based on adaptive estimation were presented for disturbance with uncertain model or unknown parameter [14,15]. For nonlinear output regulation theory, the solution is based on a Francis–Isidori–Byrnes nonlinear partial differential equation (PDE). ADRC theory has better prospects for engineering applications, but still lacks rigorous theoretical proof of the stability [16]. Besides supplying satisfactory stability performance, a desired controller should be simple in structure, fast in computation and robust against parameter variation, un-modeled dynamics and noise. Some classical control approaches can provide simple design methods but cannot achieve satisfying system performances. On the contrary, other methods may supply perfect performance, but have overly complicated controller structures or heavy computation, which cannot be used in practical engineering. Also, some strict assumptions of the models may restrict their applications for different plants. In conclusion, most of the existing methods have the following shortcomings: (1) strict limitation of plant model; (2) complexity of the algorithm, which is difficult to realize online; (3) stability cannot be guaranteed with the appearance of disturbance; (4) incomprehensive modeling of disturbance and (5) conservativeness of the algorithm.
2. Disturbance observer based control In most cases, errors or disturbances are time-varying unknown dynamics, for which observers or filters can be designed for estimation [17]. To date, the DOBC approaches have been widely used in practical applications (see [18–21] and references therein). At first, linear DOBC (LDOBC) methods were utilized for linear single input single output (SISO) systems in the frequency domain. Furthermore, nonlinear DOBC approaches were proposed to improve the control accuracy. One feature of DOBC is with simple structure. 2.1. LDOBC Disturbance observer technique was firstly presented for a robotic system in the late 1980s, where an observer was proposed to estimate external disturbance [22]. The basic idea is to estimate the external disturbance with disturbance observer, and then compensate in the feed-forward channel immediately. Since then, DOBC has been widely used in various engineering systems, such as robot manipulators [23–25], high speed direct-drive positioning tables [26], permanent magnet synchronous motors [27], table drive systems [28], hard disks [29] and magnetic hard drive servo systems [30]. In LDOBC approaches, nonlinearities and disturbances were merged into a generalized disturbance, so that linear design techniques could be used. The methodologies can be classified as frequency-domain-based approach and time-domain-based approach. Generally, for frequency-domain-based approach, a low-pass filter is sensitive to the sensor noise, and a proper cutoff frequency should be selected to attenuate sensor noise. In
addition, less systematic results of stability analysis were provided for a pure frequency-domain approach. In [18], a root locus method was proposed for stability analysis. DOBC structure and passive controller were compared in [24]. Based on the equivalence of these two methods, the stability of a special DOBC was proved. [31] studied the relationship between DOBC with H 1 control. In [32], the relationship between disturbance filter with unknown inputs observer of linear system was given in the frequency domain. The performance largely depends on the cutoff frequency of the filter for frequency-domain approaches. Due to the presence of a phase lag, the result has some conservativeness. Meanwhile, the frequency domain control structure could easily lead to instability for some special disturbance. Although simple and practicable, it is limited to the trial and error method, and lacks a rigorous theoretical analysis. Most time-domain based approaches also focused on linear models or some linearizable nonlinear systems. The time-invariant and time-varying unknown disturbances were considered in [31] and [25] respectively. In [27], a reduced-order disturbance observer was proposed for permanent magnet synchronous motors. In [33], a composite approach combining disturbance observer and variable structure systems was proposed for minimum-phase systems with arbitrary relative degree, where uncertainties and exogenous inputs as well as nonlinearities were merged into an equivalent disturbance. 2.2. NLDOBC Although LDOBC has been successfully applied in industrial processes, it is difficult to obtain a feasible LDOBC method for many complex systems. Compared with LDOBC, nonlinear DOBC (NLDOBC) is to estimate and compensate for a disturbance acting on nonlinear systems. NLDOBC may improve the performance and robustness against noises and un-modelled dynamics for some nonlinear systems by sufficiently using nonlinear dynamics. In most cases, it is difficult to design an observer in engineering especially for complex plants. In [34], an NLDOBC was presented to improve the performance and robustness against friction and uncertain dynamics for a robotic system. For systems with unified relative degree, a nonlinear DOBC method was addressed for timeinvariant disturbance in [35], where global stability was established using Lyapunov theory. In [36], the estimation of timeinvariant disturbance can be obtained by using Lyapunov theory without normal observer type. Simulation results demonstrate that DOBC is better than adaptive control and sliding mode control for tracking control problem of robotic manipulators. However, the considered disturbance was supposed to be a constant load or harmonic signal in [34–36]. Robustness analysis of DOBC was proposed in [37,38], where an outer-loop controller can be combined with an inner-loop controller to enhance the closedloop system performance. A composite controller was proposed to reject the mismatched disturbances from output channels for a nonlinear magnetic leviation suspension system [39]. By constructing a disturbance compensation gain, a nonlinear robust DOBC was proposed to attenuate the mismatched disturbances and the influence of parameter variations from output channels [40]. Most above-mentioned NLDOBC schemes only concerned time-invariant disturbances. Recently, a new NLDOBC framework has been proposed to nonlinear systems with time varying or model-free disturbance [41–43]. Refs. [16,44] discussed the unknown input observer (or extended state observer) and its application in DOBC, where the performance can be obtained by analyzing the error dynamic. It is worth noting that ADRC and the corresponding method of extended state observer do not require the model of disturbance, but it is difficult to ensure the observability, controllability and stability of controlled system [44].
Please cite this article as: Guo L, Cao S. Anti-disturbance control theory for systems with multiple disturbances: A survey. ISA Transactions (2014), http://dx.doi.org/10.1016/j.isatra.2013.10.005i
L. Guo, S. Cao / ISA Transactions ∎ (∎∎∎∎) ∎∎∎–∎∎∎
Compared with other existing control approaches for systems with unknown disturbances, DOBC has several features. First, it is possible to integrate other control strategies with DOBC. This approach provides a framework to enhance disturbance rejection by combining other (nonlinear) control methods that focus on systems in the absence of disturbances. Second, DOBC can provide a stability analysis and synthesis approach for systems with disturbances. The design procedure is relatively simple and easy to accept by engineers.
3. Composite hierarchical anti-disturbance control (CHADC) Along with the development of sensor technology and data processing, multiple disturbances exist in most practical systems and one can formulate them into different mathematical descriptions after modeling analysis and error analysis [45,46]. Fox example, spacecraft in a complex environment contains not only nonlinear dynamics, uncertainties, transit delay, vibrating structural of solar paddles, but also sensor measurement noise, control error, as well as environmental disturbance torque of outer space (such as gravity gradient moment, solar radiation pressure moment and aerodynamic moment) [47,48]. These disturbances and noises can be characterized as an uncertain norm-bounded variable, a harmonic, step signal, non-Gaussian/Gaussian random variable, a variable with bounded change rate, output variables of a neutral stable system, and other types of disturbances. Most of the above-mentioned disturbance attenuation or rejection methods, such as internal model control, robust control, and stochastic control, were used for systems with a single disturbance. In order to improve the control precision, it is necessary to study new antidisturbance approaches for systems with multiple disturbances. For systems subject to multiple disturbances, the theoretical bottleneck is that different disturbance attenuation and compensators will be coupled and it increases the complexity of closed-loop systems. The stability and disturbance attenuation performance based on a base line controller are no longer satisfied. In [21], based on nonlinear disturbance observer, a robust DOBC scheme was firstly provided for the model with modeled disturbance and uncertainties by Guo and Chen. For nonlinear systems with multiple disturbances, the H 1 and variable structure control have been integrated with DOBC by Guo and his co-operators in [49–51]. In [49,50], multiple disturbances were divided into a norm bounded variable and uncertain modeled disturbance, where DOBC was applied to reject the modeled disturbance and robust H 1 was used to attenuate the norm bounded disturbance. The robustness analysis of system with multiple disturbances was provided in [21,49–51]. In [52], a composite DOBC and an adaptive control approach were proposed for a class of nonlinear system with uncertain modeled disturbance and the disturbance signal represented by an unknown parameter function. In [51], an anti-disturbance fault tolerant controller was presented for a system with norm bounded variable, derivative bounded disturbance and fault simultaneously, where the derivative bounded disturbance was model-free. Because of considering the different disturbance characteristics, the above-mentioned composite hierarchical control methods can be considered as a composite hierarchical anti-disturbance control (CHADC) method. Compared with other control schemes, CHADC is configured as a two-part series, see Fig. 1. One part is the disturbance observer for estimation. The other one is the base line controller for a nominal system. Different types of control methodologies can be combined with DOBC for different performance requirements. It has been seen that the H 1 , PID (proportional, integral and derivative), model predictive control, adaptive control and variable structure control have been integrated with DOBC in [42,43,49, 50,53]. In [54], a nonlinear disturbance observer combined with a
3 Multiple Disturbances
Reference Signal
Base Line Controller
CHADC
Control Input
Plant Measurement Outputs
Disturbance Observer
Fig. 1. The design diagram of CHADC.
conventional controller was proposed for a nonlinear system with harmonic disturbances, where passivity-theory was applied to establish the L2 stability for the whole composite controller. A composite controller combining DOBC with PD for flexible spacecraft attitude control was proposed, in which DOBC can reject the effect of elastic vibration from flexible appendages, and a PD controller can effectively perform attitude control for the rigid hub with multiple disturbances [43]. A nonlinear DOBC was addressed for a nonlinear MIMO system with arbitrary disturbance relative degree by designing a disturbance compensation gain matrix in [55]. In [56], one part of the compound controllers was designed for the loop of product particle size and the other was designed for the loop of circulating load in control ball mill grinding process with strong disturbances. In [57], a method of DOBC and pinning control was addressed to stabilize the states of multiagent systems with time-delays and exogenous disturbances. A composite control methodology, that is DOBC control plus H 1 control, for Markovian jump systems with nonlinearity and multiple disturbances was proposed in [58]. In the design of a robust synchronization control scheme, the effect of unknown control input constraint has been explicitly considered to guarantee the synchronization performance [59]. Besides the problem of control, anti-disturbance filtering has also been received more and more attentions for systems with multiple disturbances. For systems with modeled disturbance, a class of fault diagnosis approach was firstly proposed in [60] with disturbance rejection performance. For the nonlinear system with multiple disturbances, Ref. [51] addressed a fault diagnosis technology with disturbance rejection and attenuation performances, and a robust adaptive fault diagnosis method was presented in [61]. In [62,63], the linear and nonlinear error models with multiple disturbances were firstly established for inertial navigation system (INS). The considered INS included modeling error, measurement noise of inertial sensor, the drift of inertial sensor represented by a first order Gaussian Markov process, and environmental disturbance. Then, anti-disturbance filtering approaches were presented for stationary base self-alignment of INS with multiple disturbances. Generally speaking, the CHADC is a refined anti-disturbance control approach, and is non-fragile to the disturbances. The ability of anti-disturbance and the robustness analysis were discussed for the presented CHADC methods. It can be predicted that the study of CHADC for systems with multiple disturbances has important theoretical significance and application prospects. The following problems need to be studied in-depth on the basis of existing results:
To analyse the mechanism of disturbance characteristics and disturbance modeling for different objects.
To relax the restrictions on the disturbance model matching conditions for constructing the disturbance observer.
To reduce the conservativeness of disturbance and uncertain parameter estimation.
To introduce the disturbance attenuation and rejection capability for unknown parameters and uncertain disturbances in the existing CHADC schemes.
Please cite this article as: Guo L, Cao S. Anti-disturbance control theory for systems with multiple disturbances: A survey. ISA Transactions (2014), http://dx.doi.org/10.1016/j.isatra.2013.10.005i
L. Guo, S. Cao / ISA Transactions ∎ (∎∎∎∎) ∎∎∎–∎∎∎
4
References [1] Davison EJ. The robust control of a servo mechanism problem for linear timeinvariable multivariable systems. IEEE Trans Autom Control 1976;21:25–34. [2] Astrom KJ. Introduction to stochastic control theory. New York: Academic Press; 1970. [3] Guo L, Wang H. Stochastic distribution control system design: a convex optimization approach. London: Springer; 2009. [4] Zhou KM, Doyle JC. Essentials of robust control. New Jersey: Prentice Hall; 1998. [5] der Schaft AJV. L2-gain analysis of nonlinear systems and nonlinear state feedback H 1 control. IEEE Trans Autom Control 1992;37:770–84. [6] Lin CL, Lin TY. An H 1 design approach for neural net-based control schemes. IEEE Trans Autom Control 2001;46:1599–605. [7] Canuto ES, Musso F. Embedded model control: application to web winding. Part I. Modelling. In: IEEE conference on emerging technologies and factory automation, Prague, Czech; 2006. p. 477–84. [8] Isidori A, Byrnes CI. Output regulation of nonlinear systems. IEEE Trans Autom Control 1990;35(2):131–40. [9] Marino R, Tomei P. Nonlinear control design: geometric, adaptive and robust. Englewood Cliffs, NJ: Prentice-Hall; 1995. [10] Byrnes CI, Priscoli FD, Isidori A. Output regulation of uncertain nonlinear systems. Boston: Springer; 1997. [11] Huang J, Chen Z. A general framework for tackling the output regulation problem. IEEE Trans Autom Control 2004;49(12):2203–18. [12] Xian B, Jalili N. Adaptive tracking control of linear uncertain mechanical systems subjected to unknown sinusoidal disturbances. J Dyn Syst-T ASME 2003;125(3):129–34. [13] Xi ZR, Ding Z. Global adaptive output regulation of a class of nonlinear systems with nonlinear exosystems. Automatica 2007;43(1):143–9. [14] Nikiforov V. Nonlinear servocompensation of unknown external disturbances. Automatica 2001;37(10):1647–53. [15] Bodson M, Jensen JS, Douglas SC. Active noise control for periodic disturbances. IEEE Trans Control Syst Technol 2001;9(1):200–5. [16] Han JQ. From PID to active disturbance rejection control. IEEE Trans Ind Electron 2009;56(3):900–6. [17] Radke A, Gao Z. A survey of state and disturbance observers for practitioners. In: Proceedings of the 2006 American control conference, Minneapolis, MN; 2006. p. 14–6. [18] Li HX, Bosch PVD. A robust disturbance-based control and its application. Int J Control 1993;58(3):537–54. [19] She J, Ohyama Y, Nakano M. A new approach to the estimation and rejection of disturbances in servo systems. IEEE Trans Control Syst Technol 2005;13 (3):378–85. [20] Chen WH. Nonlinear disturbance observer-enhanced dynamic inversion control of missiles. J Guid Control Dyn 2003;26(1):161–6. [21] Guo L, Chen WH. Disturbance attenuation and rejection for systems with nonlinearity via DOBC approach. Int J Robust Nonlinear 2005;15(3):109–25. [22] Nakao M, Ohnishi K, Miyachi K. A robust decentralized joint control based on interference estimation. In: Proceedings of the IEEE international conference on robotics and automation; 1987. p. 326–31. [23] Kim BK, Chung WK, Youm Y. Robust learning control for robot manipulators based on disturbance observer. In: Proceedings of the IEEE IEC; 1996. p. 1276–82. [24] Bickel R, Tomizuka R. Passivity-based versus disturbance observer based robot control: equivalence and stability. J Dyn Syst-T ASME 1999;121:41–7. [25] Oh Y, Chung WK. Disturbance-observer-based motion control of redundant manipulators using inertially decoupled dynamics. IEEE/ASME Trans Mechatron 1999;4:133–45. [26] Kemf CJ, Kobayashi S. Disturbance observer and feedforward design for a highspeed directdrive positioning table. IEEE Trans Control Syst Technol 1999;7(5):513–26. [27] Kim KH, Baik IC, Moon GW, Youn MJ. A current control for a permanent magnet synchronous motor with a simple disturbance estimation scheme. IEEE Trans Control Syst Technol 1999;7(5):630–3. [28] Iwasaki M, Shibata T, Matsui N. Disturbance-observer-based nonlinear friction compensation in the table drive systems. IEEE/ASME Trans Mechatron 1999;4 (1):3–8. [29] Ishikawa J, Tomizuka M. Pivot friction compensation using an accelerometer and a disturbance observer for hard disk. IEEE/ASME Trans Mechatron 1998;3:194–201. [30] Huang YH, Massner W. A novel disturbance observer design for magnetic hard drive servo system with rotary actuator. IEEE Trans Magn 1998;34:1892–4. [31] Mita T, Hirata M, Murata K. H 1 control versus disturbance-observer-based control. IEEE Trans Ind Electron 1998;45:488–95. [32] Schrijver E, Dijk VJ. Disturbance observers for rigid mechanical systems: equivalence, stability, and design. J Dyn Syst-T ASME 2002;124:539–48. [33] Chen X, Komada S, Fukuda T. Design of a nonlinear disturbance observer. IEEE Trans Ind Electron 2000;47:429–37.
[34] Chen WH, Ballance DJ, Gawthrop PJ, O'Reilly J. A nonlinear disturbance observer for robotic manipulators. IEEE Trans Ind Electron 2000;47(4):932–8. [35] Chen WH, Balance DJ, Gawthrop PJ, Gribble JJ, O'Reilly J. Non-linear predictive PID controller. IEE Proc Control Theory Appl 1999;146:603–11. [36] Liu CS, Peng H. Disturbance observer based tracking control. J Dyn Syst-T ASME 2000;122:332–5. [37] Back J, Shim H. Adding robustness to nominal output feedback controllers for uncertain nonlinear systems: a nonlinear version of disturbance observer. Automatica 2008;44(9):2528–37. [38] Back J, Shim H. An inner-loop controller guaranteeing robust transient performance for uncertain MIMO nonlinear systems. IEEE Trans Autom Control 2009;54(7):1601–7. [39] Yang J, Zolotas A, Chen WH, Michail K, Li SH. Robust control of nonlinear MAGLEV suspension system with mismatched uncertainties via DOBC approach. ISA Trans 2011;50(3):389–96. [40] Yang J, Chen WH, Li SH. Non-linear disturbance observer-based robust control for systems with mismatched disturbances/uncertainties. IET Control Theory A 2011;5(18):2053–62. [41] Chen WH, Guo L. Analysis of disturbance observer based control for nonlinear systems under disturbances with bounded variation. In: Proceedings of the Control Conference. University of Bath, UK; 2004. p. ID-048. [42] Yang J, Li SH. Disturbance rejection of ball mill grinding circuits using DOB and MPC. Powder Technol 2010;198:219–28. [43] Liu H, Guo L. An anti-disturbance PD control scheme for attitude control and stabilization of flexible spacecrafts. Nonlinear Dyn 2012;67(3):2081–8. [44] Gao ZQ, Huang Y, Han JQ. An alternative paradigm for control system design. In: 40th IEEE CDC; 2001. p. 4578–85. [45] Guo L, Wen XY, Xin X. Hierarchical composite anti-disturbance control for robotic systems using robust disturbance observer. In: Proceedings of the international conference on robot intelligence, advanced information and knowledge; 2010. p. 229–43. [46] Wen XY, Guo L. Attenuation and rejection for multiple disturbances of nonlinear robotic systems using nonlinear observer and PID controller. In: Proceedings of the 8th WCICA, Jinan, China; 2010. p. 2512–17. [47] Sidi MJ. Spacecraft dynamics and control. UK: Cambridge University Press; 2000. [48] Canuto E, Molano-Jimenez A, Perez-Montenegro C. Disturbance rejection in space applications: problems and solutions. Acta Astronaut 2012;72:121–31. [49] Wei XJ, Guo L. Composite disturbance-observer-based control and terminal sliding mode control for non-linear systems with disturbances. Int J Control 2009;82(6):1082–98. [50] Wei XJ, Guo L. Composite disturbance-observer-based control and H1 control for complex continuous models. Int J Robust Nonlinear 2010;20:106–18. [51] Cao SY, Guo L, Wen XY. Fault tolerant control with disturbance rejection and attenuation performance for systems with multiple disturbances. Asian J Control 2011;13(6):1056–64. [52] Guo L, Wen XY. Hierarchical anti-disturbance adaptive control for nonlinear systems with composite disturbances and applications to missile systems. Trans Inst Meas Control 2011;33(8):942–56. [53] Chen M, Chen WH. Sliding mode control for a class of uncertain nonlinear system based on disturbance observer. Int J Adapt Control 2010;24(1):51–64. [54] Chen WH. Nonlinear disturbance observer based control for nonlinear systems with harmonic disturbances. In: Proceedings of the IFAC symposium on NCSD0 01; 2001. p. 316–21. [55] Yang J, Li SH, Chen WH. Nonlinear disturbance observer-based control for multi-input multi-output nonlinear systems subject to mismatching condition. Int J Control 2012;85(8):1071–82. [56] Chen XS, Yang J, Li SH, Li Q. Disturbance observer based multi-variable control of ball mill grinding circuits. J Process Control 2009;19(7):1205–13. [57] Yang HY, Guo L, Zou HL. Robust consensus of multi-agent systems with timedelays and exogenous disturbances. Int J Control Autom 2012;10(4):797–805. [58] Yao XM, Guo L. Composite anti-disturbance control for Markovian jump nonlinear systems via disturbance observer. Automatica 2013;49(8):2538–45. [59] Chen M, Wu Q, Jiang CS. Disturbance-observer-based robust synchronization control of uncertain chaotic systems. Nonlinear Dyn 2012;70(4):2421–32. [60] Cao SY, Guo L. Fault diagnosis with disturbance rejection performance based on disturbance observer. In: Joint 48th IEEE CDC and 28th CCC, Shanghai, China; 2009. p. 6947–51. [61] Cao SY, Guo L, Yi Y. Robust adaptive fault diagnosis approach based on disturbance observer. In: 30th Chinese control conference. Yantai, China; 2011. p. 4340–45. [62] Cao SY, Guo L. Multi-objective robust initial alignment algorithm for inertial navigation system with multiple disturbances. Aerosp Sci Technol 2012;21 (1):1–6. [63] Guo L, Cao SY. Initial alignment for nonlinear inertial navigation systems with multiple disturbances based on enhanced anti-disturbance filtering. Int J Control 2012;85(5):491–501.
Please cite this article as: Guo L, Cao S. Anti-disturbance control theory for systems with multiple disturbances: A survey. ISA Transactions (2014), http://dx.doi.org/10.1016/j.isatra.2013.10.005i
Contents lists available at ScienceDirect
ISA Transactions journal homepage: www.elsevier.com/locate/isatrans
Anti-disturbance control theory for systems with multiple disturbances: A survey$ Lei Guo a,n, Songyin Cao a,b a b
National Key Laboratory on Aircraft Control Technology, Beihang University, Beijing 100191, PR China Department of Automation, College of Information Engineering, Yangzhou University, Yangzhou 225127, PR China
art ic l e i nf o
a b s t r a c t
Article history: Received 31 May 2013 Received in revised form 9 October 2013 Accepted 17 October 2013 This paper was recommended for publication by Dr. Jeff Pieper
The problem of anti-disturbance control has been an eternal topic along with the development of the control theory. However, most methodologies can only deal with systems subject to a single equivalent disturbance which was merged by various types of uncertainties. In this paper, a review on antidisturbance control is presented for systems with multiple disturbances. First, the classical control methods are briefly reviewed for disturbance attenuation or rejection problems. Then, recent advances in disturbance observer based control (DOBC) theory are introduced and especially, the composite hierarchical anti-disturbance control (CHADC) is firstly addressed. A comparison of different approaches is briefly carried out. Finally, focuses in the field on the current research are also addressed with emphasis on the practical application of the techniques. & 2013 ISA. Published by Elsevier Ltd. All rights reserved.
Keywords: Multiple disturbances Robust control Disturbance observer based control Disturbance rejection and attenuation Anti-disturbance control Composite hierarchical anti-disturbance control
1. Introduction The general purpose of a controller is to monitor and correct the actions of a given dynamical system. Along with the development of control theory, many significant approaches have been presented for different plants. A proportional integral derivative (PID) controller is a generic control loop feedback mechanism widely used in industrial control systems. However, it is difficult to adjust the controller parameters and cannot be used in complex plants. Internal model control has been developed by leaps and bounds since the 1960s [1]. Since disturbances exist in all practical processes, the problem of disturbance attenuation or rejection has been a hot topic in control fields. Stochastic control [2,3] and robust control [4], two branches of the modern control theory, are inherent with anti-disturbance capability. Gaussian control theory, such as Kalman filter and minimum variance control, is presented
☆ This work is partially supported by the National 973 Program of China (Grant no. 2012CB720003), National Natural Science Foundation of China (Grant nos. 61203195 and 61127007), China Postdoctoral Science Foundation (Grant no. 2013M530508) and Universities Natural Science Foundation of Jiangsu Province (Grant no. 12KJB510033). n Corresponding author. Tel.: þ 86 10 82339103; fax: þ 86 10 82316813. E-mail addresses: [email protected] (L. Guo), [email protected], [email protected] (S. Cao).
to control output variance for optimizing the system performance, where the disturbance is supposed to be a Gaussian noise. The performance of Gaussian control approaches could be degraded when the considered system is with model uncertainties, nonGaussian noises and other types of disturbances. Based on probability density function or statistical information set, a class of stochastic distribution control methodologies was addressed for non-Gaussian stochastic control problem (see [3] and references therein). The stochastic control theory assumes that the statistical properties of the noises are known, which is often not satisfied in practical processes. In order to overcome the drawbacks, robust control problems have been studied in the past decade. No statistical property assumptions concerning the noises are required for the robust control, where the norm bounded disturbance and uncertainty can be dealt with. Among the robust control methods, H 1 and H2 control are widely used to attenuate the influences from disturbances to reference output in a desired level (see [4–6], and references therein). However, robust control methods have a large conservativeness for disturbances described by a norm bounded variable. The control approaches can be mainly divided into disturbance attenuation methods (such as stochastic control theory and robust control theory) and disturbance rejection schemes. The typical disturbance rejection approaches include internal model control, output regulation theory, active disturbance rejection control
0019-0578/$ - see front matter & 2013 ISA. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.isatra.2013.10.005
Please cite this article as: Guo L, Cao S. Anti-disturbance control theory for systems with multiple disturbances: A survey. ISA Transactions (2014), http://dx.doi.org/10.1016/j.isatra.2013.10.005i
L. Guo, S. Cao / ISA Transactions ∎ (∎∎∎∎) ∎∎∎–∎∎∎
2
(ADRC), embedded model control [7] and disturbance observer based control (DOBC). For linear systems, internal model control can be used to compensate the disturbance input with neutral stability conditions. The classical output regulation theory is applicable to the disturbance described with exogenous model [8–10]. The feasible disturbance compensation methods or output regulation results are difficult to achieve when the model or parameter of exogenous model is unknown. For a nonlinear system with uncertainties, an adaptive internal model control method was proposed, where adaptive control technology was applied to the output regulation problem [11–13]. Furthermore, disturbance rejection methods based on adaptive estimation were presented for disturbance with uncertain model or unknown parameter [14,15]. For nonlinear output regulation theory, the solution is based on a Francis–Isidori–Byrnes nonlinear partial differential equation (PDE). ADRC theory has better prospects for engineering applications, but still lacks rigorous theoretical proof of the stability [16]. Besides supplying satisfactory stability performance, a desired controller should be simple in structure, fast in computation and robust against parameter variation, un-modeled dynamics and noise. Some classical control approaches can provide simple design methods but cannot achieve satisfying system performances. On the contrary, other methods may supply perfect performance, but have overly complicated controller structures or heavy computation, which cannot be used in practical engineering. Also, some strict assumptions of the models may restrict their applications for different plants. In conclusion, most of the existing methods have the following shortcomings: (1) strict limitation of plant model; (2) complexity of the algorithm, which is difficult to realize online; (3) stability cannot be guaranteed with the appearance of disturbance; (4) incomprehensive modeling of disturbance and (5) conservativeness of the algorithm.
2. Disturbance observer based control In most cases, errors or disturbances are time-varying unknown dynamics, for which observers or filters can be designed for estimation [17]. To date, the DOBC approaches have been widely used in practical applications (see [18–21] and references therein). At first, linear DOBC (LDOBC) methods were utilized for linear single input single output (SISO) systems in the frequency domain. Furthermore, nonlinear DOBC approaches were proposed to improve the control accuracy. One feature of DOBC is with simple structure. 2.1. LDOBC Disturbance observer technique was firstly presented for a robotic system in the late 1980s, where an observer was proposed to estimate external disturbance [22]. The basic idea is to estimate the external disturbance with disturbance observer, and then compensate in the feed-forward channel immediately. Since then, DOBC has been widely used in various engineering systems, such as robot manipulators [23–25], high speed direct-drive positioning tables [26], permanent magnet synchronous motors [27], table drive systems [28], hard disks [29] and magnetic hard drive servo systems [30]. In LDOBC approaches, nonlinearities and disturbances were merged into a generalized disturbance, so that linear design techniques could be used. The methodologies can be classified as frequency-domain-based approach and time-domain-based approach. Generally, for frequency-domain-based approach, a low-pass filter is sensitive to the sensor noise, and a proper cutoff frequency should be selected to attenuate sensor noise. In
addition, less systematic results of stability analysis were provided for a pure frequency-domain approach. In [18], a root locus method was proposed for stability analysis. DOBC structure and passive controller were compared in [24]. Based on the equivalence of these two methods, the stability of a special DOBC was proved. [31] studied the relationship between DOBC with H 1 control. In [32], the relationship between disturbance filter with unknown inputs observer of linear system was given in the frequency domain. The performance largely depends on the cutoff frequency of the filter for frequency-domain approaches. Due to the presence of a phase lag, the result has some conservativeness. Meanwhile, the frequency domain control structure could easily lead to instability for some special disturbance. Although simple and practicable, it is limited to the trial and error method, and lacks a rigorous theoretical analysis. Most time-domain based approaches also focused on linear models or some linearizable nonlinear systems. The time-invariant and time-varying unknown disturbances were considered in [31] and [25] respectively. In [27], a reduced-order disturbance observer was proposed for permanent magnet synchronous motors. In [33], a composite approach combining disturbance observer and variable structure systems was proposed for minimum-phase systems with arbitrary relative degree, where uncertainties and exogenous inputs as well as nonlinearities were merged into an equivalent disturbance. 2.2. NLDOBC Although LDOBC has been successfully applied in industrial processes, it is difficult to obtain a feasible LDOBC method for many complex systems. Compared with LDOBC, nonlinear DOBC (NLDOBC) is to estimate and compensate for a disturbance acting on nonlinear systems. NLDOBC may improve the performance and robustness against noises and un-modelled dynamics for some nonlinear systems by sufficiently using nonlinear dynamics. In most cases, it is difficult to design an observer in engineering especially for complex plants. In [34], an NLDOBC was presented to improve the performance and robustness against friction and uncertain dynamics for a robotic system. For systems with unified relative degree, a nonlinear DOBC method was addressed for timeinvariant disturbance in [35], where global stability was established using Lyapunov theory. In [36], the estimation of timeinvariant disturbance can be obtained by using Lyapunov theory without normal observer type. Simulation results demonstrate that DOBC is better than adaptive control and sliding mode control for tracking control problem of robotic manipulators. However, the considered disturbance was supposed to be a constant load or harmonic signal in [34–36]. Robustness analysis of DOBC was proposed in [37,38], where an outer-loop controller can be combined with an inner-loop controller to enhance the closedloop system performance. A composite controller was proposed to reject the mismatched disturbances from output channels for a nonlinear magnetic leviation suspension system [39]. By constructing a disturbance compensation gain, a nonlinear robust DOBC was proposed to attenuate the mismatched disturbances and the influence of parameter variations from output channels [40]. Most above-mentioned NLDOBC schemes only concerned time-invariant disturbances. Recently, a new NLDOBC framework has been proposed to nonlinear systems with time varying or model-free disturbance [41–43]. Refs. [16,44] discussed the unknown input observer (or extended state observer) and its application in DOBC, where the performance can be obtained by analyzing the error dynamic. It is worth noting that ADRC and the corresponding method of extended state observer do not require the model of disturbance, but it is difficult to ensure the observability, controllability and stability of controlled system [44].
Please cite this article as: Guo L, Cao S. Anti-disturbance control theory for systems with multiple disturbances: A survey. ISA Transactions (2014), http://dx.doi.org/10.1016/j.isatra.2013.10.005i
L. Guo, S. Cao / ISA Transactions ∎ (∎∎∎∎) ∎∎∎–∎∎∎
Compared with other existing control approaches for systems with unknown disturbances, DOBC has several features. First, it is possible to integrate other control strategies with DOBC. This approach provides a framework to enhance disturbance rejection by combining other (nonlinear) control methods that focus on systems in the absence of disturbances. Second, DOBC can provide a stability analysis and synthesis approach for systems with disturbances. The design procedure is relatively simple and easy to accept by engineers.
3. Composite hierarchical anti-disturbance control (CHADC) Along with the development of sensor technology and data processing, multiple disturbances exist in most practical systems and one can formulate them into different mathematical descriptions after modeling analysis and error analysis [45,46]. Fox example, spacecraft in a complex environment contains not only nonlinear dynamics, uncertainties, transit delay, vibrating structural of solar paddles, but also sensor measurement noise, control error, as well as environmental disturbance torque of outer space (such as gravity gradient moment, solar radiation pressure moment and aerodynamic moment) [47,48]. These disturbances and noises can be characterized as an uncertain norm-bounded variable, a harmonic, step signal, non-Gaussian/Gaussian random variable, a variable with bounded change rate, output variables of a neutral stable system, and other types of disturbances. Most of the above-mentioned disturbance attenuation or rejection methods, such as internal model control, robust control, and stochastic control, were used for systems with a single disturbance. In order to improve the control precision, it is necessary to study new antidisturbance approaches for systems with multiple disturbances. For systems subject to multiple disturbances, the theoretical bottleneck is that different disturbance attenuation and compensators will be coupled and it increases the complexity of closed-loop systems. The stability and disturbance attenuation performance based on a base line controller are no longer satisfied. In [21], based on nonlinear disturbance observer, a robust DOBC scheme was firstly provided for the model with modeled disturbance and uncertainties by Guo and Chen. For nonlinear systems with multiple disturbances, the H 1 and variable structure control have been integrated with DOBC by Guo and his co-operators in [49–51]. In [49,50], multiple disturbances were divided into a norm bounded variable and uncertain modeled disturbance, where DOBC was applied to reject the modeled disturbance and robust H 1 was used to attenuate the norm bounded disturbance. The robustness analysis of system with multiple disturbances was provided in [21,49–51]. In [52], a composite DOBC and an adaptive control approach were proposed for a class of nonlinear system with uncertain modeled disturbance and the disturbance signal represented by an unknown parameter function. In [51], an anti-disturbance fault tolerant controller was presented for a system with norm bounded variable, derivative bounded disturbance and fault simultaneously, where the derivative bounded disturbance was model-free. Because of considering the different disturbance characteristics, the above-mentioned composite hierarchical control methods can be considered as a composite hierarchical anti-disturbance control (CHADC) method. Compared with other control schemes, CHADC is configured as a two-part series, see Fig. 1. One part is the disturbance observer for estimation. The other one is the base line controller for a nominal system. Different types of control methodologies can be combined with DOBC for different performance requirements. It has been seen that the H 1 , PID (proportional, integral and derivative), model predictive control, adaptive control and variable structure control have been integrated with DOBC in [42,43,49, 50,53]. In [54], a nonlinear disturbance observer combined with a
3 Multiple Disturbances
Reference Signal
Base Line Controller
CHADC
Control Input
Plant Measurement Outputs
Disturbance Observer
Fig. 1. The design diagram of CHADC.
conventional controller was proposed for a nonlinear system with harmonic disturbances, where passivity-theory was applied to establish the L2 stability for the whole composite controller. A composite controller combining DOBC with PD for flexible spacecraft attitude control was proposed, in which DOBC can reject the effect of elastic vibration from flexible appendages, and a PD controller can effectively perform attitude control for the rigid hub with multiple disturbances [43]. A nonlinear DOBC was addressed for a nonlinear MIMO system with arbitrary disturbance relative degree by designing a disturbance compensation gain matrix in [55]. In [56], one part of the compound controllers was designed for the loop of product particle size and the other was designed for the loop of circulating load in control ball mill grinding process with strong disturbances. In [57], a method of DOBC and pinning control was addressed to stabilize the states of multiagent systems with time-delays and exogenous disturbances. A composite control methodology, that is DOBC control plus H 1 control, for Markovian jump systems with nonlinearity and multiple disturbances was proposed in [58]. In the design of a robust synchronization control scheme, the effect of unknown control input constraint has been explicitly considered to guarantee the synchronization performance [59]. Besides the problem of control, anti-disturbance filtering has also been received more and more attentions for systems with multiple disturbances. For systems with modeled disturbance, a class of fault diagnosis approach was firstly proposed in [60] with disturbance rejection performance. For the nonlinear system with multiple disturbances, Ref. [51] addressed a fault diagnosis technology with disturbance rejection and attenuation performances, and a robust adaptive fault diagnosis method was presented in [61]. In [62,63], the linear and nonlinear error models with multiple disturbances were firstly established for inertial navigation system (INS). The considered INS included modeling error, measurement noise of inertial sensor, the drift of inertial sensor represented by a first order Gaussian Markov process, and environmental disturbance. Then, anti-disturbance filtering approaches were presented for stationary base self-alignment of INS with multiple disturbances. Generally speaking, the CHADC is a refined anti-disturbance control approach, and is non-fragile to the disturbances. The ability of anti-disturbance and the robustness analysis were discussed for the presented CHADC methods. It can be predicted that the study of CHADC for systems with multiple disturbances has important theoretical significance and application prospects. The following problems need to be studied in-depth on the basis of existing results:
To analyse the mechanism of disturbance characteristics and disturbance modeling for different objects.
To relax the restrictions on the disturbance model matching conditions for constructing the disturbance observer.
To reduce the conservativeness of disturbance and uncertain parameter estimation.
To introduce the disturbance attenuation and rejection capability for unknown parameters and uncertain disturbances in the existing CHADC schemes.
Please cite this article as: Guo L, Cao S. Anti-disturbance control theory for systems with multiple disturbances: A survey. ISA Transactions (2014), http://dx.doi.org/10.1016/j.isatra.2013.10.005i
L. Guo, S. Cao / ISA Transactions ∎ (∎∎∎∎) ∎∎∎–∎∎∎
4
References [1] Davison EJ. The robust control of a servo mechanism problem for linear timeinvariable multivariable systems. IEEE Trans Autom Control 1976;21:25–34. [2] Astrom KJ. Introduction to stochastic control theory. New York: Academic Press; 1970. [3] Guo L, Wang H. Stochastic distribution control system design: a convex optimization approach. London: Springer; 2009. [4] Zhou KM, Doyle JC. Essentials of robust control. New Jersey: Prentice Hall; 1998. [5] der Schaft AJV. L2-gain analysis of nonlinear systems and nonlinear state feedback H 1 control. IEEE Trans Autom Control 1992;37:770–84. [6] Lin CL, Lin TY. An H 1 design approach for neural net-based control schemes. IEEE Trans Autom Control 2001;46:1599–605. [7] Canuto ES, Musso F. Embedded model control: application to web winding. Part I. Modelling. In: IEEE conference on emerging technologies and factory automation, Prague, Czech; 2006. p. 477–84. [8] Isidori A, Byrnes CI. Output regulation of nonlinear systems. IEEE Trans Autom Control 1990;35(2):131–40. [9] Marino R, Tomei P. Nonlinear control design: geometric, adaptive and robust. Englewood Cliffs, NJ: Prentice-Hall; 1995. [10] Byrnes CI, Priscoli FD, Isidori A. Output regulation of uncertain nonlinear systems. Boston: Springer; 1997. [11] Huang J, Chen Z. A general framework for tackling the output regulation problem. IEEE Trans Autom Control 2004;49(12):2203–18. [12] Xian B, Jalili N. Adaptive tracking control of linear uncertain mechanical systems subjected to unknown sinusoidal disturbances. J Dyn Syst-T ASME 2003;125(3):129–34. [13] Xi ZR, Ding Z. Global adaptive output regulation of a class of nonlinear systems with nonlinear exosystems. Automatica 2007;43(1):143–9. [14] Nikiforov V. Nonlinear servocompensation of unknown external disturbances. Automatica 2001;37(10):1647–53. [15] Bodson M, Jensen JS, Douglas SC. Active noise control for periodic disturbances. IEEE Trans Control Syst Technol 2001;9(1):200–5. [16] Han JQ. From PID to active disturbance rejection control. IEEE Trans Ind Electron 2009;56(3):900–6. [17] Radke A, Gao Z. A survey of state and disturbance observers for practitioners. In: Proceedings of the 2006 American control conference, Minneapolis, MN; 2006. p. 14–6. [18] Li HX, Bosch PVD. A robust disturbance-based control and its application. Int J Control 1993;58(3):537–54. [19] She J, Ohyama Y, Nakano M. A new approach to the estimation and rejection of disturbances in servo systems. IEEE Trans Control Syst Technol 2005;13 (3):378–85. [20] Chen WH. Nonlinear disturbance observer-enhanced dynamic inversion control of missiles. J Guid Control Dyn 2003;26(1):161–6. [21] Guo L, Chen WH. Disturbance attenuation and rejection for systems with nonlinearity via DOBC approach. Int J Robust Nonlinear 2005;15(3):109–25. [22] Nakao M, Ohnishi K, Miyachi K. A robust decentralized joint control based on interference estimation. In: Proceedings of the IEEE international conference on robotics and automation; 1987. p. 326–31. [23] Kim BK, Chung WK, Youm Y. Robust learning control for robot manipulators based on disturbance observer. In: Proceedings of the IEEE IEC; 1996. p. 1276–82. [24] Bickel R, Tomizuka R. Passivity-based versus disturbance observer based robot control: equivalence and stability. J Dyn Syst-T ASME 1999;121:41–7. [25] Oh Y, Chung WK. Disturbance-observer-based motion control of redundant manipulators using inertially decoupled dynamics. IEEE/ASME Trans Mechatron 1999;4:133–45. [26] Kemf CJ, Kobayashi S. Disturbance observer and feedforward design for a highspeed directdrive positioning table. IEEE Trans Control Syst Technol 1999;7(5):513–26. [27] Kim KH, Baik IC, Moon GW, Youn MJ. A current control for a permanent magnet synchronous motor with a simple disturbance estimation scheme. IEEE Trans Control Syst Technol 1999;7(5):630–3. [28] Iwasaki M, Shibata T, Matsui N. Disturbance-observer-based nonlinear friction compensation in the table drive systems. IEEE/ASME Trans Mechatron 1999;4 (1):3–8. [29] Ishikawa J, Tomizuka M. Pivot friction compensation using an accelerometer and a disturbance observer for hard disk. IEEE/ASME Trans Mechatron 1998;3:194–201. [30] Huang YH, Massner W. A novel disturbance observer design for magnetic hard drive servo system with rotary actuator. IEEE Trans Magn 1998;34:1892–4. [31] Mita T, Hirata M, Murata K. H 1 control versus disturbance-observer-based control. IEEE Trans Ind Electron 1998;45:488–95. [32] Schrijver E, Dijk VJ. Disturbance observers for rigid mechanical systems: equivalence, stability, and design. J Dyn Syst-T ASME 2002;124:539–48. [33] Chen X, Komada S, Fukuda T. Design of a nonlinear disturbance observer. IEEE Trans Ind Electron 2000;47:429–37.
[34] Chen WH, Ballance DJ, Gawthrop PJ, O'Reilly J. A nonlinear disturbance observer for robotic manipulators. IEEE Trans Ind Electron 2000;47(4):932–8. [35] Chen WH, Balance DJ, Gawthrop PJ, Gribble JJ, O'Reilly J. Non-linear predictive PID controller. IEE Proc Control Theory Appl 1999;146:603–11. [36] Liu CS, Peng H. Disturbance observer based tracking control. J Dyn Syst-T ASME 2000;122:332–5. [37] Back J, Shim H. Adding robustness to nominal output feedback controllers for uncertain nonlinear systems: a nonlinear version of disturbance observer. Automatica 2008;44(9):2528–37. [38] Back J, Shim H. An inner-loop controller guaranteeing robust transient performance for uncertain MIMO nonlinear systems. IEEE Trans Autom Control 2009;54(7):1601–7. [39] Yang J, Zolotas A, Chen WH, Michail K, Li SH. Robust control of nonlinear MAGLEV suspension system with mismatched uncertainties via DOBC approach. ISA Trans 2011;50(3):389–96. [40] Yang J, Chen WH, Li SH. Non-linear disturbance observer-based robust control for systems with mismatched disturbances/uncertainties. IET Control Theory A 2011;5(18):2053–62. [41] Chen WH, Guo L. Analysis of disturbance observer based control for nonlinear systems under disturbances with bounded variation. In: Proceedings of the Control Conference. University of Bath, UK; 2004. p. ID-048. [42] Yang J, Li SH. Disturbance rejection of ball mill grinding circuits using DOB and MPC. Powder Technol 2010;198:219–28. [43] Liu H, Guo L. An anti-disturbance PD control scheme for attitude control and stabilization of flexible spacecrafts. Nonlinear Dyn 2012;67(3):2081–8. [44] Gao ZQ, Huang Y, Han JQ. An alternative paradigm for control system design. In: 40th IEEE CDC; 2001. p. 4578–85. [45] Guo L, Wen XY, Xin X. Hierarchical composite anti-disturbance control for robotic systems using robust disturbance observer. In: Proceedings of the international conference on robot intelligence, advanced information and knowledge; 2010. p. 229–43. [46] Wen XY, Guo L. Attenuation and rejection for multiple disturbances of nonlinear robotic systems using nonlinear observer and PID controller. In: Proceedings of the 8th WCICA, Jinan, China; 2010. p. 2512–17. [47] Sidi MJ. Spacecraft dynamics and control. UK: Cambridge University Press; 2000. [48] Canuto E, Molano-Jimenez A, Perez-Montenegro C. Disturbance rejection in space applications: problems and solutions. Acta Astronaut 2012;72:121–31. [49] Wei XJ, Guo L. Composite disturbance-observer-based control and terminal sliding mode control for non-linear systems with disturbances. Int J Control 2009;82(6):1082–98. [50] Wei XJ, Guo L. Composite disturbance-observer-based control and H1 control for complex continuous models. Int J Robust Nonlinear 2010;20:106–18. [51] Cao SY, Guo L, Wen XY. Fault tolerant control with disturbance rejection and attenuation performance for systems with multiple disturbances. Asian J Control 2011;13(6):1056–64. [52] Guo L, Wen XY. Hierarchical anti-disturbance adaptive control for nonlinear systems with composite disturbances and applications to missile systems. Trans Inst Meas Control 2011;33(8):942–56. [53] Chen M, Chen WH. Sliding mode control for a class of uncertain nonlinear system based on disturbance observer. Int J Adapt Control 2010;24(1):51–64. [54] Chen WH. Nonlinear disturbance observer based control for nonlinear systems with harmonic disturbances. In: Proceedings of the IFAC symposium on NCSD0 01; 2001. p. 316–21. [55] Yang J, Li SH, Chen WH. Nonlinear disturbance observer-based control for multi-input multi-output nonlinear systems subject to mismatching condition. Int J Control 2012;85(8):1071–82. [56] Chen XS, Yang J, Li SH, Li Q. Disturbance observer based multi-variable control of ball mill grinding circuits. J Process Control 2009;19(7):1205–13. [57] Yang HY, Guo L, Zou HL. Robust consensus of multi-agent systems with timedelays and exogenous disturbances. Int J Control Autom 2012;10(4):797–805. [58] Yao XM, Guo L. Composite anti-disturbance control for Markovian jump nonlinear systems via disturbance observer. Automatica 2013;49(8):2538–45. [59] Chen M, Wu Q, Jiang CS. Disturbance-observer-based robust synchronization control of uncertain chaotic systems. Nonlinear Dyn 2012;70(4):2421–32. [60] Cao SY, Guo L. Fault diagnosis with disturbance rejection performance based on disturbance observer. In: Joint 48th IEEE CDC and 28th CCC, Shanghai, China; 2009. p. 6947–51. [61] Cao SY, Guo L, Yi Y. Robust adaptive fault diagnosis approach based on disturbance observer. In: 30th Chinese control conference. Yantai, China; 2011. p. 4340–45. [62] Cao SY, Guo L. Multi-objective robust initial alignment algorithm for inertial navigation system with multiple disturbances. Aerosp Sci Technol 2012;21 (1):1–6. [63] Guo L, Cao SY. Initial alignment for nonlinear inertial navigation systems with multiple disturbances based on enhanced anti-disturbance filtering. Int J Control 2012;85(5):491–501.
Please cite this article as: Guo L, Cao S. Anti-disturbance control theory for systems with multiple disturbances: A survey. ISA Transactions (2014), http://dx.doi.org/10.1016/j.isatra.2013.10.005i
