2012, 2(2): 413-435. doi: 10.3934/naco.2012.2.413

Control design of linear systems with saturating actuators: A survey

1. 

Systems Engineering Department, King Fahd University of Petroleum and Minerals, P. O. Box 985, Dhahran 31261, Saudi Arabia

2. 

Systems Engineering Department, King Fahd University of Petroleum and Minerals, P. O. Box 5067, Dhahran 31261, Saudi Arabia

Received  April 2011 Revised  March 2012 Published  May 2012

In this paper, a survey of the extensive research investigation performed on linear systems subject to saturation including actuator, output and state types is presented. The survey takes into consideration several technical views on the analysis and design procedures leading to global or semi-global stability results and outlines basic assumptions. Research works on the design of linear feedback laws, decentralized controllers are equally emphasized. Results related stability with enlarging the domain of attraction and systems subject to multi-layered nested saturations are provided. Some typical examples are given to illustrate relevant issues.
Citation: Magdi S. Mahmoud, Mohammed M. Hussain. Control design of linear systems with saturating actuators: A survey. Numerical Algebra, Control and Optimization, 2012, 2 (2) : 413-435. doi: 10.3934/naco.2012.2.413
References:
[1]

A. Bateman and Z. Lin, An analysis and design method for linear systems under nested saturation, System Control Letters, 8 (2003), 41-52. doi: 10.1016/S0167-6911(02)00246-3.

[2]

D. S. Bernstein, A chronological bibliography on saturating actuators, Int. J. Robust and Nonlinear Control, 5 (1995), 375-380. doi: 10.1002/rnc.4590050502.

[3]

D. S. Bernstein and A. N. Michel, Special issue on saturating actuators, Int. J. Robust and Nonlinear Control, 5 (1995), 375-540.

[4]

D. S. Bernstein and A. N. Michel, A chronological bibliography on saturating actuators, Int. J. Robust Nonlinear Control, 5 (1995), 75-80. doi: 10.1002/rnc.4590050502.

[5]

Y. Cao, Z. Lin and D. G. Ward, An anti windup approach to enlarging domain o attraction for linear systems subject to actuator saturation and disturbance, IEEE Trans on Automatic Control, 47 (2002), 140-145. doi: 10.1109/9.981734.

[6]

D. Dai, T. Hu, A. R. Teel and L. Zaccarian, Case Studies on the control input constrained linear plants via output feedback containing an internal dead zone loop, In "Advanced Startegies in Control systems with Input and Output Constraints" (Eds. S. Tabouriech, G. Garcia and A. H. Glatterfield), Springer-Verlag, London, (2007), 313-340. doi: 10.1007/978-3-540-37010-9_11.

[7]

D. Dai, T. Hu, A. R. Teel and L. Zaccarian, Control of saturated linear plants via output feedback containing an internal dead zone loop, Proc. 2006 ACC, Minneapolis, USA, (2006), 5239-5245.

[8]

D. Dai, T. Hu, A. R. Teel and L. Zaccarian, Output feedback design for saturated linear plants using dead zone loops, Automatica, 45 (2009), 2917-2924. doi: 10.1016/j.automatica.2009.09.022.

[9]

D. Dai, T. Hu, A. R. Teel and L. Zaccarian, Piecewise-quadratic Lyapunov functions for systems with dead zones or saturations, System and Control Letters, 58 (2009), 365-371. doi: 10.1016/j.sysconle.2009.01.003.

[10]

C. Deliu, B. Malek, S. Roy, A. Saberi and A. A. Stoorvogel, Decentralized control of discrete-time linear time invariant systems with input saturation, Int. J. Robust and Nonlinear Control, 20 (2010), 1353-1362.

[11]

H. Fang, Z. Lin and T. Hu, Analysis of linear systems in the presence of Actuator saturation and L2-disturbances, Automatica, 40 (2004), 1229-1238. doi: 10.1016/j.automatica.2004.02.009.

[12]

H. Fang and L. Lin, Stability analysis for linear systems under state constraints IEEE Trans. Autom. Control, 49 (2004), 950-955. doi: 10.1109/TAC.2004.829614.

[13]

J. M. Gomes da Silva, Jr. and S. Tarboureich, Anti-windup design with guaranteed regions of stability: an LMI based approach, IEEE Trans. Autom. Control, 50 (2005), 106-111. doi: 10.1109/TAC.2004.841128.

[14]

G. Grimm, J. Hatfield, I. Postlethwaite, A. R. Teel, M. C. Turner and L. Zaccarian, Anti windup for stable linear systems with input saturation: an LMI based synthesis, IEEE Trans Automatic Control, 48 (2003), 1509-1525. doi: 10.1109/TAC.2003.816965.

[15]

W. Guan and G. H. Yang, Analysis and design of output feedback control systems in the presence of actuator saturation, American Control Conference, Hyatt Regency Riverfront, St. Louis, MO, USA, 2009.

[16]

W. Guan and G. H. Yang, New controller design method for continuous-time systems with state saturation, IET Control Theory Appl., 4 (2010), 1889-1897. doi: 10.1049/iet-cta.2009.0433.

[17]

J. M. Gomes da Silva Jr., S. Tarbouriech and R. Reginatto, Analysis of regions of stability of for linear systems with saturating inputs through an anti-windup scheme, Proc. IEEE Conf. Control Applications, Glasgow, UK, (2002), 1106-1111.

[18]

H. F. Grip, A. Saberi and X. Wang, Stabilization of multiple-input multiple-output linear systems with saturated outputs, IEEE Trans. on Autom. Control, 55 (2010), 2160-2164.

[19]

L. Hou and A. N. Michel, Asymptotic stability of systems with saturation constraints, Proc. 35th IEEE Conf. on Decision Control, (1996), 2624-2629.

[20]

T. Hu, Z. Lin and B. M. Chen, An analysis and deign method for linear systems subject to actuator saturation and disturbance, Automatica, 38 (2002), 351-359. doi: 10.1016/S0005-1098(01)00209-6.

[21]

T. Hu and Z. Lin, "Control Systems with Actuator Saturation: Analysis and Design," Birkhauser-Boston, 2001. doi: 10.1007/978-1-4612-0205-9.

[22]

T. Hu, A. R. Teel and L. Zaccarian, Anti-windup synthesis for linear control systems with input saturation: achieving regional, nonlinear performance, Automatica, 44 (2008), 512-519. doi: 10.1016/j.automatica.2007.06.003.

[23]

T. Hu, A. R. Teel and L. Zaccarian, An analysis and design method for linear systems subject to actuator saturation and disturbances, Automatica, 38 (2002), 351-359. doi: 10.1016/S0005-1098(01)00209-6.

[24]

T. Hu, A. R. Teel and L. Zaccarian, Stability and performance for saturated systems via quadratic and non-quadratic Lyapunov functions, IEEE Trans. Autom. Control, 51 (2006), 2017-2022. doi: 10.1109/TAC.2006.884942.

[25]

V. Kapilla and K. Grigoriadis, "Actuator Saturation Control," Marcel Dekker, 2002. doi: 10.1201/9780203910818.

[26]

G. Kreisselmeier, Stabilization of linear systems in the presence of output measurement saturation System Control Letters, 29 (1996), 27-30. doi: 10.1016/0167-6911(96)00048-5.

[27]

Z. Li, A. Saberi and A. A. Stoorvogel, Semiglobal stabilization of linear discrete-time systems subject to input saturation via linear feedback-an ARE based approach, IEEE Trans. on Autom. Control, 41 (1996), 1203-1207.

[28]

Z. Lin, "Low Gain Feedback," Springer-Verlag, London, UK, 1998.

[29]

Z. Lin and T. Hu, Semi-global Stabilization of linear systems subject to output saturation, System Control Letters, 43 (2001), 211-217. doi: 10.1016/S0167-6911(01)00099-8.

[30]

D. Liu and A. N. Michel, "Dynamical Systems with Saturation Nonlinearities," London, UK, Springer-Verlag, 1994. doi: 10.1007/BFb0032146.

[31]

L. Lu, Z. Lin and A. Bateman, Decentralized state feedback design for large-scale linear systems subject to input saturation, IET Control Theory Appl., 4 (2010), 206-227. doi: 10.1049/iet-cta.2008.0605.

[32]

L. Lu, Z. Lin and A. Bateman, Decentralized Control design for large scale linear systems in the presence of multi-layer Nested Saturation, Proc. IEEE Intl. Symp. on Intelligent Control-IEEE Multi-conference on Systems and Control, St. Petersburg, Russia, 2009.

[33]

M. S. Mahmoud, "Decentralized Control and Filtering in Interconnected Dynamical Systems," CRC Press, New York, 2010. doi: 10.1201/b10349.

[34]

C. Pittet, S. Tarbourhiech and C. Burgat, Output feedback synthesis via the circle criterion for linear systems subject to saturating inputs, Proc. the 37th Conference on Decision and Control, Tampa, Florida-USA, 1998.

[35]

I. Postlethwaite, M. Turner and G. Herrmann, Robust control applications, Annual Reviews in Control, 31 (2007), 27-39. doi: 10.1016/j.arcontrol.2007.02.003.

[36]

A. Saberi, Z. Lin and A. R. Teel, Control of linear systems with saturating actuators, IEEE Trans. Automat. Contr., 41 (1996), 368-378. doi: 10.1109/9.486638.

[37]

A. Saberi and A. A. Stoorvogel, Special issue on control problems with constraints, Int. Journal of Robust and Nonlinear Control, 9 (1999), 583-734.

[38]

A. Saberi, A. A. Stoorvogel and P. Sannuti, Decentralized control with input saturation, Proc. of the 2004 American Control Conference, Boston, Massachusetts, 2004.

[39]

A. A. Stoorvogel, J. Minteer and C. Deliu, Decentralized control with input saturation: a first step towards design, American Control Conference, 2005.

[40]

A. A. Stoorvogel, A. Saberi, C. Deliu and P. Sannuti, Decentralized stabilization of LTI systems subject to actuator saturation, In "Advanced Strategies in Control Systems with Input and Output Constraints" (eds. S. Tarboureich, G. Garcia, A. H. Glattfelder), Lecture notes in Control and Information sciences, Springer: Berlin, 346 (2007), 397-419.

[41]

S. Tarbouriech, C. Preiur and J. M. Gomes da Silva, Jr., Stability analysis and stabilization of systems presenting nested saturation, IEEE Trans. on Autom. Control, 51 (2006), 1364-1371.

[42]

F. Wu and B. Lu, Anti windup control design for exponentially unstable LTI systems with actuator saturation, System and Control Letters, 52 (2004), 304-322. doi: 10.1016/j.sysconle.2004.02.007.

[43]

F. Wu, Z. Lin and Q. Zheng, Output feedback stabilization of linear systems with actuator saturation, IEEE Trans. Autom. Control, 52 (1997), 122-128. doi: 10.1109/TAC.2006.886498.

[44]

G. Valmorbida, S. Tarbouriech and G. Garcia, State feedback design for input-saturating quadratic systems, Automatica, 46 (2010), 1196-1202. doi: 10.1016/j.automatica.2010.03.016.

[45]

G. Zhai, M. Ikeda and Y. Fujikasi, Decentralized H-infinity Controller design: a matrix inequality approach using a homotopy method, Automatica, 37 (2001), 565-572. doi: 10.1016/S0005-1098(00)00190-4.

show all references

References:
[1]

A. Bateman and Z. Lin, An analysis and design method for linear systems under nested saturation, System Control Letters, 8 (2003), 41-52. doi: 10.1016/S0167-6911(02)00246-3.

[2]

D. S. Bernstein, A chronological bibliography on saturating actuators, Int. J. Robust and Nonlinear Control, 5 (1995), 375-380. doi: 10.1002/rnc.4590050502.

[3]

D. S. Bernstein and A. N. Michel, Special issue on saturating actuators, Int. J. Robust and Nonlinear Control, 5 (1995), 375-540.

[4]

D. S. Bernstein and A. N. Michel, A chronological bibliography on saturating actuators, Int. J. Robust Nonlinear Control, 5 (1995), 75-80. doi: 10.1002/rnc.4590050502.

[5]

Y. Cao, Z. Lin and D. G. Ward, An anti windup approach to enlarging domain o attraction for linear systems subject to actuator saturation and disturbance, IEEE Trans on Automatic Control, 47 (2002), 140-145. doi: 10.1109/9.981734.

[6]

D. Dai, T. Hu, A. R. Teel and L. Zaccarian, Case Studies on the control input constrained linear plants via output feedback containing an internal dead zone loop, In "Advanced Startegies in Control systems with Input and Output Constraints" (Eds. S. Tabouriech, G. Garcia and A. H. Glatterfield), Springer-Verlag, London, (2007), 313-340. doi: 10.1007/978-3-540-37010-9_11.

[7]

D. Dai, T. Hu, A. R. Teel and L. Zaccarian, Control of saturated linear plants via output feedback containing an internal dead zone loop, Proc. 2006 ACC, Minneapolis, USA, (2006), 5239-5245.

[8]

D. Dai, T. Hu, A. R. Teel and L. Zaccarian, Output feedback design for saturated linear plants using dead zone loops, Automatica, 45 (2009), 2917-2924. doi: 10.1016/j.automatica.2009.09.022.

[9]

D. Dai, T. Hu, A. R. Teel and L. Zaccarian, Piecewise-quadratic Lyapunov functions for systems with dead zones or saturations, System and Control Letters, 58 (2009), 365-371. doi: 10.1016/j.sysconle.2009.01.003.

[10]

C. Deliu, B. Malek, S. Roy, A. Saberi and A. A. Stoorvogel, Decentralized control of discrete-time linear time invariant systems with input saturation, Int. J. Robust and Nonlinear Control, 20 (2010), 1353-1362.

[11]

H. Fang, Z. Lin and T. Hu, Analysis of linear systems in the presence of Actuator saturation and L2-disturbances, Automatica, 40 (2004), 1229-1238. doi: 10.1016/j.automatica.2004.02.009.

[12]

H. Fang and L. Lin, Stability analysis for linear systems under state constraints IEEE Trans. Autom. Control, 49 (2004), 950-955. doi: 10.1109/TAC.2004.829614.

[13]

J. M. Gomes da Silva, Jr. and S. Tarboureich, Anti-windup design with guaranteed regions of stability: an LMI based approach, IEEE Trans. Autom. Control, 50 (2005), 106-111. doi: 10.1109/TAC.2004.841128.

[14]

G. Grimm, J. Hatfield, I. Postlethwaite, A. R. Teel, M. C. Turner and L. Zaccarian, Anti windup for stable linear systems with input saturation: an LMI based synthesis, IEEE Trans Automatic Control, 48 (2003), 1509-1525. doi: 10.1109/TAC.2003.816965.

[15]

W. Guan and G. H. Yang, Analysis and design of output feedback control systems in the presence of actuator saturation, American Control Conference, Hyatt Regency Riverfront, St. Louis, MO, USA, 2009.

[16]

W. Guan and G. H. Yang, New controller design method for continuous-time systems with state saturation, IET Control Theory Appl., 4 (2010), 1889-1897. doi: 10.1049/iet-cta.2009.0433.

[17]

J. M. Gomes da Silva Jr., S. Tarbouriech and R. Reginatto, Analysis of regions of stability of for linear systems with saturating inputs through an anti-windup scheme, Proc. IEEE Conf. Control Applications, Glasgow, UK, (2002), 1106-1111.

[18]

H. F. Grip, A. Saberi and X. Wang, Stabilization of multiple-input multiple-output linear systems with saturated outputs, IEEE Trans. on Autom. Control, 55 (2010), 2160-2164.

[19]

L. Hou and A. N. Michel, Asymptotic stability of systems with saturation constraints, Proc. 35th IEEE Conf. on Decision Control, (1996), 2624-2629.

[20]

T. Hu, Z. Lin and B. M. Chen, An analysis and deign method for linear systems subject to actuator saturation and disturbance, Automatica, 38 (2002), 351-359. doi: 10.1016/S0005-1098(01)00209-6.

[21]

T. Hu and Z. Lin, "Control Systems with Actuator Saturation: Analysis and Design," Birkhauser-Boston, 2001. doi: 10.1007/978-1-4612-0205-9.

[22]

T. Hu, A. R. Teel and L. Zaccarian, Anti-windup synthesis for linear control systems with input saturation: achieving regional, nonlinear performance, Automatica, 44 (2008), 512-519. doi: 10.1016/j.automatica.2007.06.003.

[23]

T. Hu, A. R. Teel and L. Zaccarian, An analysis and design method for linear systems subject to actuator saturation and disturbances, Automatica, 38 (2002), 351-359. doi: 10.1016/S0005-1098(01)00209-6.

[24]

T. Hu, A. R. Teel and L. Zaccarian, Stability and performance for saturated systems via quadratic and non-quadratic Lyapunov functions, IEEE Trans. Autom. Control, 51 (2006), 2017-2022. doi: 10.1109/TAC.2006.884942.

[25]

V. Kapilla and K. Grigoriadis, "Actuator Saturation Control," Marcel Dekker, 2002. doi: 10.1201/9780203910818.

[26]

G. Kreisselmeier, Stabilization of linear systems in the presence of output measurement saturation System Control Letters, 29 (1996), 27-30. doi: 10.1016/0167-6911(96)00048-5.

[27]

Z. Li, A. Saberi and A. A. Stoorvogel, Semiglobal stabilization of linear discrete-time systems subject to input saturation via linear feedback-an ARE based approach, IEEE Trans. on Autom. Control, 41 (1996), 1203-1207.

[28]

Z. Lin, "Low Gain Feedback," Springer-Verlag, London, UK, 1998.

[29]

Z. Lin and T. Hu, Semi-global Stabilization of linear systems subject to output saturation, System Control Letters, 43 (2001), 211-217. doi: 10.1016/S0167-6911(01)00099-8.

[30]

D. Liu and A. N. Michel, "Dynamical Systems with Saturation Nonlinearities," London, UK, Springer-Verlag, 1994. doi: 10.1007/BFb0032146.

[31]

L. Lu, Z. Lin and A. Bateman, Decentralized state feedback design for large-scale linear systems subject to input saturation, IET Control Theory Appl., 4 (2010), 206-227. doi: 10.1049/iet-cta.2008.0605.

[32]

L. Lu, Z. Lin and A. Bateman, Decentralized Control design for large scale linear systems in the presence of multi-layer Nested Saturation, Proc. IEEE Intl. Symp. on Intelligent Control-IEEE Multi-conference on Systems and Control, St. Petersburg, Russia, 2009.

[33]

M. S. Mahmoud, "Decentralized Control and Filtering in Interconnected Dynamical Systems," CRC Press, New York, 2010. doi: 10.1201/b10349.

[34]

C. Pittet, S. Tarbourhiech and C. Burgat, Output feedback synthesis via the circle criterion for linear systems subject to saturating inputs, Proc. the 37th Conference on Decision and Control, Tampa, Florida-USA, 1998.

[35]

I. Postlethwaite, M. Turner and G. Herrmann, Robust control applications, Annual Reviews in Control, 31 (2007), 27-39. doi: 10.1016/j.arcontrol.2007.02.003.

[36]

A. Saberi, Z. Lin and A. R. Teel, Control of linear systems with saturating actuators, IEEE Trans. Automat. Contr., 41 (1996), 368-378. doi: 10.1109/9.486638.

[37]

A. Saberi and A. A. Stoorvogel, Special issue on control problems with constraints, Int. Journal of Robust and Nonlinear Control, 9 (1999), 583-734.

[38]

A. Saberi, A. A. Stoorvogel and P. Sannuti, Decentralized control with input saturation, Proc. of the 2004 American Control Conference, Boston, Massachusetts, 2004.

[39]

A. A. Stoorvogel, J. Minteer and C. Deliu, Decentralized control with input saturation: a first step towards design, American Control Conference, 2005.

[40]

A. A. Stoorvogel, A. Saberi, C. Deliu and P. Sannuti, Decentralized stabilization of LTI systems subject to actuator saturation, In "Advanced Strategies in Control Systems with Input and Output Constraints" (eds. S. Tarboureich, G. Garcia, A. H. Glattfelder), Lecture notes in Control and Information sciences, Springer: Berlin, 346 (2007), 397-419.

[41]

S. Tarbouriech, C. Preiur and J. M. Gomes da Silva, Jr., Stability analysis and stabilization of systems presenting nested saturation, IEEE Trans. on Autom. Control, 51 (2006), 1364-1371.

[42]

F. Wu and B. Lu, Anti windup control design for exponentially unstable LTI systems with actuator saturation, System and Control Letters, 52 (2004), 304-322. doi: 10.1016/j.sysconle.2004.02.007.

[43]

F. Wu, Z. Lin and Q. Zheng, Output feedback stabilization of linear systems with actuator saturation, IEEE Trans. Autom. Control, 52 (1997), 122-128. doi: 10.1109/TAC.2006.886498.

[44]

G. Valmorbida, S. Tarbouriech and G. Garcia, State feedback design for input-saturating quadratic systems, Automatica, 46 (2010), 1196-1202. doi: 10.1016/j.automatica.2010.03.016.

[45]

G. Zhai, M. Ikeda and Y. Fujikasi, Decentralized H-infinity Controller design: a matrix inequality approach using a homotopy method, Automatica, 37 (2001), 565-572. doi: 10.1016/S0005-1098(00)00190-4.

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