Desired Compensation Adaptive Robust Control ∗

A desired compensation adaptive robust control (DCARC) framework is presented for nonlinear systems having both parametric uncertainties and uncertain nonlinearities. The paper first considers a class of higher order nonlinear systems transformable to a normal form with matched model uncertainties. For this class of uncertain systems, the desired values of all states for tracking a known desired trajectory can be predetermined and the usual desired compensation concept can be used to synthesize DCARC laws. The paper then focuses on systems with unmatched model uncertainties, in which the desired values of the intermediate state variables for perfect output tracking of a known desired trajectory cannot be predetermined. A novel way of formulating desired compensation concept is proposed and a DCARC backstepping design is developed to overcome the design difficulties associated with unmatched model uncertainties. The proposed DCARC framework has the unique feature that the adaptive model compensation and the regressor depend on the reference output trajectory and on-line parameter estimates only. Such a structure has several implementation advantages. First, the adaptive model compensation is always bounded when projection type adaption law is used, and thus does not affect the closed-loop system stability. As a result, the interaction between the parameter adaptation and the robust control law is reduced, which may facilitate the controller gain tuning process considerably. Second, the effect of measurement noise on the adaptive model compensation and on the parameter adaptation law is minimized. Consequently, a faster adaptation rate can be chosen in implementation to speed up the transient response and to improve overall tracking performance. These claims have been verified in the comparative experimental studies of several applications. DOI: 10.1115/1.3211087

[1]  M. Corless,et al.  Continuous state feedback guaranteeing uniform ultimate boundedness for uncertain dynamic systems , 1981 .

[2]  Anuradha M. Annaswamy,et al.  Robust Adaptive Control , 1984, 1984 American Control Conference.

[3]  Michael Athans,et al.  Nonlinear and Adaptive Control , 1989 .

[4]  Petros A. Ioannou,et al.  Instability analysis and robust adaptive control of robotic manipulators , 1989, IEEE Trans. Robotics Autom..

[5]  Roberto Horowitz,et al.  Stability and Robustness Analysis of a Class of Adaptive Controllers for Robotic Manipulators , 1990, Int. J. Robotics Res..

[6]  Z. Qu,et al.  Robust Control of Generalized Dynamic Systems Without the Matching Conditions , 1991 .

[7]  Vadim I. Utkin,et al.  Sliding Modes in Control and Optimization , 1992, Communications and Control Engineering Series.

[8]  Marios M. Polycarpou,et al.  A Robust Adaptive Nonlinear Control Design , 1993, 1993 American Control Conference.

[9]  Masayoshi Tomizuka,et al.  Robust desired compensation adaptive control of robot manipulators with guaranteed transient performance , 1994, Proceedings of the 1994 IEEE International Conference on Robotics and Automation.

[10]  Masayoshi Tomizuka,et al.  Comparative experiments of robust and adaptive control with new robust adaptive controllers for robot manipulators , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[11]  Masayoshi Tomizuka,et al.  Adaptive Control of Robot Manipulators in Constrained Motion—Controller Design , 1995 .

[12]  Riccardo Marino,et al.  Nonlinear control design: geometric, adaptive and robust , 1995 .

[13]  Masayoshi Tomizuka,et al.  Smooth Robust Adaptive Sliding Mode Control of Manipulators With Guaranteed Transient Performance , 1996 .

[14]  Miroslav Krstic,et al.  Robustness of adaptive nonlinear control to bounded uncertainties , 1996 .

[15]  Bin Yao,et al.  High performance adaptive robust control of nonlinear systems: a general framework and new schemes , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

[16]  M. Tomizuka,et al.  High performance robust motion control of machine tools: an adaptive robust control approach and comparative experiments , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).

[17]  Masayoshi Tomizuka,et al.  Adaptive robust control of SISO nonlinear systems in a semi-strict feedback form , 1997, Autom..

[18]  Miroslav Krstic,et al.  Adaptive Backstepping with Parameter Projection: Robustness and Asymptotic Performance , 1998, Autom..

[19]  Masayoshi Tomizuka,et al.  Adaptive Robust Motion and Force Tracking Control of Robot Manipulators in Contact With Compliant Surfaces With Unknown Stiffness , 1998 .

[20]  George T.-C. Chiu,et al.  Adaptive robust motion control of single-rod hydraulic actuators: Theory and experiments , 1999, Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251).

[21]  Li Xu,et al.  Adaptive robust precision motion control of linear motors with negligible electrical dynamics: theory and experiments , 2001, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).

[22]  P. P. Yip,et al.  Multiple Sliding Surface Control: Theory and Application , 2000 .