Bounded tracking for nonminimum phase nonlinear systems with fast zero dynamics

We derive tracking control laws for nonminimum phase nonlinear systems with both fast and slow, possibly unstable, zero dynamics. The fast zero dynamics arise from a perturbation of a nominal system. These fast zeros can be problematic in that they may be in the right half plane and may cause large magnitude tracking control inputs. In this paper, we combine the ideas from work of Hunt, Meyer, and Su (1995)with that of Devasia, Paden, and Chen (1996) on an asymptotic tracking procedure for nonminimum phase nonlinear systems. We give (somewhat subtle) conditions under which the tracking control input is bounded as the magnitude of the perturbation of the nominal system becomes zero. Explicit bounds on the control inputs are calculated using some interesting non-standard singular perturbation techniques. The method is applied to the simplified planar dynamics of VTOL and CTOL aircraft.

[1]  P. Hartman.  Ordinary Differential Equations , 1965 .

[2]  A. R. Bergen,et al.  Justification of the Describing Function Method , 1971 .

[3]  V. Cheng.  A direct way to stabilize continuous-time and discrete-time linear time-varying systems , 1979 .

[4]  J. Descusse,et al.  Decoupling with Dynamic Compensation for Strong Invertible Affine Non Linear Systems , 1985 .

[5]  S. Sastry,et al.  Adaptive Control: Stability, Convergence and Robustness , 1989 .

[6]  S. Shankar Sastry,et al.  Zero dynamics of regularly perturbed systems may be singularly , 1989 .

[7]  A. Isidori,et al.  Output regulation of nonlinear systems , 1990 .

[8]  S. Shankar Sastry,et al.  The analysis of singularly perturbed zero dynamics , 1990 .

[9]  Leonardo Lanari,et al.  Feedforward calculation in tracking control of flexible robots , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.

[10]  S. Shankar Sastry,et al.  Singularly perturbed zero dynamics of nonlinear systems , 1992 .

[11]  S. Shankar Sastry,et al.  Nonlinear control design for slightly non-minimum phase systems: Application to V/STOL aircraft , 1992, Autom..

[12]  P. Kokotovic,et al.  Nonlinear control via approximate input-output linearization: the ball and beam example , 1992 .

[13]  S. Shankar Sastry,et al.  Stabilization of trajectories for systems with nonholonomic constraints , 1992, Proceedings 1992 IEEE International Conference on Robotics and Automation.

[14]  S.S. Sastry,et al.  Approximate decoupling and asymptotic tracking for MIMO systems , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[15]  B. Paden,et al.  Exact output tracking for nonlinear time-varying systems , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[16]  Sahjendra N. Singh,et al.  Invertibility and trajectory control for nonlinear maneuvers of aircraft , 1994 .

[17]  J. Grizzle,et al.  Approximate output tracking for nonlinear non-minimum phase systems with an application to flight control , 1994 .

[18]  Salvatore Monaco,et al.  On the control of regularly e-perturbed nonlinear systems , 1994 .

[19]  George Meyer,et al.  Nonlinear system guidance in the presence of transmission zero dynamics , 1995 .

[20]  L. Hunt,et al.  Nonlinear system guidance , 1995, Proceedings of 1995 34th IEEE Conference on Decision and Control.

[21]  John Lygeros,et al.  Output tracking for a non-minimum phase dynamic CTOL aircraft model , 1995, Proceedings of 1995 34th IEEE Conference on Decision and Control.

[22]  B. Paden,et al.  Nonlinear inversion-based output tracking , 1996, IEEE Trans. Autom. Control..

[23]  George Meyer,et al.  Stable inversion for nonlinear systems , 1997, Autom..