In this paper, a tracking control problem for discrete-time linear systems with actuator saturation is addressed. The reference signal is assumed to be generated by an external dynamics. First, a design condition of a controller parameterized by a single scheduling parameter is introduced. The controller includes a servo compensator to achieve zero steady-state error. Then, a control algorithm that guarantees closed-loop stability and makes the tracking error converge to zero is given. In the control algorithm, the controller state as well as the scheduling parameter is updated online so that the tracking control performance is improved. Then, it is shown that the decision problem of the scheduling parameter and the controller state can be transformed into a convex optimization problem with respect to a scalar parameter. Based on this fact, we propose a numerically efficient algorithm for solving the optimization problem. Further, we propose a method of modifying the control algorithm so that the asymptotic tracking property is ensured even when the numerical error exists in the optimal solution. A numerical example and an experimental result are provided to illustrate effectiveness of the proposed control method.
Constrained Tracking Control by Gain-Scheduled Feedback With Optimal State Resets: A General Servo Problem and an Online Optimization Method
Higashi-Hiroshima 739-8527, Japan
Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received March 6, 2015; final manuscript received July 14, 2016; published online August 24, 2016. Assoc. Editor: Evangelos Papadopoulos.
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Wada, N., Miyahara, H., and Saeki, M. (August 24, 2016). "Constrained Tracking Control by Gain-Scheduled Feedback With Optimal State Resets: A General Servo Problem and an Online Optimization Method." ASME. J. Dyn. Sys., Meas., Control. December 2016; 138(12): 121008. https://doi.org/10.1115/1.4034243
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