Research Papers

Constrained Tracking Control by Gain-Scheduled Feedback With Optimal State Resets: A General Servo Problem and an Online Optimization Method

[+] Author and Article Information
Nobutaka Wada

Division of Mechanical Systems
and Applied Mechanics,
Hiroshima University,
1-4-1 Kagamiyama,
Higashi-Hiroshima739-8527, Japan
e-mail: nwada@hiroshima-u.ac.jp

Hidekazu Miyahara

Department of Mechanical Systems Engineering,
Hiroshima University,
1-4-1 Kagamiyama,
Higashi-Hiroshima 739-8527, Japan

Masami Saeki

Division of Mechanical Systems
and Applied Mechanics,
Hiroshima University,
1-4-1 Kagamiyama,
Higashi-Hiroshima 739-8527, Japan
e-mail: saeki@hiroshima-u.ac.jp

1Corresponding author.

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.

J. Dyn. Sys., Meas., Control 138(12), 121008 (Aug 24, 2016) (11 pages) Paper No: DS-15-1090; doi: 10.1115/1.4034243 History: Received March 06, 2015; Revised July 14, 2016

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.

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Fig. 2

Convergence of the cost function Jt(t)

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Fig. 10

Tracking error e(t)

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Fig. 11

Scheduling parameter α(t)

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Fig. 13

Experimental apparatus

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Fig. 14

Two-mass-spring system model

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Fig. 5

Tracking error e(t)

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Fig. 6

Control input Φ(u(t))

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Fig. 7

Scheduling parameter α(t)

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Fig. 8

Controller state xc1(t)

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Fig. 9

Cost function Jt(t)

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Fig. 12

Maximum computation time versus imax

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Fig. 19

Plant output y (rad/s) (case II)

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Fig. 20

Control input uT (Nm) (case II)

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Fig. 21

Central processing unit time (ms/sample) (case I)

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Fig. 22

Graphical interpretation of the reset of the controller state in Algorithm 1 in case of nc = 1 and np = 1

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Fig. 15

Plant output y (rad/s) (case I)

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Fig. 16

Control input uT (N·m) (case I)

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Fig. 17

Angle of torsion θ (rad) (case I)

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Fig. 18

Scheduling parameter α (case I)



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