Precision tracking control of non-minimum phase systems with zero phase error

1995 ◽  
Vol 61 (4) ◽  
pp. 791-807 ◽  
Author(s):  
JACK ZHIJIE XIA ◽  
CHIA-HSIANG MENQ
Author(s):  
Molong Duan ◽  
Keval S. Ramani ◽  
Chinedum E. Okwudire

This paper proposes an approach for minimizing tracking errors in systems with non-minimum phase (NMP) zeros by using filtered basis functions. The output of the tracking controller is represented as a linear combination of basis functions having unknown coefficients. The basis functions are forward filtered using the dynamics of the NMP system and their coefficients selected to minimize the errors in tracking a given trajectory. The control designer is free to choose any suitable set of basis functions but, in this paper, a set of basis functions derived from the widely-used non uniform rational B-spline (NURBS) curve is employed. Analyses and illustrative examples are presented to demonstrate the effectiveness of the proposed approach in comparison to popular approximate model inversion methods like zero phase error tracking control.


1993 ◽  
Vol 115 (2A) ◽  
pp. 238-245 ◽  
Author(s):  
Chia-Hsiang Menq ◽  
Jin-jae Chen

In this paper, a precision tracking control scheme for linear discrete time nonminimum-phase systems is proposed. This control scheme consists of a preview filter, a tracking-performance filter, a command feedforward controller, and a feedback controller. A command feedforward controller, whose design is based on the minimal order inverse model of the plant being controlled, will result in a completely decoupled system. The preview filter is introduced to compensate the phase and gain errors induced by the nonminimum phase zeros or lightly damped zeros of the system. Using the command feedforward controller along with the proposed preview filter, the tracking performance of the proposed control scheme can be characterized by the frequency response of the tracking-performance filter. For the design of the preview filter, a generalized Nth order preview filter and its associated penalty function that quantifies the tracking error of a design are defined. It is shown that, given the desired bandwidth and the order of the preview filter, the optimal solution for the design of the preview filter can be obtained explicitly. The proposed control scheme together with the optimal preview filter is shown to be very effective in achieving precision tracking control of discrete time MIMO nonminimum phase systems. It is also shown that the tracking performance is improved as the order N of the preview filter is increased.


1992 ◽  
Vol 114 (3) ◽  
pp. 347-351 ◽  
Author(s):  
D. Torfs ◽  
J. De Schutter ◽  
J. Swevers

This paper describes a new feedforward algorithm for accurate tracking control of nonminimal phase systems. Accurate feedforward calculation involves a prefilter design using the inverse system model. Nonminimal phase systems cause problems with this prefilter design, because unstable zeros become unstable poles in the inverse model. The zero phase error tracking control algorithm (ZPETC) consists of a substitution scheme, which removes the unstable zeros. This scheme introduces a small gain error, which increases with frequency, but no phase error. This paper investigates additional properties which give more insight into the ZPETC algorithm, and allow to improve it. The improved algorithm is based on the same substitution scheme as ZPETC, but adds additional feedforward terms to compensate for the gain error. These additional terms increase the frequency range for which the overall transfer function has only limited gain error, without introducing phase errors. The additional feedforward terms repeatedly reduce the tracking error proportional to ε2, ε4, ε6, …, where ε is the ZPETC tracking error. The new feedforward algorithm or new substitution scheme is therefore called “extended bandwidth zero phase error tracking control algorithm” (EBZPETC). Experimental results on a one-link flexible robot compares both methods.


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