Adaptive feedforward Zero Phase Error Tracking Control for minimum phase and non-minimum phase systems - XY table real-time application

2012 ◽  
Author(s):  
Ramli Adnan ◽  
Hashimah Ismail ◽  
Norlela Ishak ◽  
Mazidah Tajjudin ◽  
Mohd Hezri Fazalul Rahiman
Keyword(s):  
Real Time ◽  
Tracking Control ◽  
Phase Error ◽  
Minimum Phase ◽  
Phase Systems ◽  
Adaptive Feedforward ◽  
Real Time Application ◽  
Zero Phase

Tracking Control of Non-Minimum Phase Systems Using Filtered Basis Functions: A NURBS-Based Approach

2015 ◽  
Author(s):  
Molong Duan ◽  
Keval S. Ramani ◽  
Chinedum E. Okwudire
Keyword(s):  
Tracking Control ◽  
Phase Error ◽  
Approximate Model ◽  
Basis Functions ◽  
Minimum Phase ◽  
Tracking Errors ◽  
Model Inversion ◽  
B Spline ◽  
Phase Systems ◽  
Zero Phase

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.

Extended Bandwidth Zero Phase Error Tracking Control of Nonminimal Phase Systems

1992 ◽  
Vol 114 (3) ◽  
pp. 347-351 ◽  
Author(s):  
D. Torfs ◽  
J. De Schutter ◽  
J. Swevers
Keyword(s):  
Tracking Control ◽  
Control Algorithm ◽  
Phase Error ◽  
Tracking Error ◽  
Flexible Robot ◽  
Phase Errors ◽  
Gain Error ◽  
Small Gain ◽  
Phase Systems ◽  
Zero Phase

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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