H/sub infinity / controller design for the SISO case using a Wiener approach

Fragopoulos, D.; Grimble, M.J.; Shaked, U.

doi:10.1109/9.90237

Cited by 9 publications

(5 citation statements)

References 8 publications

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“…This non-generic case is discussed in reference (6). In all results presented in this paper a generic optimal solution was found.…”

Section: (B) Problem Definitionmentioning

confidence: 94%

“…In general when the cost function is a minimum it can be shown that X (e ÀjùT ) is constant with frequency (5,6). In order to shape the sensitivity functions appropriately, the weighting function W s (z À1 ) would normally be large at low frequency, keeping S(z À1 ) small at low frequency, and W u (z À1 ) would be large at high frequency, keeping U (z À1 ) small at high frequency.…”

Section: H I Controlmentioning

confidence: 99%

“…The method by which the controller polynomials F(z À1 ) and G(z À1 ) are calculated from the plant model and weighting functions is described in Appendix 1. The derivation largely follows the work of Grimble (6,7), which in turn mirrors the continuous-time polynomial approach of Kwakernaak (5,8). Appendix 2 is a summary of the controller design algorithm.…”

Section: H I Controlmentioning

confidence: 99%

“…In general, the H I solution is an equalizing solution, i.e. the magnitude of X is the same at all frequencies (5,6). It will be shown in this section how to calculate an equalizing solution.…”

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confidence: 98%

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A comparison of linear discrete-time design methods for servosystem control

Plummer

1997

Proceedings of the Institution of Mechanical Engineers, Part I:

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Three linear discrete-time model-based controller design techniques are compared: pole placement, linear quadratic Gaussian (LQG) and H I control. It is shown that design choices can be made for all three controllers by considering the effect on the sensitivity functions of the closed-loop system. Also all three controllers can be implemented using an identical controller structure. A comparative study of the application of the techniques to an electromechanical servosystem is made. The controllers are designed from a discrete-time plant model estimated from experimental data, and a polynomial-based solution method is used in each case. It is concluded that acceptable performance can be achieved using any of the controllers if informed design choices are made. NOTATIONfunction of plant and weighting polynomials [equation (65)]function of plant and weighting polynomials [equation (42)] e t additive plant noise=disturbance signalfactor of G(z À1 ) in LQG controller N 1 (z À1 ) diophantine equation (75) solution in H I minimization p degree of F(z À1 ) polynomial p i desired closed-loop poles (roots of closed-loop characteristic polynomial) P(z À1 ) transfer function equated to T 1 in forming equalizing solution q degree of G(z À1 ) polynomial Q(z À1 ) diophantine equation (45) product of weighting function numerators and noise model [equation (89)]The MS was Downloaded from w degree of A m (z À1 ) W s (z À1 ) output sensitivity weighting transfer function W 9 s (z À1 ) factor of output sensitivity weighting (without noise=disturbance model) W sd (z À1 ) denominator of W 9 s (z À1 ) W sn (z À1 ) numerator of W 9 s (z À1 ) W u (z À1 ) control sensitivity weighting transfer function W 9 u (z À1 ) factor of control sensitivity weighting (without noise=disturbance model) W ud (z À1 ) denominator of W 9 u (z À1 ) W un (z À1 ) numerator of W 9 u (z À1 ) W ó (z À1 ) transfer function used in H I minimization X (z À1 ) function whose norm is minimized in LQG and H I y t output signal Y (z À1 ) denominator of P(z À1 ) Y i (z À1 ) estimate of V (z À1 ) at iteration i z À1 backward shift operator Ã(z À1 ) function to be minimized in H I

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“…This non-generic case is discussed in reference (6). In all results presented in this paper a generic optimal solution was found.…”

Section: (B) Problem Definitionmentioning

confidence: 94%

Section: H I Controlmentioning

confidence: 99%

Section: H I Controlmentioning

confidence: 99%

mentioning

confidence: 98%

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A comparison of linear discrete-time design methods for servosystem control

Plummer

1997

Proceedings of the Institution of Mechanical Engineers, Part I:

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“…Some of them is limited 131. Polynomial solutions of the H, control problem developed in discrete time by Grimble appear to be both simple and numerically reliable[4]. The highlight of the algorithm is as follows.…”

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confidence: 99%

Robust H/sub ∞/ control of a traction drive system for precision motion

Proceedings of 1994 American Control Conference - ACC '94

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The control system for a traction drive must produce robust response with respect to a change in the mass of the workpiece on the slide. It has been found that a conventional controller cannot tolerate a large range of mass change. In this paper, a discrete-time H, controller is described that has achieved robustness with respect to a change in mass. Comparison between the robustness of two controllers, PID and H, , is given by the experimental results and shows the improvement using the H, controller.

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