Name
Abstract | ||
|---|---|---|
This note presents a method for the reduction of controller fragility. The method is based on the sensitivity of closed-loop poles to per- turbations in the controller parameters. By means of a state space parame- terization of the controller, the closed-loop pole sensitivity can be reduced. A controller fragility measure based on the closed-loop pole sensitivity is proposed. Conditions for the optimal state-space realization of the con- troller are presented, along with a numerical method for obtaining the so- lution. Index Terms—Controller fragility, controller implementation, optimal structure, pole sensitivity, stability. I. INTRODUCTION The problem of "fragile" controllers has recently been raised by Keel and Bhattacharryya (1); a controller is fragile in the sense that very small perturbations in the coefficients of the designed controller desta- bilize the closed-loop control system. This is an important and funda- mental issue in control system design. In the usual design process, the assumption is often made that the controller can be implemented exactly. This assumption is to some extent valid, since, clearly, the plant uncertainty is the most signifi- cant source of uncertainty in the control system, whilst controllers are implemented with high precision hardware. However, there will in- evitably be some amount of uncertainty in the controller, a fact that is sometimes ignored in advanced robust control design. If the con- troller is implemented by analog means, there are some tolerances in the analog components. More commonly, the controller will be imple- mented digitally, and consequently there will be some rounding the controller parameters. The rounding effects are even more problematic if, for reasons of safety, cost and execution speed, the implementation is with fixed-point rather than floating point processors. The question of controller fragility has only recently been explicitly raised, but it is certainly not new (see (2) for a brief overview). In fact, the closely re- lated problem of finite word-length implementations of controllers was considered over 30 years ago (3), and has been the subject of continuing work since (4)-(11). It is clear that many of these developed techniques can be applied directly to the controller fragility problem. |
Year | DOI | Venue |
|---|---|---|
2001 | 10.1109/9.905702 | IEEE Trans. Automat. Contr. |
Keywords | Field | DocType |
Control systems,Open loop systems,Optimal control,Eigenvalues and eigenfunctions,Uncertainty,State-space methods,Industrial control,Stability,Process design,Hardware | Closed-loop pole,Control theory,Mathematical optimization,Optimal control,Pole–zero plot,Control theory,Fragility,Sensitivity (control systems),State space,Open-loop controller,Mathematics | Journal |
Volume | Issue | ISSN |
46 | 2 | 0018-9286 |
Citations | PageRank | References |
12 | 1.47 | 5 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| James F. Whidborne | 1 | 66 | 14.67 |
| Robert S. H. Istepanian | 2 | 109 | 13.22 |
| Jun Wu | 3 | 72 | 16.70 |