scholarly journals A Unified Framework for the H∞ Mixed-Sensitivity Design of Fixed Structure Controllers through Putinar Positivstellensatz

Machines ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 176
Author(s):  
Valentino Razza ◽  
Abdul Salam
Keyword(s):  
Controller Design ◽  
Convex Relaxation ◽  
Closed Loop System ◽  
Unified Framework ◽  
Controller Parameter ◽  
Performance Requirements ◽  
Discrete Time Systems ◽  
Nominal Performance ◽  
Fixed Structure ◽  
Time Systems

In this paper, we present a novel technique to design fixed structure controllers, for both continuous-time and discrete-time systems, through an H∞ mixed sensitivity approach. We first define the feasible controller parameter set, which is the set of the controller parameters that guarantee robust stability of the closed-loop system and the achievement of the nominal performance requirements. Then, thanks to Putinar positivstellensatz, we compute a convex relaxation of the original feasible controller parameter set and we formulate the original H∞ controller design problem as the non-emptiness test of a set defined by sum-of-squares polynomials. Two numerical simulations and one experimental example show the effectiveness of the proposed approach.

Mixed-Sensitivity H∞ Control and µ Analysis of Active Automobile Suspension

2004 ◽  
Author(s):  
Hemanth Porumamilla ◽  
Atul G. Kelkar
Keyword(s):  
Transfer Functions ◽  
Ride Comfort ◽  
Controller Design ◽  
Contemporary Literature ◽  
Pi Controller ◽  
Closed Loop System ◽  
Automobile Suspension ◽  
Performance Problem ◽  
Robust Control Design ◽  
Nominal Performance

This study presents an H∞-based robust control design for an active automobile suspension system and compares its performance with a previously designed robust LQG controller and a well tuned PI controller from contemporary literature. The robustness of the controller designs is assessed by performing μ analysis of the closed loop system. The H∞ problem is formulated as a stacked nominal performance problem. The weighting functions on complementary sensitivity, sensitivity, and controller transfer functions are chosen to obtain desirable trade-off in performance and robustness. The main objective of the controller design is to provide ride comfort for passengers. The controller design presented in this paper is shown to provide robust stability as well as desirable robust performance which is an improvement over the previously designed robust LQG controller and a PI controller chosen from contemporary literature.

Adaptive Sinusoidal Disturbance Rejection in Linear Discrete-Time Systems—Part II: Experiments

1999 ◽  
Vol 121 (4) ◽  
pp. 655-659 ◽  
Author(s):  
Foued Ben Amara ◽  
Pierre T. Kabamba ◽  
A. Galip Ulsoy
Keyword(s):  
Controller Design ◽  
Adaptive Controller ◽  
Companion Paper ◽  
Noise Cancellation ◽  
Adaptive Noise Cancellation ◽  
Stabilizing Controllers ◽  
Discrete Time Systems ◽  
Sinusoidal Disturbance ◽  
Adaptive Noise ◽  
Time Systems

The problem of adaptive noise cancellation in an acoustic duct is discussed. An adaptive controller design approach based on parametrizing the set of stabilizing controllers using the Youla parametrization and tuning the Youla parameter to achieve regulation was presented in a companion paper [3]. Three controller adaptation algorithms are implemented to solve the noise cancellation problem in an acoustic duct. The experimental results indicate a mixed performance for each of the adaptation algorithms, with good performances observed only in some frequency ranges. The discrepancy between the expected and the observed performances is attributed to unmodeled nonlinearities in the speakers.

Stability and robustness for discrete-time systems with control signal saturation

2000 ◽  
Vol 214 (1) ◽  
pp. 65-76 ◽  
Author(s):  
A R Plummer ◽  
C S Ling
Keyword(s):  
Discrete Time ◽  
Controller Design ◽  
Control Signal ◽  
Design Stage ◽  
System Control ◽  
Stability Robustness ◽  
Discrete Time Systems ◽  
The Stability ◽  
Time Systems ◽  
Signal Saturation

All practical control systems exhibit control signal saturation. The effect that this saturation has on the control system performance, especially stability and robustness, can be significant and must be understood at the controller design stage. This paper presents conditions for global asymptotic stability and measures of stability robustness for such systems. These are demonstrated through simulation examples, and it is shown how an understanding of the stability conditions can inform the controller design process. The off-axis circle criterion is used as the basis for a sufficient condition for stability, and it is argued that this is not overly restrictive in practice. The derivations are carried out in discrete time, and servo-system control is envisaged as an important application area for the techniques; however, the results are applicable more widely.

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