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.

scholarly journals A unified approach to fixed-order controller design via linear matrix inequalities

1995 ◽  
Vol 1 (1) ◽  
pp. 59-75 ◽  
Author(s):  
T. Iwasaki ◽  
R. E. Skelton
Keyword(s):  
Convex Sets ◽  
Controller Design ◽  
Robust Stabilization ◽  
Sufficient Conditions ◽  
Positive Definite Matrix ◽  
Linear Matrix ◽  
Computational Aspects ◽  
Fixed Order ◽  
Performance Problem ◽  
Nominal Performance

We consider the design of fixed-order (or low-order) linear controllers which meet certain performance and/or robustness specifications. The following three problems are considered; covariance control as a nominal performance problem,𝒬-stabilization as a robust stabilization problem, and robustL∞control problem as a robust performance problem. All three control problems are converted to a single linear algebra problem of solving a linear matrix inequality (LMI) of the typeBGC+(BGC)T+Q<0for the unknown matrixG. Thus this paper addresses the fixed-order controller design problem in a unified way. Necessary and sufficient conditions for the existence of a fixed-order controller which satisfies the design specifications for each problem are derived, and an explicit controller formula is given. In any case, the resulting problem is shown to be a search for a (structured) positive definite matrixXsuch thatX∈𝒞1andX−1∈𝒞2where𝒞1and𝒞2are convex sets defined by LMIs. Computational aspects of the nonconvex LMI problem are discussed.

LQG-Based Robust Control of Active Automobile Suspension

2003 ◽  
Author(s):  
H. Porumamilla ◽  
A. G. Kelkar
Keyword(s):  
Closed Loop ◽  
Ride Comfort ◽  
Controller Design ◽  
Control Design ◽  
Suspension System ◽  
Robust Controller ◽  
Automobile Suspension ◽  
Active Feedback ◽  
Active Feedback Control ◽  
Robust Controller Design

This paper presents robust controller design for an active automobile suspension system using an interative LQG design technique. The main objective is to design an active feedback control for an automobile suspension system to ensure the ride comfort for passengers in the presence of unknown road disturbances. The control system designed is shown to be robust to uncertainties and parametric variations. The resulting interative LQG-based control design is shown to achieve a significant improvement in the performance, while maintaining a desired level of closed-loop stability that is robust to plant uncertainties and parametric variations. The controller design is also compared to some other active suspension designs published in the literature.

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.

scholarly journals Controller Design of UPQC for Enhancing Power Quality in Distribution System

2018 ◽  
Vol 9 (4) ◽  
pp. 1591
Author(s):  
Kittaya Somsai
Keyword(s):  
Mathematical Model ◽  
Power Quality ◽  
Distribution System ◽  
Optimization Design ◽  
Transfer Functions ◽  
Controller Design ◽  
Dynamic Performance ◽  
Parameter Tuning ◽  
Pi Controller ◽  
Approximation Technique

This paper presents the procedure of PI controller design of Unified Power Quality Conditioner (UPQC) for improving power quality in the distribution system. A mathematical model of the distribution system with the UPQC is thoroughly explained in this paper. The mathematical model that is founded has been used for designing the PI controller. In order to investigate the dynamic performance and design the controller, linear approximation technique is used. Linearization of the systems that is around the operating point provides a set of linear equations, and then multi-input multi-output (MIMO) transfer functions of the systems are obtained. Two controller design techniques are presented and compared. One is the sequential loop closure controller design with parameter tuning through the Bode diagram (SLC-BD). The other one is the controller optimization design with the genetic algorithms (CO-GA). The performances of these techniques are verified and compared by using MATLAB program. Simulation results reveal that the power quality in the distribution system can be enhanced by using UPQC with the proposed controller design.

scholarly journals Robust H∞ Loop Shaping Controller Synthesis for SISO Systems by Complex Modular Functions

2021 ◽  
Vol 26 (1) ◽  
pp. 21
Author(s):  
Ahmad Taher Azar ◽  
Fernando E. Serrano ◽  
Nashwa Ahmad Kamal
Keyword(s):  
Design Methodology ◽  
Closed Loop ◽  
Complex Analysis ◽  
Controller Design ◽  
Filter Design ◽  
Design Procedure ◽  
Elliptic Functions ◽  
Loop System ◽  
Closed Loop System ◽  
Loop Shaping

In this paper, a loop shaping controller design methodology for single input and a single output (SISO) system is proposed. The theoretical background for this approach is based on complex elliptic functions which allow a flexible design of a SISO controller considering that elliptic functions have a double periodicity. The gain and phase margins of the closed-loop system can be selected appropriately with this new loop shaping design procedure. The loop shaping design methodology consists of implementing suitable filters to obtain a desired frequency response of the closed-loop system by selecting appropriate poles and zeros by the Abel theorem that are fundamental in the theory of the elliptic functions. The elliptic function properties are implemented to facilitate the loop shaping controller design along with their fundamental background and contributions from the complex analysis that are very useful in the automatic control field. Finally, apart from the filter design, a PID controller loop shaping synthesis is proposed implementing a similar design procedure as the first part of this study.

Decentralized robust PI controller design for an industrial boiler

2009 ◽  
Vol 19 (2) ◽  
pp. 216-230 ◽  
Author(s):  
Batool Labibi ◽  
Horacio Jose Marquez ◽  
Tongwen Chen
Keyword(s):  
Controller Design ◽  
Pi Controller ◽  
Industrial Boiler

Backstepping Based Adaptive Control of Magnetic Levitation System

2013 ◽  
Vol 341-342 ◽  
pp. 945-948 ◽  
Author(s):  
Wei Zhou ◽  
Bao Bin Liu
Keyword(s):  
Parameter Uncertainty ◽  
Closed Loop ◽  
Controller Design ◽  
Magnetic Levitation ◽  
Adaptive Controller ◽  
Closed Loop System ◽  
Actual System ◽  
Levitation System ◽  
Magnetic Levitation System ◽  
Control Accuracy

In view of parameter uncertainty in the magnetic levitation system, the adaptive controller design problem is investigated for the system. Nonlinear adaptive controller based on backstepping is proposed for the design of the actual system with parameter uncertainty. The controller can estimate the uncertainty parameter online so as to improve control accuracy. Theoretical analysis shows that the closed-loop system is stable regardless of parameter uncertainty. Simulation results demonstrate the effectiveness of the presented method.

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