Multimodel Control of Nonlinear Systems: An Integrated Design Procedure Based on Gap Metric and H∞ 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.

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A Hadamard weighted loop shaping design procedure

[1992] Proceedings of the 31st IEEE Conference on Decision and Control ◽

10.1109/cdc.1992.371404 ◽

2005 ◽

Cited By ~ 5

Author(s):

F. van Diggelen ◽

K. Glover

Keyword(s):

Design Procedure ◽

Loop Shaping

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Electromagnetic Shock Absorbers for Automotive Suspensions: Electromechanical Design

Volume 2: Automotive Systems, Bioengineering and Biomedical Technology, Fluids Engineering, Maintenance Engineering and Non-Destructive Evaluation, and Nanotechnology ◽

10.1115/esda2006-95339 ◽

2006 ◽

Cited By ~ 3

Author(s):

Nicola Amati ◽

Aldo Canova ◽

Fabio Cavalli ◽

Stefano Carabelli ◽

Andrea Festini ◽

...

Keyword(s):

Shock Absorber ◽

Dynamic Performance ◽

Integrated Design ◽

Design Procedure ◽

Resistive Load ◽

Added Resistance ◽

Damping Force ◽

Quarter Car Model ◽

Car Model ◽

Shock Absorbers

This article illustrates the modeling and design of electromechanical shock absorbers for automotive applications. Relative to the commonly used hydraulic shock absorbers, electromechanical ones are based on the use of linear or rotative electric motors. If electric motor is of the DC-brushless type, the shock absorber can be devised by shunting its electric terminals with a resistive load. The damping force can be modified by acting on the added resistance. An integrated design procedure of the electrical and mechanical parameters is presented in the article. The dynamic performance that can be obtained by a vehicle with electromechanical dampers is verified on a quarter car model.

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A PWA model identification method for nonlinear systems using hierarchical clustering based on the gap metric

Computers & Chemical Engineering ◽

10.1016/j.compchemeng.2020.106838 ◽

2020 ◽

Vol 138 ◽

pp. 106838

Author(s):

Jiaorao Wang ◽

Chunyue Song ◽

Jun Zhao ◽

Zuhua Xu

Keyword(s):

Nonlinear Systems ◽

Hierarchical Clustering ◽

Model Identification ◽

Gap Metric ◽

Identification Method

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Multimodel Scheduling Control of Nonlinear Systems Using Gap Metric

Industrial & Engineering Chemistry Research ◽

10.1021/ie049610o ◽

2004 ◽

Vol 43 (26) ◽

pp. 8275-8283 ◽

Cited By ~ 35

Author(s):

Erdem Arslan ◽

Mehmet C. Çamurdan ◽

Ahmet Palazoglu ◽

Yaman Arkun

Keyword(s):

Nonlinear Systems ◽

Gap Metric

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“Loop-at-a-Time” Design of Dynamic Surface Controllers for Nonlinear Systems

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.1433804 ◽

1998 ◽

Vol 124 (1) ◽

pp. 104-110 ◽

Cited By ~ 7

Author(s):

J. Christian Gerdes ◽

J. Karl Hedrick

Keyword(s):

Robust Control ◽

Nonlinear Systems ◽

Engine Speed ◽

Design Procedure ◽

Sequential Design ◽

Bounded Region ◽

Dynamic Surface ◽

Mismatched Uncertainties ◽

The Common ◽

Derivatives Of

The use of multiple surface sliding controllers for robust control of nonlinear systems with mismatched uncertainties has produced a number of impressive applications, but also raised a few theoretical questions. Among the latter are the use of numerical differencing to obtain derivatives of desired trajectories, robustness to uncertainties in the gain terms and the common practice of filtering desired trajectories for implementation. This paper seeks to address these issues through the concept of a Dynamic Surface Controller, in which filters form an integral part of the structure. This filtering removes the need for numerical differencing and guarantees a certain smoothness, enabling other assumptions of smoothness to be relaxed. In this paper, the Dynamic Surface Controller is coupled with a sequential design procedure that carves a system workspace out of the state space. Within this bounded region, bounded tracking performance can be rigorously guaranteed in the presence of uncertainties and constraints such as rate limits and saturation can be systematically avoided. The design of a Dynamic Surface Controller and the advantages of the workspace concept are demonstrated in the context of engine speed control.

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