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2013 | Book

Introduction Read chapter Read first chapter

Linear Parameter-Varying Control for Engineering Applications

Authors: Andrew P. White, Guoming Zhu, Jongeun Choi

Publisher: Springer London

Book Series : SpringerBriefs in Electrical and Computer Engineering

Part of: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik"

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About this book

The subject of this brief is the application of linear parameter-varying (LPV) control to a class of dynamic systems to provide a systematic synthesis of gain-scheduling controllers with guaranteed stability and performance.

An important step in LPV control design, which is not well covered in the present literature, is the selection of weighting functions. The proper selection of weighting functions tunes the controller to obtain the desired closed-loop response. The selection of appropriate weighting functions is difficult and sometimes appears arbitrary. In this brief, gain-scheduling control with engineering applications is covered in detail, including the LPV modeling, the control problem formulation, and the weighting function optimization. In addition, an iterative algorithm for obtaining optimal output weighting functions with respect to the H2 norm bound is presented in this brief. Using this algorithm, the selection of appropriate weighting functions becomes an automatic process. The LPV design and control synthesis procedures in this brief are illustrated using:

• air-to-fuel ratio control for port-fuel-injection engines;

• variable valve timing control; and

• application to a vibration control problem.

After reading this brief, the reader will be able to apply its concepts to design gain-scheduling controllers for their own engineering applications. This brief provides detailed step-by-step LPV modeling and control design strategies along with an automatic weight-selection algorithm so that engineers can apply state-of-the-art LPV control synthesis to solve their own engineering problems. In addition, this brief should serve as a bridge between the H-infinity and H2 control theory and the real-world application of gain-scheduling control.

Table of Contents

Frontmatter
Chapter 1. Introduction
Abstract
The goal of the research that this book is based on has been to establish a systematic procedure for the design of gain-scheduling controllers. In industry, gain-scheduled controllers are normally developed with long hours of ad-hoc tuning and calibration through, for example, engine dynamometer and vehicle field tests. While these controllers are often used successfully in many practical applications, the design process through which they are obtained is less than ideal. Not only is the process expensive and time consuming, but more importantly it may not guarantee the stability and performance of the closed-loop system for all possible time-varying parameters. In addition, the performance of the closed-loop system with gain-scheduling controllers designed in this way is dependent on the experience of person doing the calibration. In order to meet the challenges posed by the strict requirements facing many industries these days, a systematic process for designing gain-scheduled controllers with guaranteed performance and stability for all time-varying parameters is needed.
Andrew P. White, Guoming Zhu, Jongeun Choi
Chapter 2. Linear Parameter-Varying Modeling and Control Synthesis Methods
Abstract
This chapter is split into the following two main parts: modeling of LPV systems and control synthesis methods for LPV systems.
Andrew P. White, Guoming Zhu, Jongeun Choi
Chapter 3. Guaranteed $$\ell _2-\ell _{\infty }$$ ℓ 2 − ℓ ∞ Gain Control for LPV Systems
Abstract
This chapter considers the optimal control of polytopic, discrete-time LPV systems with a guaranteed \(\ell _2\) to \(\ell _{\infty }\) gain. Additionally, to guarantee robust stability of the closed-loop system under parameter variations, \(\fancyscript{H}_{\infty }\) performance criterion is also considered as well. Controllers with a guaranteed \(\ell _2\) to \(\ell _{\infty }\) gain and a guaranteed \(\fancyscript{H}_{\infty }\) performance (\(\ell _2\) to \(\ell _2\) gain) are mixed \(\fancyscript{H}_2/\fancyscript{H}_{\infty }\) controllers. Normally, \(\fancyscript{H}_2\) controllers are obtained by considering a quadratic cost function that balances the output performance with the control input needed to achieve that performance. However, to obtain a controller with a guaranteed \(\ell _2\) to \(\ell _{\infty }\) gain (closely related to the physical performance constraint), the cost function used in the \(\fancyscript{H}_2\) control synthesis minimizes the control input subject to maximal singular-value performance constraints on the output. This problem can be efficiently solved by a convex optimization with LMI constraints. The contribution of this chapter is the characterization of the control synthesis LMIs used to obtain an LPV controller with a guaranteed \(\ell _2\) to \(\ell _{\infty }\) gain and \(\fancyscript{H}_{\infty }\) performance while the control \(\ell _2\) to \(\ell _{\infty }\) gain is minimized. A numerical example is presented to demonstrate the effectiveness of the convex optimization.
Andrew P. White, Guoming Zhu, Jongeun Choi
Chapter 4. Gain-Scheduling Control of Port-Fuel-Injection Processes
Abstract
In this chapter, an LPV design example [61, 62] that demonstrates how to design gain-scheduling proportional-integral (PI) and proportional-integral-derivative (PID) controllers using the LPV methods from Chap. 2 is presented. First, physics-based modeling is used to create an event-based sampled discrete-time linear system representing a port-fuel-injection process based on wall-wetting dynamics, which is then formulated as an LPV system.
Andrew P. White, Guoming Zhu, Jongeun Choi
Chapter 5. LPV Control of a Hydraulic Engine Cam Phasing Actuator
Abstract
In this chapter, an LPV design example [63] that demonstrates how to design a dynamic, output-feedback gain scheduling controller using the LPV methods from Chap. 2 is presented. First, an LPV model is formulated from a family of linear models that were obtained from a series of closed-loop system identification tests for a variable valve timing cam phaser system [49]. Then a control strategy is developed and relevant control structures are appended onto the LPV system to produce the generalized LPV plant. A discussion on weighting function selection for mixed controller synthesis is presented, with an emphasis placed on examining various frequency responses of the system.
Andrew P. White, Guoming Zhu, Jongeun Choi
Backmatter
Metadata
Title
Linear Parameter-Varying Control for Engineering Applications
Authors
Andrew P. White
Guoming Zhu
Jongeun Choi
Copyright Year
2013
Publisher
Springer London
Electronic ISBN
978-1-4471-5040-4
Print ISBN
978-1-4471-5039-8
DOI
https://doi.org/10.1007/978-1-4471-5040-4