Linear Parameter-Varying Control for Engineering Applications

1. Front Matter

   Pages i-xiii

   PDF

2. Introduction

   • Andrew P. White, Guoming Zhu, Jongeun Choi

   Pages 1-5

3. Linear Parameter-Varying Modeling and Control Synthesis Methods

   • Andrew P. White, Guoming Zhu, Jongeun Choi

   Pages 7-25

4. Guaranteed \(\ell _2-\ell _{\infty }\) Gain Control for LPV Systems

   • Andrew P. White, Guoming Zhu, Jongeun Choi

   Pages 27-38

5. Gain-Scheduling Control of Port-Fuel-Injection Processes

   • Andrew P. White, Guoming Zhu, Jongeun Choi

   Pages 39-78

6. LPV Control of a Hydraulic Engine Cam Phasing Actuator

   • Andrew P. White, Guoming Zhu, Jongeun Choi

   Pages 79-97

7. Back Matter

   Pages 99-110

   PDF

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.

• Control Applications
• Gain-scheduling Control
• Linear Parameter-varying Systems
• Mixed H2/H-infinity Control
• Mixed L2-to-L-infinity Control

From the reviews:

“The authors present in this book of 110 pages, different applications in engineering of the Linear Parameter-Varying (LPV) method. The book contains 5 main chapters and two appendices. … The book is interesting and useful for those using the LPV method.” (Gheorghe Tigan, zbMATH, Vol. 1272, 2013)

• , Department of Mechanical Engineering, State University of Michigan, East Lansing, USA

  Andrew P. White

• , Department of Mechanical Engineering, Michigan State University, East Lansing, USA

  Guoming Zhu, Jongeun Choi

Dr. Zhu worked in the automotive industry for 15 years before he joined MSU as a faculty member. Drawing on his rich industrial background he believes that this brief will bridge the gap between the academic theory of LPV control and industrial gain-scheduling control applications. The key issue for industrial application of LPV control is how to select design gains to meet the desired performance and control gains. For example, PI (proportional and integral) control gains can be tuned manually since only two control parameters need to be tuned; while for LPV control, both estimation and control gains need to be designed which make them impossible to be tuned manually. The weight selection scheme discussed in this book provides a systematic approach for LPV gain tuning in practical engineering applications. Dr. Zhu teaches "Robust Control" for graduate students at Michigan State University. He believes that this brief can be used as supplemental material for mixed H2 and H-infinity control. It can also be used as a text book for advanced topics in control classes for those students who complete the robust control class.
Dr. Choi has been working on model set estimation for robust controller design; robust track-following controller design in hard disk drives (HHDs); and LPV modeling and controller synthesis for energy-efficient automotive engine systems and mobile robotic sensors based on LMI optimization. In his experience, the LPV modeling and control approach plays an important role in addressing challenging control problems in many applications ranging from HHDs and engine control to unmanned robotic vehicles. He also teaches graduate-level control systems courses such as ‘Linear Systems and Control’, and ‘Nonlinear Systems and Control’ at Michigan State University.

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