© 2013

Linear Parameter-Varying Control for Engineering Applications


Part of the SpringerBriefs in Electrical and Computer Engineering book series (BRIEFSELECTRIC)

Also part of the SpringerBriefs in Control, Automation and Robotics book sub series (BRIEFSCONTROL)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Andrew P. White, Guoming Zhu, Jongeun Choi
    Pages 1-5
  3. Andrew P. White, Guoming Zhu, Jongeun Choi
    Pages 7-25
  4. Andrew P. White, Guoming Zhu, Jongeun Choi
    Pages 27-38
  5. Andrew P. White, Guoming Zhu, Jongeun Choi
    Pages 39-78
  6. Andrew P. White, Guoming Zhu, Jongeun Choi
    Pages 79-97
  7. Back Matter
    Pages 99-110

About this book


The objective of this brief is to carefully illustrate a procedure of applying linear parameter-varying (LPV) control to a class of dynamic systems via a systematic synthesis of gain-scheduling controllers with guaranteed stability and performance. The existing LPV control theories rely on the use of either H-infinity or H2 norm to specify the performance of the LPV system.  The challenge that arises with LPV control for engineers is twofold. First, there is no systematic procedure for applying existing LPV control system theory to solve practical engineering problems from modeling to control design. Second, there exists no LPV control synthesis theory to design LPV controllers with hard constraints. For example, physical systems usually have hard constraints on their required performance outputs along with their sensors and actuators. Furthermore, the H-infinity and H2 performance criteria cannot provide hard constraints on system outputs. As a result, engineers in industry could find it difficult to utilize the current LPV methods in practical applications.

To address these challenges, gain-scheduling control with engineering applications is covered in detail, including the LPV modeling, the control problem formulation, and the LPV system performance specification. In addition, a new performance specification is considered which is capable of providing LPV control design with hard constraints on system outputs. The LPV design and control synthesis procedures in this brief are illustrated through an engine air-to-fuel ratio control system, an engine variable valve timing control system, and an LPV control design example with hard constraints.
After reading this brief, the reader will be able to apply a collection of LPV control synthesis techniques 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 a new performance specification 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

Authors and affiliations

  1. 1., Department of Mechanical EngineeringState University of MichiganEast LansingUSA
  2. 2., Department of Mechanical EngineeringMichigan State UniversityEast LansingUSA
  3. 3., Department of Mechanical EngineeringMichigan State UniversityEast LansingUSA

About the authors

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.

Bibliographic information

  • Book Title Linear Parameter-Varying Control for Engineering Applications
  • Authors Andrew P. White
    Guoming Zhu
    Jongeun Choi
  • Series Title SpringerBriefs in Electrical and Computer Engineering
  • Series Abbreviated Title SpringerBriefs in Electrical
  • DOI
  • Copyright Information The Author(s) 2013
  • Publisher Name Springer, London
  • eBook Packages Engineering Engineering (R0)
  • Softcover ISBN 978-1-4471-5039-8
  • eBook ISBN 978-1-4471-5040-4
  • Series ISSN 2191-8112
  • Series E-ISSN 2191-8120
  • Edition Number 1
  • Number of Pages XIII, 110
  • Number of Illustrations 35 b/w illustrations, 2 illustrations in colour
  • Topics Control and Systems Theory
    Automotive Engineering
    Systems Theory, Control
  • Buy this book on publisher's site


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)