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 performancespecification 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.

Autorentext
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.

Zusammenfassung
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.

Inhalt
Introduction.- Linear Parameter-Varying Modeling and Control Synthesis Methods.- Weight Selection and Tuning.- Gain-Scheduling Control of Port-Fuel-Injection Processes.- Mixed H2/H-infinity Observer-Based LPV Control of a Hydraulic Engine Cam Phasing Actuator.