Quasilinear Control: Performance Analysis and Design of Feedback Systems with Nonlinear Actuators and Sensors
Quasilinear Control (QLC) is a set of methods for performance analysis and design of linear plant/nonlinear instrumentation (LPNI) feedback systems. The approach of QLC is based on the method of stochastic linearization, which reduces the nonlinearities of actuators and sensors to quasilinear gains. Unlike the usual, Jacobian linearization, stochastic linearization is global. The price to pay is that the quasilinear gain depends not on the operating point but on all functional blocks and exogenous signals of the system. Using this approximation, QLC extends most methods of linear control to LPNI systems. These include system type, error coefficients, root locus, LQR/LQG, H∞, LMI, etc. The resulting equations consist of the usual control-theoretic relationships (e.g., Lyapunov and Ricatti equations) coupled with transcendental equations, which account for the quasilinear gains; a bisection algorithm for solving these equations is provided. In addition, QLC addresses LPNI-specific problems: instrumented LQR/LQG, where the optimal controller is designed simultaneously with the optimal actuator and sensor, and partial and complete performance recovery, where the degradation of linear performance is either contained or completely eliminated. In this talk, the theory of QLC will be overviewed and the topics of saturated root locus, instrumented LQR/LQG, and performance recovery will be discussed in some details.
Semyon M. Meerkov received his MSEE degree from the Polytechnic of Kharkov, Ukraine, in 1962 and Ph.D. in Systems Science from the Institute of Controlow, Russia, in 1966. He was with the Institute of Control Sciences until 1977. From 1979 to 1984 he was with the Department of Electrical and Computer Engineering, Illinois Institute of Technology, Chicago, IL. Since 1984 he has been a Professor at the Department of Electrical Engineering and Computer Science of the University of Michigan, Ann Arbor, MI. He has held visiting positions at UCLA (1978- 1979), Stanford University (1991), Technion, Israel (1997-1998 and 2008), Tsinghua University, Beijing, China (2008), and Ben-Gurion University of the Negev, Beer-Sheva, Israel (2011). He was the Editor-in-Chief of Mathematical Problems in Engineering, Department Editor for Manufacturing Systems of IIE Transactions and Associate Editor of several other journals. His research interests are in Systems and Control with applications to production systems and communication networks and in Mathematical Theory of Rational Behavior with applications resilient monitoring and control.