新加坡国立大学王庆国教授来空天院讲学
2010年5月30日，新加坡国立大学电气与计算机工程系王庆国教授莅临空天院，在1413会议室作了题为《Robust Stability of MIMO Feedback Systems》的学术报告，信控所师生聆听了报告，报告会由航空航天学院副教授杨永胜主持。
报告内容分为两个部分，
Part I: Theory，
Part II: New development: Stability Margins of Multivariable Feedback Systems。
报告主要讲述了：
Stability robustness is a key issue in feedback control systems, and is often measured by gain and phase margins. The controller design based on gain and phase margin specifications is common and is widely used in practice. The SISO gain margin is one of most popular tools for control system analysis and design due to its well-postedness, easy computation, and clear measure of stability and performance. The MIMO gain margin would have enjoyed the same degree of popularity if it would also have been developed similarly and successfully. But unfortunately, gain margin cannot be extended straightforward to a multi-input and multi-output (MIMO) system, because of the interactions between the control loops. Historically, people started MIMO control study with the state space approach, which was thought to be much powerful than traditional frequency domain methods which seemed dead at early time of modern control. Only when one began to address model uncertainties and robust control, is there renewed interest in frequency domain approach for both SISO and MIMO cases. In the standard framework of modern robust control with respect to unstructured uncertainty, robust stability conditions or stability margins are given in terms of norm of a transfer function matrix. The relevant uncertainty is complex-valued, which does not corresponding to intuitive measures of respective real valued gain and phase, and is very conservative if only respective gain or phase change is of interest; and it is also matrix-valued, from which one can hardly see how individual elements of a controller matrix or plant matrix effects stability. Control engineers tune controllers by individual elements/parameters, not the whole matrix at a time.
In the view of the above observations, we introduce the independent loop gain margins for multivariable feedback systems as the allowed perturbation ranges of gains for each loop such that the closed-loop system remains stable. The so-defined loop gain margins enable and facilitate independent loop tuning for MIMO control systems, which dominates process control practice. You can think about these gain margins like the SISO case: you tune a MIMO system loop by loop, and for each loop, that loop gain margin functions alike the SISO gain margin for that loop. But note that the so found loop gain margin already takes into account of multivariable interactions, which is not the case if the SISO gain margin is used for each loop. Thus, when you change gain of one loop, the entire MIMO system remains stable as long as the gain value is within our loop gain margin range. In this connection, one readily sees that our independent loop gain margins enable independent tuning of loops, and they appeal to process control engineers as an easy, intuitive, attractive tuning tool for MIMO control, and becomes practically useful. This success is due to the fact that complex loop interactions are well taken care of during computation of such margins.
A time domain method is developed for computation of MIMO loop gain margins in a more general framework of determining the parameter ranges of multi-loop proportional-integral-derivative (PID) controllers which stabilize a given process. An effective computational scheme is established by converting the considered problem to a quasi-LMI problem connected with robust stability test. The descriptor model approach is employed together with linearly parameter dependent Lyapunov function method. Numerical examples are given for illustration. The results are believed to facilitate real time tuning of multi-loop PID controllers for practical applications. It shows better results than mu-analysis method. The loop gain margins obtained with this approach are indeed stability margins but not the exact or the maximum margins available due to the inherent conservativeness of LMI framework. Besides, the method was developed for delay free systems only. If the plant has time delay, one has to make approximation for time delay to apply this method. Fundamentally, it is always desirable to find the exact or the maximum controller parameter regions for stabilizing a giving process. Therefore, we further develop a frequency domain method to remove the above-mentioned conservativeness and compute exact loop gain margins of MIMO feedback systems. We have to discard a time domain/Lyapunov/LMI framework which is the root cause of conservativeness, and rather work in a frequency domain. We first transform the fundamental MIMO margin equation with the diagonal structure of gain perturbations into a constrained quadratic optimization problem. Next, we utilize the Lagrange multiplier method to obtain an unconstrained optimization problem, whose necessary/stationery condition is numerically solved by the Newton-Raphson iteration algorithm and whose sufficient condition is checked from the eigenvalues.
Similarly, loop phase margins of a multivariable system are defined as the allowable individual loop phase perturbations within which stability of the closed-loop system is guaranteed. Two approaches using time and frequency domain information are proposed for computing the loop phase margins. The time domain algorithm is composed of two steps: Firstly, find the stabilizing ranges of loop time delays using delay-dependent stability criteria; Secondly, convert these stabilizing ranges of loop delays into respective loop phase margins by multiplying a fixed frequency. The frequency domain algorithm makes use of unitary mapping between frequency responses of the system output and input, which is then converted, using the Nyquist stability analysis, to a simple constrained optimization problem solved numerically with the Lagrange multiplier and Newton-Raphson method. This frequency domain approach provides exact loop phase margins and thus improves the LMI results obtained by time domain algorithm, which could be conservative.
报告结束后，王教授与我所师生进行了深入交流和讨论。
王庆国教授简历：
Qing-Guo WANG was born in Suzhou, the People's Republic of China (PRC), 1958. He received, respectively, the B.Eng. in Chemical Engineering in 1982, the M. Eng. in 1984 and Ph.D. in 1987 both in Industrial Automation, all from Zhejiang University (ZU) of the PRC. From 1987 to 1989 he was a PRC Postdoctoral Fellow with the Institute for Fluid Power Transmission and Control/Department of Mechanical Engineering, ZU. In 1989 he joined the Department of Chemical Engineering/the Research Institute of Industrial Process Control, ZU, as an Associate Professor. Since 1992 he has been with the Department of Electrical and Computer Engineering of the National University of Singapore where he is currently a Full Professor.
发布时间：2010年6月2日