Control of multiterminal HVDC systems embedded in AC networks. Volume 2. Robustness of multivariable control systems
Abstract
The robustness of the stability of multivariable linear timeinvariant feedback control systems with respect to model uncertainty is considered using frequency domain criteria. Available and new robustness tests are unified under a common framework based on the nature and structure of model errors. These results are derived using a multivariable version of Nyquist's stability theorem in which the minimum singular value of the return difference transfer matrix is shown to be the multivariable generalization of the distance to the critical point of a singleinput, singleoutput (SISO) Nyquist diagram. Using the return difference transfer matrix a very general robustness theorem is presented from which all of the robustness tests dealing with specific model errors may be derived. The robustness of linearquadraticGaussian control systems are analyzed via this robustness theory and multiloop stability margins are presented; in particular, a new type of margin, a crossfeed margin, is introduced. Other frequency domain analysis and design techniques are also briefly discussed and their relation to the present robustness analysis is examined. In addition a linearquadratic based design procedure that quarantees a prescribed degree of stability is developed, with special emphasis upon its robustness properties.
 Publication:

Massachusetts Inst. of Tech. Report
 Pub Date:
 May 1982
 Bibcode:
 1982mit..reptX....A
 Keywords:

 Alternating Current;
 Control Stability;
 Direct Current;
 Feedback Control;
 High Voltages;
 Robustness (Mathematics);
 Linear Systems;
 Matrices (Mathematics);
 Networks;
 Nyquist Diagram;
 Siso (Control Systems);
 Electronics and Electrical Engineering