Phase-space analysis and design of linear discontinuously damped feedback control systems

LINEAR SYSTEMS can be designed having very fast responses with essentially deadbeat performance by the inclusion of compensating loops which are switched in and out of the system as required. Fast response is obtained by using an unstable or nearly unstable uncompensated system to provide the desired rise time. Deadbeat performance is obtained by designing the compensation loops so that they provide an overdamped system when the compensation is switched in. Selection of the real roots for the overdamped system is based on the desired location of the eigenvectors in the phase space. A switching computer is required which connects the compensation loops as the state point reaches a hyperplane which is related to the eigenvector in a special way. The computer is readily realized from derivative signals and considerable engineering simplification is permissible in both the compensation design and the switching computer because of the topological nature of the phase portrait in the vicinity of properly chosen eigenvectors. Experimental results verify the theoretical conclusions.