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On Controlling the Transient Response of Linear Time Invariant Systems with Fixed Structure Controllers

The problem of controlling transient response is important in many industrial applications; for example, the speed and accuracy of motion control of robots directly relates to the productivity of the robot. The objective of transient control is to determine a feedback controller of a fixed structure that renders the closed loop response of a specified system to lie in a specified envelope. One may associate a set of errors which measures the deviation of the response from the envelope. The set of errors may be defined in such a way that all the errors are non‐negative if and only if the response does not deviate from the envelope at any time. The transient problem can be thus posed as the problem of determining a stabilizing controller that renders the set of all errors to be non‐negative at every time. One may associate a control parameter vector K with a controller of a specified structure. The main topic of investigation of this paper is to find a bound for the set of real control parameters, K, so that a rational, proper transfer function, N   ( s , K ) D ( s , K ) has a decaying, non‐negative impulse response. It is assumed that the coefficients of the polynomials N(s, k) and D(s, K) are affine in K.