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The integral of the squared error is often used as a
performance index in the design of control systems. The
evaluation of ISE for systems having no delays can be easily
accomplished by a parametric method which does not need to find
the time response of the system. For systems with time delays,
however, the evaluation of ISE is not an easy task. In this
thesis, a direct numerical approach is presented to the
evaluation of quadratic cost functionals for linear systems
having multiple time delays. It is based on making use of the
Parseval theorem and the bilinear transformation so that the
computation of ISE involving time delays can be evaluated
accurately and efficiently by means of a numerical integration
method with automatic step-size adjustment. With this numerical
algorithm of computing ISE, the following three control
problems are solved: (1)Optimal reduced-order models with time
delay: By representing the delay-free part of the reduced-order
model in the Routh .gamma.-.delta. canonical form, the optimal
parameters and the time delay are searched by an existing
gradient-based method such that the ISE between the unit step
responses of the system and model is minimized. (2)Design of an
optimal PID controller satisfying prescribed gain and phase
margins: The PID controller is find for a system such that the
integral of the squared error of the closed-loop system subject
to a unit step input is minimized, while satisfying the
prescribed gain and phase margins. (3)Design of an optimal
digital controller for sampled-data systems: With the integral
of squared-error as the performance index, the parameters of
the digital PID controller are searched to minimize the
performance index.
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