Optimal design of sampled-data control systems by linear programming†

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Abstract
This paper is devoted to the design of digital compensators for a special class of fnite-settling-time, linear, sampled-data control systems which are required to track both step and ramp inputs with no steady-state error. A general procedure is given to design the digital compensator so that the system is optimum on the basis of the ITAE (integral of time-weighted absolute value of error) criterion, subject to the constraint that the peak overshoot of the system for a step input is less than a certain percentage. Linear programming is used to find the optimum solution. Suitable upper bounds are imposed on the variables involved so that the peak overshoot of the system for a unit step input may not exceed a given value. A method of incorporating a specification on the acceleration constant (K a ) in the design is given, as also is a design example. For the case where finite settling time to a ramp input is not required, the design procedure is modified: a velocity constant (K a specification is incorporated in the design in place of the K a specification.

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