Synthesis of a Non-linear Feedback System with Significant Punt-ignorance for Prescribed Time-domain Tolerances

The problem considered is the design of a feedback system containing a linear, time-invariant, minimum-phase plant, whose parameters are known only within given bounds, such that the time-response of the system remains within specified limits. A quasi-optimal design, for given design constraints, is one which minimizes the effect of white sensor-noise on the input to the plant. Horowitz and Sidi have presented a method for the design of such a quasioptimal, linear time-invariant system. This report investigates the use of the non-linear device known as the Clegg Integrator in the design of such a system. The describing-function of the Clegg Integrator has the same magnitude characteristic, apart from a scale factor, as the linear integrator, but has 52° less phase-lag, at all frequencies, than the linear integrator; thus, when used in a feedback system, it provides a larger stability margin than the linear integrator. This property allows the non-linear feedback system to be designed so that the sensor-noise is attenuated more than in the linear design. The non-linear time-response is calculated in terms of an equivalent linear representation, and the reduced phase-lag in the frequency-domain is seen to correspond, in general, to smaller overshoot in the time-response. In order to obtain satisfactory steady-state response, the non-linear device is modified by putting a linear integrator in parallel with it. It is shown that for given bounds on plant-ignorance and time-response tolerances, the non-linear feedback system can be designed such that the effect of white sensor-noise on the plant-input is smaller than in a linear design. A method is developed for implementing the non-linear design in terms of an equivalent linear design by Horowitz and Sidi's method. CHAPTER I STATEMENT OF THE PROBLEM 1.