Dynamic analysis of fourth-order feedback control systems†

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Abstract
Analytic expressions relating deterministic performance criteria to s-plane geometry are developed for fourth-order unity numerator feedback control systems. It is shown that system responses can be placed in one of three categories, and that a relationship exists between the form of system response and the transfer function coefficients. Dominant mode approximations are quantified. Some of the conclusions presented are applicable to more complex and higher-order systems than those discussed in the paper. It is shown that the optimization of performance in the presence of saturating plant dynamics is achieved at the expense of increased sensitivity to changes in component values. Some consideration is given to problems which arise in the practical measurement of performance of systems with lightly damped secondary resonances such as on-countered in machine tool drives and servos with floxible gearing. It is shown that the use of those test signals, leading to an estimate of the impulse response, can be extremely helpful under such circumstances.

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