Question

A) Can P-controlled firs order unity feedback system show oscillatory response to a step input? Explain your reasoning the possible values the poles can have.

B) Now assume the system is not unity feedback. Consider a 1st order sensor transfer function at least two times faster than the original system. If this system is P-controlled, can it exhibit oscillatory response to a step input? Explain your reasoning

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Answer 1

A) A first order system has only one energy storage element.In order to oscillate, at least two energy storage elements are required, so that the energy can be swapped back and forth between them.

The characteristic equation for an oscillatory system will have at least one pair of Complex poles always occur in conjugate pairs.
If the characteristic equation has only real roots, then the system is over damped and will not have an oscillatory response.This means the damping is sufficient to absorb all the energy without overshoot.

B)  For overshoot, you need complex poles and we know that complex poles come in pairs. That means you need at least 2 poles. That is why first order systems never overshoot. They have just one.