# How can I design a suitable controller for this given system?

How can I design a proportional controller to make closed loop transfer function stable? Parameter of the P controller is $$P[z]=K_P$$ Closed loop transfer function of the system is shown below. In this case the transfer function shown below must be made stable. $$\dfrac{K_PG[z]}{1+K_PG[z]}$$ $G[z]$ is the plant as can be seen from image. To make this system stable, we must find the values of $K_P$ that make the system is stable. Schematic of the system is shown below.

• Do you know Nyquist stability criterion? – the_candyman Mar 27 '18 at 18:02
• Can somebody at least show me a way? – Aldrich Taylor Apr 1 '18 at 18:21
• A good place to start is always by finding the poles of the open loop. Is it stable or unstable? You next need to find a gain such that (1) the closed loop error is stable, (2) the transient response has all desired characteristics, (3) the margins are good. Root locus and Nyquist are the classic ways to do that. – Mortified Through Math Apr 18 '18 at 3:05