Consider the discrete-time control system with a proportional controller K as shown in the following figure. The sampling period T is 0.1 second.
- Determine the pulse transfer function of the closed-loop system.
- Determine the range of gain K for stability of the closed-loop system.
- When K=1, draw Bode diagram of the open loop system in the w-plane by using any available method.
- Design the controller gain K so that the phase margin of the digital control system is 50o . With this value of K, determine the gain margin.
