A closed loop negative feedback control system has a combined transfer function as: G(s)=GpGaGs=(s+1)(2s+1)1 where Gp,Ga, and Gs are the transfer function of the process, the valve, and the sensor, respectively. (a) Draw the block diagram of the closed loop system. (Hint, in your block diagram, you can just use, Gp,Ga, and Gs to represent your transfer function of the process, valve, and sensor, respectively; do not forget controller, since it is a closed loop system.) (b) Using a P-only controller, your colleague claims that a high controller gain (Kc) can cause the closed loop system to go unstable. Prove whether your colleague is right or wrong. Show your calculation procedures. (c) For the G(s) given above, assume Gs=1, and a P-only control with a parameter of Kc=1 is used. (i) write down the closed loop system overall transfer function, and (ii) predict the dynamic behavior, e.g., overdamped (or critically damped or underdamped), oscillatory, and unstable. (d) For the G(s) given above, assume Gs=1 and assume a P-only controller is used. When a stepwise change with a magnitude of M is applied to the set point. Is there any offset for a very large controller parameter, e.g., Kc ? Show your calculation procedures. A closed loop negative feedback control system has a combined transfer function as: G(s)=GpGaGs=(s+1)(2s+1)1 where Gp,Ga, and Gs are the transfer function of the process, the valve, and the sensor, respectively. (a) Draw the block diagram of the closed loop system. (Hint, in your block diagram, you can just use, Gp,Ga, and Gs to represent your transfer function of the process, valve, and sensor, respectively; do not forget controller, since it is a closed loop system.) (b) Using a P-only controller, your colleague claims that a high controller gain (Kc) can cause the closed loop system to go unstable. Prove whether your colleague is right or wrong. Show your calculation procedures. (c) For the G(s) given above, assume Gs=1, and a P-only control with a parameter of Kc=1 is used. (i) write down the closed loop system overall transfer function, and (ii) predict the dynamic behavior, e.g., overdamped (or critically damped or underdamped), oscillatory, and unstable. (d) For the G(s) given above, assume Gs=1 and assume a P-only controller is used. When a stepwise change with a magnitude of M is applied to the set point. Is there any offset for a very large controller parameter, e.g., Kc ? Show your calculation procedures