In The Heating Tank Example Discussed In Section 13.1, Suppose That The Operation Of The Valve Is Subject To Random Disturbances, So That The Steam Flow Rate Is Given By À 3 = K,U+V 496 CHAPTER 13 Where V Is Random Noise. A) Re-Derive The State Space Description Of The Closed Loop System Under PI Control, With V Being An Additional Disturbance Input.

 

13.10 In the heating tank example discussed in section 13.1, suppose that the operation of the valve is subject to random disturbances, so that the steam flow rate is given by Mst = ku+v 496 CHAPTER 13 where v is random noise. a) Re-derive the state space description of the closed loop system under PI control, with v being an additional disturbance input. b) For the following values of process and controller parameters F =1, Ahyap,s V V pcp -=1, k =0.2, m=0.1, kc =50, t =1 discretize the closed loop system with sampling period Ts=0.01. c) Use the discretized closed loop system equations to simulate the closed loop response of Tm(t) to a unit step change in the set point in the presence of valve noise, where the discrete values of v are normally distributed random numbers with zero mean and standard deviation 0.8 (use MATLAB's normrnd or randn function). Comment on the ability of the control system to handle the given level of valve noise.