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1. Given the following feedback control diagram: D{(s) D2(s) Gd1 Gd2 Cisp(s) + + Gc Ga + + s'(s) Gp C'(s) c'(s) F,(s) C'ANIAS(S) Gg a. Derive the transfer function that relates changes in Disturbance 1 [D1'(s)] to the regulated state variable [X'(s)]. b. Derive the transfer function that relates changes in Disturbance 2 [D2'(s)] to the regulated state variable [X'(s)]. 2. Using SIMULINK, create the following control system block diagram. F((s) 4e**' (3s+1) Cisp(s) 5 -3 Gg C'(s) + s'(s) c'(s) 3s+1 F6(s) (10s+1) 1 (5s+1) We will explore how well a simple proportional-only (P-only) controller can regulate this system. Simulate the behavior of the control system to a 1 unit increase in the setpoint using the following different controller transfer functions: a. What choice of controller gain sign should be chosen for this system and why? b. Assume the controller in this case is a simple proportional-only (P- only) controller Explore a range of different Kc values. Is there a range of Kc values where the system behaves better or in a more stable manner? Is there an ultimate gain for this system and if so what is your estimate of it? c. Write down the closed loop transfer function for setpoint tracking in this system. d. What is the characteristic equation for this system? e. Plot the root locus diagram for this system. You can plot it by hand, using Excel, and/or using MATLAB, but be sure to show some important values of Kcon the plot. f. What is the ultimate gain for this system based on your root locus diagram?

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