1. Homework 3.1. Consider the closed-loop block diagram and transfer functions below.
Find the closed-loop transfer function in terms of Gİ.
Find the closed-loop transfer function H(s) using the transfer functions given below for P control (Kp=140).
Find the closed-loop transfer function H(s) using the transfer functions given below for PI control (Kp=140, Ki=50).
Find the closed-loop transfer function H(s) using the transfer functions given below for PID control (Kp=140, Ki=50, Kd=80 ). G1 Gc G2 K + -

2. Homework 3.2. Consider the closed-loop block diagram and transfer functions below.
Find the eigenvalues of the closed-loop system.
Find the dynamic behaviour parameters (, fn, t, ts) of the system.
Find the steady-state value of the step response for PD control (Kp=140, Kd=80).
Find the sensitivity of the system for PID control (Kp=140, Ki=50, Kd=80). G1 Gc G2 K + -

3. Homework 3.3. Consider the closed-loop block diagram.
Find the closed-loop transfer function from R(s) to C(s).
Find the closed-loop transfer function from N(s) to C(s).
N(s)

4. Control action: PID control
Homework 3.4. Find the closed-loop response of 2-DOF mechanical system (Example 3.2)
Control action: PID control
r(t) is the step input with the amplitude of 0.05 m, f2(t) is the step input with the amplitude
of 3 N. The transfer function of the sensor Gs(s) is given above. (Ks=10/0.4 V/m, s=10 ms)
Find the step response of the closed-loop system for P or PID control by considering Gs(s) on the forward path.
Find the step response of the closed-loop system for P or PID control by considering Gs(s) on the feedback path.
Compare the results obtained in (a) and (b), comment the effect of the disturbance and sensor dynamics on the closed-loop system.