Reference no: EM13704675
1. Shown in is the control system for one joint of a robot arm. The controller is a PD compensator, given by the transfer function below.
The block diagram describing the system is shown in Figure 2
Find the plant transfer function of the motor and arm: G(s) = θ(s)/Ea(s), as in Figure 3.
1. Find the closed loop transfer function Gcl(s) = θL(s)/ θs(s)
2. Determine the initial and final values of θL(t) for a step input θc(t).
3. Assume KD = 1. Find Kp such that the closed loop system will have a damping ratio of 0.8 and a critically damped response, respectively.
4. Then, with KD =1 and the values of Kp found in 4), sketch the responses of the system θL(t) to a unit step input.
5. Sketch the step response of the closed-loop system manually and comment on upon the effect of proportional action (Provide the details of calculation of time response)
(1 ) KD = 1, KP= 2
(2) KD = 1, KP= 6
(3) KD = 1, Kp= 18
(4) KD = 1, Kp= 28
6. For different values of KID and Kp, analyse the stability of the closed loop system using Routh Hurwitz.
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