Lecture 07+08_1st & 2nd Order Control Systems (1).pptx

Control Engineering

1. Control Engineering Lab Engr. Adnan Rasheed

2. A first-order system without zeros The Step Response of the above system will be,

3. 2nd Order Control Systems

4. Damping Cases (2 nd Order) w.r.t Step Responses

5. MATLAB Control Functions step (num,den) : To plot the step response of the system impulse(num,den) : To plot the impulse response of the system. [y,x,t]=step(num,den): To store the values of the step response function in an array. ym=max(y): To get the maximum amplitude of a response value. ys = dcgain(num,den) : To get the d.c. gain of the system (steady state value) yovrsht = (ym-yt)/ys * 100; To calculate the % over shoot.

6. Example 5.2. 5.2 Closed-loop speed tachometer control system R(S) is the input voltage w(S) is the output angular movement of motor Td(S) is the external disturbance signal 5.2.1 Requirement: Analyze under external Disturbance Closed loop with feedback is better:

7. 5.2.1 MATLAB Code for the Open-loop without tachometer feedback of the above example (Case-I) % ---------------------------------------------------------------------------MEEN-4263 Control Engineering Lab ------------------------------------------------------------- % Author : Engr. Adnan Rasheed % Date : xxxxxxxx % Lab No. : 5 % Class : BEMTS VI (A & B) % File name : opentach.m % Description : The function implements the speed tachometer example. %------------------------------------------------------------------------------------- % Define Tachometer control system parameters Ra = 1; Km = 10; J= 2; b = 0.5; Kb = 0.1; Ka = 54; Kt = 1; num1 = [1]; den1 = [J b]; % Define G(s)= 1 / Js+b num2 = [Km*Kb/Ra]; den2 = [1]; % Define H(s) = Km*Kb/Ra [num,den] = feedback(num1,den1,num2,den2); % Find the T(S)= w(s) / Td(s) num = -num % Change the sign of T(s) since Td(s) is negative printsys(num,den); % print the final T(S) [step_resp,x,t] = step(num,den); % Compute response to step disturbance figure plot(t,step_resp); % plot step response title('Open-loop Disturbance Step Response'); xlabel('time[sec]'); ylabel('speed'); grid; Final_val = step_resp(length(t)) % Find steady-state error, last value of output %------------------------------------------------------------------------------------- % End Function %-------------------------------------------------------------------------------------

8. 5.2.3 MATLAB Code for the Open-loop without tachometer feedback of the above example (Case-I) The resulting system reduced to the following taking step Td(s):   Figure 5.3 : Open-Loop system Disturbance Step Response The approximate steady state value is: w(7) = -0.66 rad/s at t = 7 sec