I couldn't do the 2nd question in my project homework

I need urgent help for question 2.

Answer 1

[Sam Chak]

You should at least provide the model of the harmonic drive in order to work on Q2.

If you do it properly, then it is possible to guide you along the way.

[Sam Chak]

@Emre Komur

Please check if you obtain the same model from your derivation of the Laplace transforms.

A   = [0 0 1 0; 0 0 0 1; -100/10 100/10 -1/10 0; 100/2 -100/2 0 -0.5/2];
B   = [0; 0; 0; 1/2];
C   = [1 0 0 0];        % only gives theta_l as output
D   = 0;
sys = ss(A, B, C, D);
Gp  = tf(sys)

Gp =
 
                        5
  ----------------------------------------------
  s^4 + 0.35 s^3 + 60.02 s^2 + 7.5 s + 1.557e-13
 
Continuous-time transfer function.

n = order(Gp)   % system order

n = 4

z = zero(Gp)    % zeros of the TF

z =

  0×1 empty double column vector

p = pole(Gp)    % poles of the TF

p = 
  -0.1125 + 7.7449i
  -0.1125 - 7.7449i
  -0.1250 + 0.0000i
  -0.0000 + 0.0000i

impulse(Gp)

The impulse response of the system can be used to determine the stability of harmonic drive system. Comment based on the observation.

1.d requires you to plot the step responses of the angular positions and velocities of the link and motor. So, the output matrix needs to modified.

Cc  = eye(n);
Dd  = zeros(4, 1);
sys = ss(A, B, Cc, Dd);
step(sys, 30)

[Emre Komur]

The second question says to use the above model.

I think he wants us to use the model and equations in question one.

I do not understand. I have added the solution to the 1st question. Maybe it will help

[Sam Chak]

This is a 4th-order system. It is still possible to achieve the response with the percentage overshoot is less than 5%. However, to achieve a peak time of 1 second, the motor will have to exert a pretty aggressive torque and it may destabilize the system. A high gain compensator is possible.

I didn't use the root locus, but the pidtune instead. You can use the root locus to show that you can design a similar gain value of Gc as shown below:

A   = [0 0 1 0; 0 0 0 1; -100/10 100/10 -1/10 0; 100/2 -100/2 0 -0.5/2];
B   = [0; 0; 0; 1/2];
C   = [1 0 0 0];        % only gives theta_l as output
D   = 0;
sys = ss(A, B, C, D);
Gp  = tf(sys)

Gp =
 
                        5
  ----------------------------------------------
  s^4 + 0.35 s^3 + 60.02 s^2 + 7.5 s + 1.557e-13
 
Continuous-time transfer function.

Gc = pidtune(Gp, 'PD', 0.0592)

Gc =
 
  Kp = 0.0982
 
P-only controller.

Gcl = feedback(Gc*Gp, 1);
step(Gcl, 120)

S = stepinfo(Gcl)

S = struct with fields:
         RiseTime: 23.1876
    TransientTime: 66.2475
     SettlingTime: 66.2475
      SettlingMin: 0.9138
      SettlingMax: 1.0498
        Overshoot: 4.9791
       Undershoot: 0
             Peak: 1.0498
         PeakTime: 47.8965

[Emre Komur]

I don't understand how to answer the question

[Sam Chak]

If you don't how to answer in words, then don't so or do it with minimal words. Quantitative technical questions are usually best answered and justtified with graphs. In your case, I think you just need to follow the instruction and run the simulations accordingly with the proposed gain shown above. Of course, technically you should answer with the knowledge learned in MCH-3008 course.

[Emre Komur]

Thank you for your time

God bless you

[Sam Chak]

You are welcome, @Emre Komur. If my demonstration of using pidtune() in the Comment has helped in your project, consider accepting ✔ and voting 👍 the Answer as a closure to this. Thanks!