Assignment Applied Mec.

Part 1: Design of the control of the production system  Problem 1:
From the equations given in the statement and the numerical values given in Appendix A the values obtained in the command windoware:

 Problem 2:
In order to obtain the transfer function G(s), we have to use command ss2tf and tf (lines 42-44 appendix, at the end of the report). The following expression is obtained: Transferfunction: 263.6 ----------------s^2 + 90 s + 2103

 Problem 3:
We are asked to obtain . First, we obtain the expressions of the control parameters as a function of ‘a’ by equaling the CE of theproduction system to the desired CE. Then, we choose a value for ‘a’, in our case 60, that satisfy the requirements so this has to be positive (to obtain negative poles). By hand, we obtain theexpressions: (see lines 46-49 Appendix)

In the command window, we check the requirements, with the system poles and the closed system’s bandwidth which are showed in next problems. Kd = 0.3414; Kp =32.9939, Ki = 819.4234.

 Problem 4:
The closed loop system poles are the roots from the denominator of the close loop transfer function (Lines 51-58 Appendix) With the values we obtain in the commandwindow, we prove the system is stable and as we expected, the poles are close to the value given before.
POL = -59.9995 -60.0002 + 0.0004i -60.0002 - 0.0004i

 Problem 5:
The bandwidth is easilyobtained with the command BW=bandwidth(Gcl). The value obtained, 97.4824 rad/s is higher than 75 rad/s, as the closed system specifications ask for.

 Problem 6:
The sampling rate needs to be 10or more times higher than the closed-loop system bandwidth in order to ensure that sample doesn’t affect the closed loop system bandwidth. So that, we choose:

 Problem 7:
Proving thespecifications: - The error between the reference signal and the output signal should be less than 0.1m/s.

REFERENCE SIGNAL

OUTPUT SIGNAL

ERROR SIGNAL

-

The accumulated absolute error should be...