ME 450 ME450 Homework 5 ANSWERS (Penn State University)

ME450 Homework 5 Solution (Penn State University)

Consider a single link robot manipulator driven by a DC motor. The mass and length of the link are 30 kg. and 1.2 meter, respectively. The payload is 20 kg. Following Luh’s paper [1], design a position control system using data for U9M4T(See Table in

the Paper) DC motor. Parameters are as follows: Ja  5.663105kg. m2,

Bm 8.1123104Nmsec./rad.,KI 0.0432Nm/Amp,

Kb 0.0432Voltsec./rad., n0.01, R1.02ohm
Assume that the structural resonant frequency for the joint is 100 rad./sec.

1. Evaluate the performance of your controller by MATLAB/Simulink. Assume that motor shafts are rigid. 
2. Include armature inductance L . Using MATLAB/Simulink, examine the performance of your controller for designed values of controller gains. 
3. Include armature inductance L . With designed value of k1 , find the range of k for the closed loop stability via Routh-Hurwitz method. 
4. Include armature inductance L . Find the steady state error, e  lim e(t) , as a ss t
   function of k for (a) unit step reference input d (t) and (b) unit ramp reference input
    d (t ) . Note that the error e(t )   d (t )   (t ) . 

Reference:

[1] Luh, J. Y. S., “Conventional Controller Design for Industrial Robots – A Tutorial,” IEEE Trans. On Systems, Man and Cybernetics, Vol. SMC – 13, 1983.