 # ME 450 ME450 Homework 5 ANSWERS (Penn State University)

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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 , 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,

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:

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

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