Answer Happy

DC motors used in robots are too fast and cannot provide enough torque for most applications. Therefore harmonic gears are used when connecting robot links with the motors. The advantages include: no backlash, compactness and light weight, high gear ratios, reconfigurable ratios within a standard housing, good resolution and excellent repeatability when repositioning inertial loads, high torque capability, and coaxial input and output shafts. oooooo Figure 1 - Spring effect of harmonic drive The spring effect of harmonic drive is shown in Figure 1. As can be seen, the motor with inertia J and viscous friction B is connected to the robot link with inertia J, and viscous friction B, with a gear and a rotational spring coefficient of k. The parameters are, J-10, B-1, k-100, J-2, B-0.5 Equations of motion of the harmonic drive system are given below: JÖ + B₁0₁ +k(0₁-0m) = 0 JmOm + BmOm-k(0₁-0m) = u (1) (2) 1. Assuming the angular position of link is output, input torque ut is input, a. Take laplace transform of both equations and derive the transfer function: (s) u(s) b. Define the transfer function of system in Matlab (with tf function). What is the system order? Find zeros and poles of the transfer function. Comment on the stability of the system. c. Find the step response in Matlab, using step function within 30 seconds.

MCH3008 CONTROL SYSTEMS LABORATORY d. Build the block diagram in Matlab/Simulink by using the equation (1) and (2) and plot the link and motor position and velocities for the first 30 seconds (applying u is step input with an amplitude 1, initial time Os) Show your final Simulink model and 4 plots (position and velocities of link and motor) 2. Use the block diagram above, take torque u as input, and angular position of link 8₁ as output, and create a subsystem named "harmonic drive" and build a PID Control feedback loop. (Figure 2) Integrator integral Gain tarque reference & theta reference Proportional Gain harmonic dive duld Derivative Derivative Gain Figure 2 - PID Control loop Use root locus analysis to determine parameters of the PD controller so that the overshoot is less than 5%, and the peak time is less than 1 second while integral term is 0. Using Matlab/Simulink, plot the response of the link position within 30 seconds while initial time and final value of step reference are 0 and 5, respectively. 19