Harmonic drives are very popular for use in robotic

Chapter 8, Problem 64

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Harmonic drives are very popular for use in robotic ML manipulators due to their low backlash, high torque transmission, and compact size (Spong, 2006). The problem of joint flexibility is sometimes a limiting factor in achieving good performance. Consider that the idealized model representing joint flexibility is shown in Figure P8.18. The input to the drive is from an actuator and is applied at \(\theta_m\). The output is connected to a load at \(\theta_l\). The spring represents the joint flexibility and \(B_m\) and \(B_l\) represent the viscous damping of the actuator and load, respectively. Now we insert the device into the feedback loop shown in Figure P8.19. The first block in the forward path is a PD controller, which we will study in the next chapter. The PD controller is used to improve transient response performance.

Use MATLAB to find the gain \(K_D\) to yield an approximate 58 overshoot in the step response given the following parameters: \(J_1\) = 10 ; \(B_I\) = 1 ; k = 100 ; \(J_m\) = 2 ; \(B_m\) = 0.5 ; \(\frac{K_P}{K_D}\) = 0.25 ; \(p_1(s)\) = \(J_1 s^2+B_1 s+k\); and \(p_m(s)\) = \(J_m s^2\) + \(B_m s\) + k