Consider the robot joint control system of Problem 5.3-13 and Fig. P5.3-13. Let D(z) = 1 ,T = 0.1 s, and K = 2.4 .

(a) Using the closed-loop transfer function, derive a discrete state model for the system.

(b) Derive a discrete state model for the plant from the plant transfer function. Then derive a state model for the closed-loop system by adding the feedback path and system input to a flow graph of the plant.

(c) Calculate the system transfer function from the state model found in part (b), to verify the state

model.

Problem 5.3-13

Consider the robot-joint control system of Fig. P5.3-13. This system is described in Problem 1.5-4.

(a) The sensor input is θa in degrees and the output is in volts. If the robot joint movement is mechanically restricted to ±135°, find the range of the sensor output voltage. What should be the input voltage range for the A/D?

(b) Let G_p(s) be the transfer function of the servomotor and gears, and H_k = 0.05 be the sensor gain. Find the system transfer function as a function of K, G_p(s), and so on.

(c) Evaluate the system transfer function for K = 1.4, T = 0.3 s, and D(z) = 1.1.

Fig. P5.3-13

Transcribed Image Text:

0 + T - Controller D(z) Volts Zero-order hold amplifier K Volts Sensor 0.05 Ea Servomotor 200 s (0.5 s + 1) S 0m Gears 1 100 a