An open-loop swivel controller and plant for an industrial robot has the transfer function where o (s) is the Laplace transform of the robots

An open-loop swivel controller and plant for an industrial robot has the transfer function

where ω_o(s) is the Laplace transform of the robot’s angular swivel velocity and V_i(s) is the input voltage to the controller. Assume G_e(s) is the forward transfer function of a velocity control loop with an input transducer and sensor, each represented by a constant gain of 3 (Schneider, 1992).

a. Find the value of gain, K, to minimize the steady state error between the input commanded angular swivel velocity and the output actual angular swivel velocity.

b. What is the steady-state error for the value of K found in Part a?

c. For what kind of input does the design in Part a apply?

w,(s) K G(s) = V:(s) (s+ 10)(s + 4s + 10)