4.7 PRACTICE PROBLEMS

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1. a) We are developing a freight elevator control system. The first major task is developing a height positioning controller. The elevator is moved to a new floor by issuing a step function for the new floor height. The transfer function below relates the voltage supplied to the elevator motor to the height of the elevator. Develop a controller transfer function that has a first order response, and draw a complete block diagram.

b) Develop the discrete equation for the controller if the time constant for the first order response is 5 seconds and the sampling time is 1 second.

2. c) Write a computer program (in the computer language of your choice) that implements the controller in question 1. Assume the input and output values are set using the two functions below.

3. Redraw the following system and add a feedforward controller. Develop the function used for the feed forward controller.

4. The control system below will be used for positioning the height of an elevator.

a) Find a controller transfer function that gives a first order response for a time step of T=1 and a time constant of 3.

b) Develop the discrete equation and determine if the controller is realizable.

c) Develop a transfer function for the final system and determine if the system is stable.

4. We want to design a control system to minimize the effects of disturbance. Given a step input of magnitude 1, we are willing to accept a maximum error of 0.5 for one time step.

a) Find a controller transfer function.

b) Develop the discrete equation for the system and determine if the controller is realizable?