1. Experimental Setup

The experimental set up consists of a motor that drives a revolute joint via a gear box. The motor is mounted vertically, inside a safety box and carries an arm that can be extended or shortened along an axis that is perpendicular to the axis of rotation of the motor. The inertia of the revolute joint can be changed by changing the extension of the arm. 

The control input to the system is the voltage to be applied to the motor. To generate the applied voltage, a pulse width modulation (PWM) amplifier is used. Hence, we can consider the controller output as the input to the PWM amplifier. Therefore the units of the output of the controller you would design is “PWM Units”. The controller makes its decision based on the error in speed. To complete the position control loop, position feedback loop is created and the desired speed for the speed controller is determined based on the position error.

The motor has two encoders, one on the input shaft and another on the output shaft of the gear box. As the point of interest is the output shaft, the position controller loop uses the output shaft encoder. The encoder on the input shaft is used to obtain the shaft speed for the speed controller. The gear ratio of the gear box is 38.4 : 1.

2. The Experiment

The following two parts form the experiment.

2.1 Part A - Design Verification

This part is designed to verify if you have carried out the position controller design correctly. The design is correct, if the actual response shows zero steady state error and a second order response that corresponds to the point chosen on the root locus.

2.2 Part B - Effect of Modelling Uncertainties

In this part, the controller designed for a given system is tested on a different system. This is equivalent to designing a controller without knowing the system parameters exactly. An explainable deviation in the responses should be seen.

3. Report Content

The report must have the following.

Introduction - brief background and what you expect to achieve at the end of the experiment

4. Aim - the purpose of the experiment

Brief description of the experimental procedure

6. Controller design calculation

7. Simulink block diagram of the experiment.

Part A - Input to the Simulink block diagram the desired input position profile. This can be found in your A data file. Generate the Simulink block diagram’s output and then compare the results by superimposing the experimental plot on it. Explain any discrepancies.

Part B - Replace the above Simulink block diagram’s plant transfer function (do not change or redesign the controller) by the transfer function of the incorrect system allocated to you and generate position outputs. Superimpose the experimental data plot on the Simulink generated data plots and explain any discrepancies.

10. In a conclusion discuss what you learnt from this experiment explaining any discrepancies between the plots of Part A and Part B. Explain how this design methodology can be applied using a real-life example.