Report presentation: [10 marks]
Do not re-write the questions. It is sufficient to indicate question numbers. The individual report should include as a minimum: a cover page, a summary, a table of contents and should be organised into 3 main sections corresponding to the three parts of the coursework. The coursework should have a general conclusion. A list of references will be provided using Harvard referencing system. All references must be cited in the text. Lists of figures are optional but desirable.
Part 1 [30 marks]
PI and PID control are currently being applied to a wide variety of applications from motor speed and position control to robotics, automotive and aerospace applications, as well as the control of power plants.
- a) Explain the role of the proportional, integral and derivative gains in PID control. Cite one example of a system that can be controlled by PI and another one using PID. Describe the control system’s inputs and outputs and the sensing/actuation methods used.
- b) Explain with your own words the strengths and limitations of PID control. In your answer, take into consideration ease of implementation, stabilisation requirements, performance, robustness, energy consumption, static errors and any practical issues that may arise with PID control.
- c) Explain the role of motor position control in robotic manipulators.
- d) Provide a brief survey of modern alternatives to PID control for slow processes and systems with uncertain parameters. Compare and contrast these approaches against PID control and explain how that depends on the control application.
Part 2 [40 marks]
The position of an electric DC motor is controlled by varying an input voltage U in the following circuit where current i flows through the resistor R and the inductor L. The motor moment of inertia J=0.12 and the motor viscous friction constant b=0.01. The electromotive force constant and the motor torque constant are equal to K=0.015. The values of the resistance R and inductance L in the motor driving circuit are listed in the coursework class list table file.
R= 3, L=0.9
- a) Write and explain the electric and mechanical equations for this system.
- b) Prove that the system transfer function from U to motor position Y can be written as:
PID control is applied to control the motor position Y and track a desired reference angular position R that you will specify.
- c) Perform a root locus analysis for this system using Matlab software and explain how this can be used for PID control.
- d) Apply the Ziegler Nichols PID control method and a second alternative PID control method for this motor position control problem using Matlab simulations. Explain your implementation of PID tuning. Perform an analysis of controller performance using performance metrics of your own choice. Evaluate the robustness of this controller to external disturbances using numerical simulations.
- e) Provide your conclusions from this simulation analysis.
Part 3 [20 marks]
The control system in question 2 is now discretised.
- a) Use Matlab to determine the closed loop Z-domain transfer functions of the discretised system.
- b) Perform a root locus analysis of the discretised system in the Z domain. Select different values of the sampling time period to evaluate the effect of discretisation on stability.
- c) Apply PID control in discrete time using Matlab simulations with the same sampling time periods as in 3.b. Compare the performance against an equivalent continuous time PID implementation using performance metrics of your own choice.
- d) Provide your conclusions from this simulation analysis.
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