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Assignment Task :

Assignment Details
1.1 Coursework Objectives

A classical control strategy (I-PD) is required for the control of a DC motor: You are expected to:
• Determine the system transfer function
• Design an IPD controller to meet/exceed response requirements from first principles.
• Apply PID tuning rules in SIMULINK to meet/exceed response requirements.
 

1.2 Submission
The assignment submission should include: the report, a MATLAB script file (.m file) containing your calculation data (e.g. calculated gain values) and a SIMULINK file (.slx file) with your overall system (including controller implementation).
All calculations must be presented within the report. The report should include an introduction, results for each task, a discussion of findings, concluding statements and references. For each task, a proper description of the methodology is expected. For example, during block simplification, it is important to outline the process undertaken.
Page Limit 15 A4 Pages (single sided), with a minimum of 11 point font size. Appendices are not allowed.
Assignment must be submitted in accordance with the guidance provided in the assignment document.
*Assignment report along with MATLAB files must be submitted through email ( email to )
*You need to compress all the files into a folder (.zip) and name the folder with your name followed by your UWE ID (example : Sulaiman Al hasani _1805853.zip)
*Your report should be in a PDF format and should include the cover page as a first page followed by safe assign report.
* Your submission will not be accepted in you are not following the above rules
*Any copied or plagiarised part without proper referencing will be awarded ZERO!
*In case of copying from your classmate, both students will be awarded a mark of ZERO!
*Do not leave submission to the very last minute. Always allow time and plan ahead

 

1.3 Marking Scheme
Coursework marks distribution is presented below. Refer to Marking Scheme (last page) for the overall mark scheme, which will be used to grade discussion, introduction and conclusions components of the report, report presentation and referencing, and programs. Additional marks breakdown for calculations is provided in Section 2.

 

Report Marks Allocated

  • Calculations 50%
  • Discussion (mark scheme) 15%
  • Introduction and conclusions (mark scheme) 15%
  • Report presentation and referencing (mark scheme) 10% (total)
  • Programs 10%
     

2 Assignment Task
2.1 System Modelling

A common actuator in control systems is the DC motor. It directly provides rotary motion and, coupled with mechanical load such as wheels or drums and cables, can provide translational motion. The electric circuit of the armature and the free-body diagram of the rotor are shown in the following figure:

Mechanical Load

 

 

In the figure above, v is the armature voltage, i is the armature current, e is the back electromotive force (emf), R is the armature resistance, L is the armature inductance and ω is the shaft speed of the motor; J is the equivalent inertia on the motor shaft, T is the driving torque generated by the motor, and TL is the resistive torque from the load. It is known that e

Motor

 

 

In general, the torque generated by a DC motor is proportional to the armature current (i) and the strength of the magnetic field. Here, we assume that the magnetic field is constant and, therefore, the motor torque is proportional to only the armature current i by a constant factor Kt as shown in the equation below. This is referred to as an armature-controlled motor. For a small motor, the armature inductance is small, ieL ≈ 0, and hence can be neglected.
Also, at the start of the motor, e = Keω≈0.Your task is to develop the controller algorithms to control the rotation of the load. That is, to control the angular position of the DC motor with certain performance parameters.
First, For system modelling, derive the transfer function G(s) that represent the relationship between the angular velocity ω(s) and input Torque (s)). Then find the transfer function that represent the relationship between the angular position (s) and input Torque(s)).

Open Loop

 

 

2.2 Controller Design
An IPD Controller can be incorporated into the closed loop model (Figure 2.2) in order to meet a set of time response related requirements (e.g. overshoot).

IPD Control

 

 

2.2.1 System closed loop equivalent form
Determine the simplified closed loop equivalent form of the overall system block diagram presented in Figure 2.2.


2.3 Controller requirements
The I-PD controller is required to meet or exceed the following response characteristics for a step
change in demand position:
1) Maximum rise time tr of 0.2s.
2) Overshoot Mp less than 7%.
3) Settling time (error ≤ 5%) Ts less than 0.35s.
4) Steady-state error of 0 for step.

 

2.3.1 Determining gains
Use standard transfer functions or pole position methods to calculate the proportional (Kp), integral (Ki) and derivative (Kd) IPD controller gains for the overall system.

  • Verify the gains calculated by implementing the system in Simulink.
  • Discuss any trade-offs for exceeding the response requirements presented in Section 2.3.

 

 

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