Assignment Details
1.1 Coursework Objectives
A classical control strategy (I-PD) is required for the control of a single axis camera: You are expected to:
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.
( with a minimum of 11 point font size. Appendices are not allowed.
Submission deadline: 2pm (at the latest), Thursday, 20/04/17
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 Tasks
2.1 System Modelling
A gimballed surveillance camera is mounted to a fixed location with the ability to move in a single axis. A video example of a single axis camera gimbal can be found here https://vimeo.com/22670438
Your task is to develop the controller algorithms to enable the operator of the gimballed camera to track an object of interest. That is, to control the angular position of the camera with certain performance parameters.
The single axis gimbal mechanism is driven by a servomotor which provides a torque τ. The torque is applied to the gimbal mechanism which comprises of:
An Inertia of the rotor and associated platform parts including the camera J
A viscous damping effect D arising from bearing friction etc.
Thus, the mechanism can be represented as a differential equation relating input Torque and output angle θ representing the angular position of the gimballed camera.
Τ is the input torque provided by the servomotor (Nm)
J is the combined Inertia of the moving parts (Kg m2)
D is the combined viscous damping (Kg m2/s )
θ Camera directional angle (rad)
ω is the camera angular velocity (rad/s)
produce a Laplace transfer function for the system relating output speed ω to input Torque
(Calculations 5 marks)
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).
Figure 2.2: Overall System Block Diagram with IPD Control Configuration
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.
(Calculations – 10 marks)
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:
overshoot ≤ 10%
95% settling time ≤ 2:5 seconds
rise time ≤1 seconds
Given the system specification is:
J = 0.2 Kgm2
D =0.7 Kgm2/s
Kt = 1.6 V/rad
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 presented in Figure 2.2.
Verify the gains calculated by implementing the system in Simulink.
Discuss any trade-offs for exceeding the response requirements presented in Section 2.3.
(Calculations – 20 marks)
2.4 Trial-error rules for PID tuning — Ziegler-Nichols approaches
This section is used to demonstrate your ability to use the course knowledge to learn to use a new technique. Assumingly you have got a job in a control engineering company, your manages have asked to take the following work
Research the literature and find out about manual tuning rules such as the Ziegler-Nichols technique. Tuning rules such as Ziegler-Nichols are difficult to implement on I-PD controller configurations. Convert your system to a PID controller configuration and apply a suitable tuning process (e.g. Ziegler-Nichols tuning rules) in order to meet/exceed the response characteristics outlined in Section 2.3. You should give a concise overview of PID tuning methods in this section and demonstrate the designed control system by Simulink.
(Calculations 15 marks)
