**Subject Code & Title :** ENG742S1 M24344 Control Systems**Assignment Type :** Coursework 1**Aim :** The aim of this assignment is to determine the transfer function of a servo set system, representing a Radar Scanner system using time response techniques and design a velocity feedback controller to achieve the required specifications of the position feedback control system. Root-locus technique will be used to analyse the system performance improved with the introduction of a velocity feedback.**ENG742S1 M24344 Control Systems Coursework 1 – Portsmouth University UK.**

**Assessment Guidelines :**

You will be marked solely on the content of the report. Please make sure that the work you submit is clear, comprehensive and well presented. Presentation that is either untidy, or lacks mathematical precision, will be penalized. Finally, you should read this coursework brief in full so that you are aware of the tasks ahead. In general you should be familiar with time response analysis. You will be required to demonstrate an understanding of the theory of first and second order responses via the results and experimental data provided. You also should be familiar with Root-Locus method. You will use MATLAB as a simulation package to produce time response graphs that will be the basis for your assessment. Your graphs should be well presented (neat, clear and contain all necessary information). It is very important to focus your effort on producing results, interpreting and offering explanations, analysis and conclusions where appropriate.

**ENG742S1 M24344 Control Systems Coursework 1 – Portsmouth University UK.**

**Radar Scanner System :****Introduction:** A company has built a laboratory model of a proposed radar scanner in order to assess its performance prior to building a full-scale version. The scanner system is shown in Figure 1 below:

The servo set representing the Radar Scanner system (supplied by Valeac Company) is shown in Figure 2 below:

The system is the combination of an amplifier, servomotor, gearbox and flywheel, with associated electronics allowing various angular displacements, velocities and accelerations to be monitored. The bock diagram of the servo set system is shown in Figure 3 below:

The system is subjected to a 5 volts step input. The actuator response is recorded in the data set Set 1_1 and the overall system response at the flywheel output is recorded in Set 1_2.

**4.System Identification4.1 Actuator Transfer Function (approximation):**

The actuator is a second order over-damped system. Approximate it to a first order system with a transfer function of the form:

where k is the gain and τ is the time constant.

Having plotted the response of the experimental system, a simulation of a first order system can be attempted with the MATLAB transfer function estimation function (see MATLAB for Control Systems document).

1.Get a graph of the experimental and the simulated responses (superimposed on each other), and comment on your results. Give the following title to your graph: First order (simulated) response superimposed on a second order over-damped system output response (experimental).

2. Compare the experimental and the simulated responses. Comment on your results.

**4.2 Actuator Transfer Function (second order system):**

The actuator is a second order over-damped system. The second order system has a transfer function of the form:

where kss is the steady state gain , ωn is the undamped natural frequency and ζ is the damping ratio.

i) Estimate with MATLAB a second order transfer function for the actuator and plot its step response.

ii)Get a graph of the experimental and the simulated responses (superimposed on each other), and comment on your results. Give the following title to your graph: Second order (simulated) response superimposed on a second order over-damped system output response (experimental).

iii) Compare the experimental and the simulated responses. Comment on your results.

**4.3 Actuator + Shaft + Dish Dynamics: **The shaft and dish combination may be modelled as a second order system. Therefore the servo set system can either be modelled as a fourth order system or an approximated third order model.

A.Get the 3rd order system graph of the experimental and the MATLAB simulated responses (superimposed on each other), and comment on your results. Give the following title to your graph: Third order servo set system (experimental and simulation).

B.Write down the 3rd order Models.

C.Get the 4rd order system graph of the experimental and the simulated responses (superimposed on each other), and comment on your results. Give the following title to your graph: Fourth order servoset system (experimental and simulation).

D.Write down the 4th order Models.

E.Comment on the accuracy of both models.

**5.Unity Feedback. **The company is thinking of damping out the highly oscillatory step response by introducing unity feedback – see Figure 4. However, there is a concern that this may result in an unstable system. Verify that this is indeed the case by simulating in MATLAB the step response of the complete third order system when unity feedback is applied.

Get the graph of the output response for the closed loop unity feedback system. Give the following title to your graph: Unstable system.

**6.Velocity Feedback:** It is suggested that velocity feedback could be used to improve the response of the third order system.

**ENG742S1 M24344 Control Systems Coursework 1 – Portsmouth University UK.**

For the third order model, get the graphs of the output response and comment on the performance of the system (for various values of Kt , e.g. 0.05, 0.1,0.3 and 0.5). Give the following title to your graph: Servo set output response with velocity feedback

**7.Root-locus analysis:** **You are required to:**

I) Determine the poles of the open loop system (3rd order model) and the plot of the poles on the s-plan.

II) Determine the poles of the closed loop unity feedback system (3rd order model) and the plot of the poles on the s-plan.

III) Determine the poles of the closed loop system (3rd order model) with Kt = 0.3 and the plot of the poles on the s-plan.

IV)Obtain the root locus for the servo set system (Third order) with Kt = 0.3

**8.Discussion**

Discuss the effect of the velocity feedback on the system.

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