MEC2342: In this project you will be exposed to implement control synthesis methods using computer simulation: Control Engineering, Assignment, UOG, Singapore

 Project Scope

In this project you will be exposed to implement control synthesis methods using computer simulation. Starting from a pitch dynamic model, you will get to:

1) Analyse the 1DoF model of the system (plant) and its open-loop response to an impulse and step input. Describe the steady state and dynamic responses of systems in the time domain.

2) Analyse the stability of the control system using a pole-zero map, Rout’s Stability criterion and Nyquist stability criterion.

3) Design a controller to derive desired properties in the output response. Determine what kind of controller is necessary: Proportional, Proportional Integral (PI) or Proportional-Integral Derivative (PID). Describe how the properties of the PID feedback controller impact the output response.

4) Design the controller using the Root-Locus method, tune it through iterations, and propose possible solutions.

5) Evaluate the design solutions against the design’s specifications using time-domain and frequency-domain techniques.

6) Evaluate the controller’s energy consumption.

7) When inserting a constraint or limit on the control action signal, evaluate the saturation effect.

8) Analyse the multiple-input and multiple-output (MIMO) 2DoF helicopter model and explain the coupling effect when implementing both the pitch 1DoF model system and the given yaw controller system.

You can work in groups of 4 to complete the tasks defined in Section 4.

Project Tasks

Task 1 – Modelling and Transfer function representation of the system.

1) Starting from the free body diagram of the 2DOF helicopter system derive the equations of motion (EOM) Eq. 1 and Eq. 2. Assume small angle approximation to derive the EOM. Explain with mathematical evidence the implication of the small angle approximation (e.g., linearity).

2) Derive the transfer functions (i.e., 𝐺1(𝑠), 𝐺2(𝑠), 𝐺3(𝑠), 𝐺4(𝑠) ) to obtain the following block diagram, see Figure 3a.

Figure 3a: Block Diagram of the 2DOF helicopter System Model.

1) Analyse the cross-coupling effects by showing the open-loop system response plots for the following three cases:

•  Set the voltage of the yaw motor to zero and apply a step input of 2 volts on the pitch motor.
• Set the voltage of the pitch motor to zero and apply a step input of 5 volts on the yaw motor.
• Apply a step input of 5 volts on the yaw motor and 2 volts on the pitch motor.

2) You are required to summarise all these findings in the report.

Download the files TASK1_Model_2DOF_Helicopter.zip

To test that your model is working, input the four transfer function in the Simulink Model
FILE3_s_2dof_Model_vis.slx and run the MATLAB file named:
FILE2_Model_2DOF_Helicopter_PlotFigures_Simulation_vis.m

You should get step response as in Figure 3b

Figure 3b: Simulation Results of the 2DOF helicopter System Model.

Task 2 – Transfer function and State-space representation.

Using the models from task 1, analyse the open-loop system response of the pitch angle:

Figure 4: Transfer Function of the Pitch Angle Model.

3) Show how the open-loop system response to a step input of 2 volts.

4) Would the open-loop response satisfy the design specifications?

5) Explain how to analyse the stability of the open-loop system.

6) Show how the close-loop system or feedback system performs to a step input of 15 degrees (11 degrees), use a proportional controller set to 1 (unit gain).

7) Would the closed-loop response satisfy the design criteria? Explain your findings.

8) Explain how to analyse the stability of the closed-loop system or feedback system. It is recommended to use Routh’s stability criterion.

9) Create MATLAB scripts to simulate and show the step response of your control system and you are required to summarise all these findings in the report.

Task 3 – Root Locus Approach:

Based on the design specification design a controller using classical control techniques for the closed-loop control system depicted in Figure 5:

10) Design a controller to derive desired properties in the output response. Determine what kind of controller is necessary: Proportional, Proportional-Integral (PI) or ProportionalIntegral Derivative (PID). Describe how the properties of the chosen feedback controller impact the output response.

11) You are required to provide details of the steps taken to design the controller. Use the lecture slides provided.

12) Design the controller using the Root-Locus method, tune it through iterations, and propose possible solutions.

13) Use MATLAB commands to create plots and using the plots explain how the controller is ‘’shaped’’.

14) Explain the characteristics of your controller and how the controller was designed to meet the design specifications.

15) Show how the close-loop system or feedback system performs to a step input of 15 degrees of pitch angle.

16) Would the closed-loop response satisfy the design criteria? If not tune the controller and report your design iterations.

17) Create a Simulink model to simulate and show the step response of your control system. You are required to summarise all these findings in the report.

18) What are the closed loop stability margins? Show both the Nyquist plot and the Bode plot to respond to the question. You may use MATLAB plots to provide your answers.

Figure 5: Closed-Loop Control System of the Pitch Angle System.

Task 4 – Evaluation of Control System

19) Improve the initial or inferior controller by tuning the controller using heuristic techniques.

20) Create a table to report all the iterations by means of comparing against the design specifications.

21) Illustrate the evolution of design iterations using the step response (time domain analysis).

22) Identify trade-offs between design specifications by means of comparing all the design iterations. Explain your findings. Use parallel coordinates or any other appropriate visualisation techniques to compare multiple objectives or specifications, show objectives or specifications are conflicting.

23) Prove or disprove hypothesis 1 and 2 with evidence of your results.

24) You are required to summarise all these findings in the report.

 Task 5 – Evaluation of Energy Consumption & performance in the 2DOF helicopter control system.

25) Implement both the pitch 1DoF model system and the given yaw controller system to control the full 2DOF helicopter, see Figure 6. Note that the controller 𝐾2(𝑠) will be given and the controller 𝐾1(𝑠) will be the one calculated in the previous tasks.

Figure 6: 2DOF helicopter control system

26) Evaluate the controller’s notional cost of energy consumption by computing the following equation:

Create a MATLAB script to compute the 𝑁𝑜𝑡𝑖𝑜𝑛𝑎𝑙 𝐶𝑜𝑠𝑡 𝑜𝑓 𝐸𝑛𝑒𝑟𝑔𝑦 𝐶𝑜𝑛𝑠𝑢𝑚𝑝𝑡𝑖𝑜𝑛,𝐽𝐶. Check the MATLAB function “trapz”, in MATLAB enter ‘’>help trapz’’. This function is used to integrate time domain signals.

27) When inserting a constraint or limit on the control action signal, evaluate the saturation effect. Evaluate once again the notional cost of energy consumption. The response will be evaluated with a series of step inputs and changes. The Simulink file is available in the xSiTe page.

28) Analyse the multiple-input and multiple-output (MIMO) 2DoF helicopter model (See Figure 7) and explain the coupling effect when implementing both the pitch 1DoF model system and the given yaw controller system.

Figure 7: 2DOF helicopter control system with limit on the control action