MEC2342: Modelling and Transfer function representation of the system: Control Engineering, Assignment, UOG, Singapore

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.