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The Quanser VTOL rig is a single degree-of-freedom system which simulates the problem of pitch angle control in flight dynamics

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The Quanser VTOL rig is a single degree-of-freedom system which simulates the problem of pitch angle control in flight dynamics. It consists of a motor-driven propeller attached to a pivoted beam with a counterbalance. The input to the system is the motor current, Im¬ and the output is the pitch angle, ?.

 

Figure 1. Free Body Diagram of VTOL rig

A transfer function model, G(s) of the system was derived previously:

                 (1)

 

Where, θ is the pitch angle, J is the moment of inertia about the pitch axis, b is the viscous damping constant, k is the stiffness, kt is the thrust current-torque constant and Im¬ is the motor current.

 

The parameters of the system are given in Table 1.

 

Table 1. Parameter values of VTOL system

J              As stated in Appendix    kgm2

b             4.3?10-3               Ns/rad

k              0.108     N/m

kt            18.3?10-3            Nm/A

 

It was determined that a proportional controller for the VTOL system led to too little damping in the system, resulting in excessing overshoot and oscillation. Further, the system had a steady state error in response to a step change in the pitch angle setpoint. In this assignment you are required to design a full PID controller in order to achieve the performance specifications of the system.

 

Performance Specification

 

The controller should yield zero steady state error in response to a step input. Further the controller should be designed to satisfy the peak time and percentage overshoot specifications individually assigned in the Appendix.

 

Control Design

It was previously determined that a proportional controller for the VTOL system led to too little damping in the system, resulting in excessing overshoot and oscillation. Further, the system had a steady state error in response to a step change in the pitch angle setpoint. In this assignment you are required to design a full PID controller in order to achieve the performance specifications of the system. You should use root locus analysis to select the values of the P, I and D gains. Specifically, the following steps should be followed:

1. Determine the required closed loop pole locations from the transient performance specification (i.e. peak time and percentage overshoot requirements).

2. Using MATLAB, plot the root locus plot for the VTOL transfer function and show that the transient performance criteria cannot be met by proportional control.

3. The transient performance can be improved by adding derivative action – this is achieved by adding a zero to the controller. I.e. the controller transfer function becomes:

     (2)

Using the root locus plot determine the required value of z (following the method outlined in Lecture 7)

4. Once, z has been determined, use MATLAB to plot the root locus for:

      (3)

Check that the desired closed loop pole locations (calculated in step 1) are on the new root locus plot (and hence the transient performance specifications satisfied).

5. Add PI control by adding a pole to the controller at the origin and by adding another zero to the controller which is negative but close to the origin (as described in the lecture notes).

6. Draw the root locus plot for the full PID control system, and hence determine the controller gain, K, which best satisfies the control design specification.

 

7. Using MATLAB determine the closed loop transfer function of the PID controller VTOL system (Define the controller transfer function and use the ‘feedback command) and then simulate the step response of the system. Check if the performance specifications have been satisfied.

 

 

Report

You should write a report of the control design process outlined above. Your report should include the following sections:

?             Introduction – this can be taken from the Introduction given in this handout.

?             Specification – state the required performance of the control system in your case.

?             Control Design – describe the control design process (steps 1-5 above).

?             Simulation – present and discuss the results of the simulated step response of the closed-loop PID system. Have the performance specifications been met? What is the settling time like? Would you recommend any further actions to improve performance (You are not required to carry out any additional steps and it is fine if the specification is not satisfied – just describe how it could potentially be improved).

?             Conclusions – Briefly conclude whether the control design has been successful according to the simulation. Also briefly outline the limitations of the simulation (does good simulated performance guarantee good performance on the real plant? why/why not?)

Appendix

Individually Assigned Parameters

Individual Parameters are in an Excel spreadsheet on the Moodle page.

Please ensure you have values assigned to you.