The objective of this experiment is to design a position control system for the Quanser Aero system in the 2 DOF configuration. The angular position controller should meet the following specifications:
Download the setup aero file below and fill in the system parameters, control parameters and other necessary values to store in the MATLAB workspace. Use these variables in building Simulink so it is easier for you to put values. Make sure to check your values with TAs before running Simulink.
We will start our controller design by considering first the decoupled system. In this case, the Multiple-Input Multiple-Output (MIMO) system is represented as two separate Single-Input Single-Output (SISO) systems.
The pitch dynamics of the 2D Aero system is a Type 0 system, i.e., no pole at the origin. As such, we will select the PID controller structure for the pitch control design, which will meet the specification of zero steady-state error to a step command input. The yaw dynamics of the 2D Aero system is a Type 1 system, i.e., there is one pole at the origin. As such, we will select the PD controller structure for the yaw control design, which will meet the specification of zero steady-state error to a step command input.
Create a SIMULINK model of the system. (a) Create subsystem blocks representing the plant. Figure 2 shows separate pitch and yaw plants. Note: Plants account for coupling (see Figures 3(a) and 3(b)). (b) Create subsystem blocks representing the decoupled pitch and yaw controllers. Figure 2 shows the input/output structure of these blocks. (c) Using the completed subsystem blocks, finish the diagram of the closed-loop system. Make sure to include pitch and yaw inputs, saturation blocks, and appropriate outputs. Use scopes and To Workspace blocks so that reference, output, and response signals can be tracked. (Make sure to maintain consistency between deg and rad in SIMULINK) (d) Set the sampling time to Fixed-step of step-size 0.002s in Modeling -> Model Settings.
Include a screenshot of the complete SIMULINK model (block diagram). In addition, include the following subsystem block diagram screenshots:
Pitch and Yaw plants
Pitch and Yaw controllers
Mention the final yaw PD gains (Step 3).
Mention the final tuned pitch PID gains (Step 7).
Pitch-only command case: Plot the pitch and yaw data (commanded angles, simulation responses and motor input voltages) for pitch-only command (Step 2) and check if the design specifications were met in pitch.
Yaw-only command case: Plot the pitch and yaw data (commanded angles, simulation responses and motor input voltages) for yaw-only command (Step 3) and check if the design specifications were met in yaw.
Note: It is possible that specifications are not met due to coupling between pitch and yaw dynamics.
Mention the feedforward gain values.
Pitch-only command case: Plot the pitch and yaw data (commanded angles, simulation responses and motor input voltages) for pitch-only command (Step 2) and check if the design specifications were met in pitch.
Yaw-only command case: Plot the pitch and yaw data (commanded angles, simulation responses and motor input voltages) for yaw-only command (Step 3) and check if the design specifications were met in yaw.
How does accounting for the coupling affect the performance of the controller? (a) What happens when you neglect the coupling effect (in simulation)? (b) What is a physical explanation for the coupling effect?
Why a PID controller is used for the pitch and a PD controller for the yaw?
Estimate gain and phase margins of the closed loop systems individually with your pitch and yaw controllers. Hint: Use the margin command in MATLAB. Gain and phase margins