Design of a PID-Lead Compensator for a Twin Rotor Aerodynamic System (TRAS)

This paper deals with a Twin Rotor Aerodynamic System (TRAS). It is a Multi-Input Multi-Output (MIMO) system with high crosscoupling between its two channels. It proposes a hybrid design procedure that combines frequency response and root locus approaches. The proposed controller is designated as PID-Lead Compensator (PIDLC); the PID controller was designed in previous work using frequency response design specifications, while the lead compensator is proposed in this paper and is designed using the root locus method. A general explicit formula for angle computations in any of the four quadrants is also given. The lead compensator is designed by shifting the dominant closed-loop poles slightly to the left in the s-plane. This has the effect of enhancing the relative stability of the closed-loop system by eliminating the oscillation in its transient part but at the expense of greater rise time. However, for some applications, long rise time may be an allowable price to get rid of undesired oscillation. To demonstrate the proposed hybrid controller's performance numerically, a new performance index, designated by Integral Reciprocal Time Absolute Error (IRTAE), is defined as a figure to measure the oscillation of the response in its transient part. The proposed controller enhances this performance index by 0.6771%. Although the relative enhancement of the performance index is small, it contributes to eliminating the oscillation of the response in its transient part. Simulation results are performed on the MATLAB/Simulink environment.