The work describes the design of a proportional and derivative (PD) controller for a pitch rate control system for a fighter aircraft. The root locus method is used to determine the locus of the roots of the characteristic equation, and Matlab’s sisotool is used to choose the gain k that maximizes the damping when the natural frequency is over 2. For the PD controller, the gain k is moved along the trajectory of the roots to find the best damping possible. The document also includes Matlab code, figures, and a procedure to open the files and work with them.
The document explains the root locus method and how it is used for the design and analysis of feedback control systems. It also introduces Matlab’s sisotool, which allows designers to create and modify controllers, compensators, and filters and visualize the frequency response of the system.
Problem: The pitch rate control system for a fighter aircraft at 10.000 m and Mach 0.9 is represented by a transfer function. The task is to find the gain k that maximizes the damping when the natural frequency is over 2 for a proportional controller and a PD controller.
Solution: For the proportional controller, the root locus method and Matlab’s sisotool are used to find the gain k that maximizes the damping when the natural frequency is over 2. For the PD controller, the same procedure is followed, but the gain k is moved along the trajectory of the roots to find the best damping possible. Matlab code, figures, and a procedure to open the files and work with them are provided.
References: The document cites two references: [1] Matlab’s Control System Designer App and [2] Modern Control Dorf-Bishop 10 ed.pdf.
