Matlab software for inversion of describing functions

In a reference of the previous work, a new systematic design method for fractional order proportional and derivative (FOPD) controller is proposed for a class of typical second-order plants. Simulation and experimental results in the reference show that, the dynamic performance and robustness with the designed FOPD controller outperforms that with the optimized traditional integer order proportional integral (IOPI) controller at normal speed. Furthermore, it is found that, for the ultra low-speed position tracking with a significant friction effect, the tracking performance using the designed FOPD controller is much better than that using the optimized IOPI controller. However, the reason of this advantage is unclear. In this paper, using the describing function method and Bode plots analysis, the observed advantage of the designed FOPD controller over the optimized IOPI controller, for the nonlinear low-speed position tracking system with friction effect, is explained with the theoretical analysis. This explanation for the priority of the designed FOPD controller is consistently demonstrated by the extended experimental results in this paper.

Fractional order ultra low-speed position servo: Improved performance via describing function analysis

The paper is devoted to such an important problem of piloted aircraft control as an unfavorable aircraft-pilot coupling. Mainly, the so-called Pilot-Induced Oscillations, i.e., long uncontrolled irregular oscillations which may happen due to the controlling surface magnitude and rate limitations when pilot attempts to control the aircraft with the high rate and accuracy. The simulation and in-flight test results of several PIO events are described, and the literature overview of the PIO prevention method is given.

Pilot-Induced Oscillations and Their Prevention

Hidden Oscillations In The Closed-Loop Aircraft-Pilot System And Their Prevention

The purpose of this paper is to present a new systematic procedure for synthesis of nonlinear controllers for single-input multiple-output systems. The procedure is based on several describing function models of the plant, and the nonlinear gains are obtained via an inverse describing function technique. The procedure and associated software are applied to control the bank angle of a cruise missile. The results are compared with a linear controller and another nonlinear controller that was previously reported in the open literature; it is shown that the developed procedure has resulted in a less conservative design (i.e., performance is not sacrificed to assure absolute stability).

Nonlinear Controller Synthesis for Single-Input Multiple-Output Systems with Application to Cruise Missile

A known nonlinear compensator design approach is adapted to allow design of nonlinear lead and/or lag compensators, and a number of MATLAB functions are developed that automate the compensator design procedure. With this design tool, control engineers would be able to rapidly design nonlinear lead and/or lag compensators. An example of a tutorial nature is presented.

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Seyed Reza Mousavi Firdeh

Papers

Design of Nonlinear Lead and/or Lag Compensators