Describing function analysis using MATLAB and Simulink

This article uses computer-aided design tools to develop a describing function analysis of a pendulum clock. We design the escapement as a control system that allows the pendulum to provide the required time keeping and, at the same time, add enough energy to the pendulum to overcome the damping caused by friction. We use analysis tools in the MATLAB Control System Toolbox to accomplish the design and analysis. A by-product of our analysis is a simple MATLAB/Simulink model and a script that generates describing functions for any arbitrary nonlinear system (including systems with multiple nonlinearities and with frequency-dependent describing functions). We also develop a Simulink model of the clock to verify the results of the analysis. The analysis described here uses some object-oriented programming features of MATLAB.