Combining MATLAB & EXCEL to improve understanding in controls

Control systems are modeled by using differential equations. The same control system can be stable or unstable depending on the input parameters into the system. Stability or lack of stability of a control system can theoretically be determined by solving the control system differential equation(s). The differential equation(s) can be solved numerically. A numerical solution of a differential equation produces numbers. The differential equations can also be solved by classical differential equation techniques. The classical differential equation solution techniques can be supplemented by using Laplace Transform and using the MATLAB software to expedite the Laplace Transform formulations. Damping level(s) in a vibrating system greatly influence the stability level of the system. The influence of damping on the vibration system characteristic is used as the example in this article. It is shown that the system can be stable or unstable depending on the system parameters, namely the system natural frequency, system damping level and the frequency of the external excitation force. The similarity and differences of the EXCEL based numerical solutions and the MATLAB based theoretical solution are discussed. The use of the numerical technique and MATLAB will help students with less than perfect mathematical skills to be able to learn practical control engineering. The use of these techniques eliminates the need for physical labs which will reduce the possibility of Covid-19 virus spreading.