What is system dynamics & controls competency?

Dynamic systems are all pervasive. Physical phenomena that can be formulated using ordinary differential equations have a wonderful quality of commonality between them. As a consequence, system dynamic competency may not get restricted by a specific physical domain; be it mechanical, electrical or even economics & finance! The respective domain knowledge is necessarily required to derive the governing ODE of the physical phenomenon but once it’s achieved, the discerning eye of an analyst should be able to establish an equivalence between them.

All this is possible because of the essential form of an ODE which defines the relationship between the rate of change of a physical parameter which is being evaluated, the present state of that parameter & a time dependent inducing signal. This inducing signal can be a combination of an actuating signal & a disturbance signal.

Now this is where the control system competency steps in. The motivation behind modelling, simulating & analyzing any dynamic physical system is to get a desired parametric output from it & control logic development is all about minimizing the error by producing the necessary actuating signal. This becomes challenging due to the unknown mathematical model of the disturbance force!

Solving ODEs

Once the governing ODE of a physical system has been derived using the basic principles pertaining to the relevant domain, the obvious next step would be to obtain a time dependent function of the desired parameter by solving the ODE.

It’s known by experience that the lesser mathematicians amongst us dread the sight of ODEs! This apprehension is further accentuated if the system has multiple parameters (akin to a multiple degrees of freedom system in multi body dynamics domain) to be accounted for, which is usually the case with real life systems. The same can be attributed to the intricate conventional methods of solving the non-homogenous ODEs (that have inducing signal terms) like the method of undetermined coefficients & variation of parameters. On top of this, in the case of a multi variable system, extensive linear algebra concepts involving matrices, determinants, eigenvalues & eigenvectors also need to be applied to get the solution. Therefore, if given a choice, one would prefer solving an algebraic equation than a differential equation.

System Dynamics and Controls

Sameer Gupta

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System Dynamics and Controls

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