Question

Explain why modelling is an important tool for designing control systems. Briefly describe a typical design procedure for control systems which employs modeling.

Answer 1

Modelling of any physical system is a process of converting a system into control system  by set of techniques like differential equation , laplace transformation to generate transfer function and state space model. Any electrical or mechanical system can be analysed by such techniques that include initial conditions as well as behavior of system i e impulse response to obtain governing parameter variation like current , voltage , displacement , velocity etc with respect to time . This also help in modifying response of system with help of controller.

One of procedure i e explained here is for modelling control system is differential equation model whose example is mass spring system as below.

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Modeling of any physical system is a process of converting a system into control system by set of techniques like differential equation, Laplace transformation to generate transfer function and state space model. Any electrical or mechanical system can be analysed by such techniques that include initial conditions as well as behavior of system i e impulse response to obtain governing parameter variation like current, voltage, displacement, velocity etc with respect to time. This also help in modifying response of system with help of controller. One of procedure i.e explained here is for modeling control system is differential equation model whose example is mass spring system as below. set displacement is x(t) then velocity = d/dt x(t) acceleration = d^2 x/dt^2 Applying Free body diagram equation F - kx + Bv = ma m d^2 x/dt^2 + B dx/dt + kx = F(t) This is second order differential equation.