2.22 a. Linearized models of nonlinear systems are commonly used in model-based

Question

2.22 a. Linearized models of nonlinear systems are commonly used in model-based control of processes. What is the main assumption that is made in using a linearized model to represent a nonlinear system? b. A three-phase induction motor is used to drive a centrifugal pump for incompressible fluids. To reduce misalignment and associated problems such as vibration, noise, and wear, a flexible coupling is used for connecting the motor shaft to the pump shaft. A schematic representation of the system is shown in Figure

Explanation / Answer

1. for nolinear system can be liniearised at any operating by using partial derivative given non linear given experssion with single input variable and keeping remaining variables as constant.

2.state model of above system can be done by following procedure

it is given Q as output and Tm as input

lets take p and m as two state variables

we know that

Jmd(m)/dt=Tm-TL+bmm .................eq1    where TL is net load to motor

TL=bpp+kTm assuming there is no troque requried to pump water

so eq1 becomes

Jmd(m)/dt=Tm-bpp+kTm+bmm.............eq2

if we first order dynamic equation to pump

Jpd(p)/dt=kTm+bpp........................eq3

form equation 1,2,3

we can write state equation as below

[dm dp] =[bm bp : 0 bp][m p] +[k k][Tm]

Q=[0 1][m p]

A=[bm bp : 0 bp]

B=[k k]

C=[0 1]

D=0

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