Control Theory

P control [and first order processes] – part II

Last week we ended here…I want to design a control system for the process

using a P controller.

I choose the bias for a reference r=4 and a disturbance d=3: b=1.5.I choose a control gain Kc=3.

What is the steady state error when r->5 and d=3?What is the steady state error when r=4 and d->2?

)(5)(3

10)(5

)(11 tdtutz

dt

tdz

u(t) z(t)P

d(t)r(t)

Group TaskI want to design a control system for the process

using a P controller.

I choose the bias for a reference r=4 and a disturbance d=3: b=1.5.I choose a control gain Kc=3.Assume initially the desired equilibrium is reached.

z(t),u(t) for servo and control problem described on slide nr. 2?Do the same for Kc=300.

)(5)(3

10)(5

)(11 tdtutz

dt

tdz

u(t) z(t)P

d(t)r(t)

Result for servo problem (Kc=3)z(t)

t

Result for servo problem (Kc=3)u(t)

t

Result for servo problem (Kc=300)z(t)

But… u(t) becomes 301.5 already at t=1s !!!

Moreover, no real process is truely first order – see later…

Pre-class assignment

LC

Using P control, find the closed loop equationElaborate on the size of the steady state error

for both servo and control problem!

Disturbance

Manipulated Variable