Control Theory

Closed Loop Transfer Functions

Group Task 2

m=1 [kg]c=2 [Ns/m]k=1 [N/m]

Can we now add a P controller and calculate thetransfer function of the closed loop?

(by the way, what’s the transfer function of a P controller?)

General formulas

First example

1

2)(

2

sssp,uT 1)()(,0)( sss SAp,d TTT

cc Ks )(T

BTW – Representation with static characteristics

u = OP

y = z = PVr0

r1

b Control 2

Control 1

Process

z1

SS=8

b and r0 chosen randomly

Second example

)4)(2(

1)(

sssp,uT 1)()(,0)( sss SAp,d TTT

cc Ks )(T

Group Task 1

)3(

1)(

s

sp,uT 0)( sp,dT

cc Ks )(T 5

1)(

1

1)(

ss

ss

S

A

T

T

Find Kc > 0 that makes this control system marginally stable.