Control Theory - Control-Intro PPT

7/29/2019 Control Theory - Control-Intro PPT

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Copyright 1998, Dr. Piero P. Bonissone, All Rights Reserved

Control Theor

Open Loop

Plant Characteristics

Linearity

Linear or State variable repr.

State variable repr.

Transfer Function (observable & controllable part): Y(s)/U(s)

Non Linear

State Variable repr.

Linear Approximation (Linerarization at operational points,

Describing Function, etc)

PlantU(t) Y(t)

X AX BU Y CX DU= + = +

( , ) ( , )X f X U Y g X U= =


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Control Theor

Time

Time Invariance (fixed coefficients)

Time Variance (dynamic coefficients)

Granularity

lumped parameters (linear differential equations) distributed parameters (partial differential equations)

Number of Inputs and Outputs

SISO, SIMO, MISO, MIMO

( ( ), ( ), ) ( ( ), ( ), )X f X t U t t Y g X t U t t= =


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Control Theor

Closed Loop (Output feedback)

Bang-Bang Control

E = SP - YU = Sign(E) orU = Sign(E+/- 1/2gap)

gap

Issues:

Limit Cycles and Overshooting

Gap reduces cycling frequency

PlantU(t) Y(t)ControllerSP+

-

E

E

U


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Control Theor


Proportional Control

KP = Proportional Gain (to control rise time)

M = Manual reset

Issues: Offset Error (SSE)

E = SP - Y

U K E M P= +


-

E

E

M

UKP

1


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Control Theor


Proportional Integral (PI) Control

E = SP - YEdtKEKU IP +=

KP = Proportional Gain (to control rise time)KI = Integral Gain (to control SSE)

M = Manual reset

Issues: Slow in correcting SSE


-

E

E

U

E ControlSurface


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Control Theor



-

E

Proportional Integral Derivative (PID) Control

E = SP - Y

dt

dEKEdtKEKU DIP ++=

KP = Proportional Gain (to control rise time)KI = Integral Gain (to control SSE)

KD = Derivate Gain (to anticipate error)

Issues: Pure Derivative term not realizable (non-causal)


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Control Theor

dt

dEKEdtKEKU DIP ++=

Issues: Pure Derivative term not realizable (non-causal)

Usually solved by placing a pole with large negative value (-A):

U s

E sK

T sT s

KT s

Ts

s A

I

D

I

D

( )

( )( )

( )

= + +

+ ++

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Control Theory - Control-Intro PPT