PID Implementation

7/27/2019 PID Implementation

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12/6/04 BAE 3023 1

Advanced Embedded Systems Design

Lecture 14 Implementation of a PID controller

BAE 5030 - 003

Fall 2004

Instructor: Marvin Stone

Biosystems and Agricultural EngineeringOklahoma State University


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Goals for Class Today

Questions over reading / homework (CAN Implementation)

Zigbee and 802.14.5 (Kyle)

PID implementation (Stone)


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Elements of a feedback control system

Review elements and

variables

Gc G2

G3

Error

Manipulated

Variable

D

Controlled

Variableout

+

+

G1

out

-

+

out

Load

in

Setpointset

outout_measured


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)1()1( 232

23

1GGG

GG

GGG

G

c

cset

c

inout

)( _measuredoutsetcGD

21 DGGinout

3_ Goutmeasuredout

Output (out) is readily calculated as a function of:Load (

in) and

Setpoint (set

)

Manipulation is a simple function of the controller TF and error.


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Digital form of a classic feedback controlled system

If sampling rate is fast and holds are employed, this

system approaches the analog system

Gc G2

G3

Error

ManipulatedVariable

D* D

ControlledVariable

out

+

+

G1

out

-

+

out

Load

in

Setpoint

set

out

out_measured

out_measured

*

Computer based controller


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One of the conventional models used to express a PID controller is:

dt

deedteKM d

t

ti

c

0

1

rateDerivitive

rateReset

signalErrore

gainControllerK

onManipulatiM

d

i

c

Time Domain PID Controller Equation

Where:


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Derivitive Form of a PID Controller

A convenient way to implement this equation in a controller is as the

derivative of manipulation known as the velocity form of the equationas shown below:

2

2

dt

ede

dt

deK

dt

dMd

i

c

In a practical system this equation will work well and does not require

any steady-state references, but eliminating the iand

dterm

completely results in:

dtdeK

dtdM c deKdM cor,

This equation has no positional reference and error accumulation is a

problem. Use velocity form only for PI or PID modes.


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Conversion of the DE to a Difference Equation

To begin the conversion of the PID equation to a difference

equation, the equation is multiplied by dt.

dt

ded

edtdeKdM d

i

c

Note that since Mis a differential and ess

is zero, this equation

conveniently applies to the absolute variables as well as the

deviation variables.

For small Dt, the equation can be approximated as:

D

DD

DDD

t

tKm d

i

c


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Representation with Discrete Time Variables

Each of the differences (D) can be expressed as discrete values ofeach of the variables (mand ) at the times 0, 1, and 2 as shownbelow:

t0 t2t1

M

1

2

0

M0 M

1

M2

The equation can be simplified with the assumption that Dtisconstant:

DD

DDDD

t

tKm d

i

c


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Discrete form of PID controller

Replacement of the differences (D) with the discretevariables ( m and ) results in:

DD

D

D 12

21212 )(

t

tKmm d

i

c

D

D 0112

21212 )(

t

tKmm d

i

c

DD

01221212 2)(

t

tKmm d

i

c

Note that D is assumed to be a constant. IfDtvaries, the equationsshould be derived with that in mind.


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Discrete form of PID controller

This equation can be solved for the current manipulation, m2, in terms

of values known at time t2: m

1,e

2, e

1, and e

0.

The other parameters in the equation are constants.

D

D

D

D

01212

211

ttt

tKmm ddd

ic

Where C1,C2, and C3are constants and the current manipulation isexpressed in terms of known values, the current and past errors.

03122112 cccKmm c or,


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Translation of PID Equation into Algorithm

This equation may be translated directly into a computer language, for

example:

m2 = m1 + k*(C1*e2 C2*e1 + C3*e0);

Within a computer program, the current error

is calculated from the current measurement ofthe controlled variable and the setpoint, for example:

e2 = T_setpoint T_measured;

The current manipulation m2 is then computed using the previouscontroller equation, and finally, at the end of the time step, each of thevariables is shifted forward for the next calculation.


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Translation of PID Equation into Algorithm

For example in C, the code might look like:

measure_and_manipulate() //Call once per delta T

begin

T_measured = measure_T(); //Get the measured temperature

e2 = T_setpoint T_measured //Calculate the current error

m2 = m1 + k*(C1*e2 C2*e1 + C3*e0); //Calculate the manipulation

set_manupilation(m2); //Output the manipulatione0 = e1; //Shift the error and manipulation

e1 = e2; //forward one time step

m1= m2;

end;

Note that the time step Dtis controlled by the time required to executethe loop. C1,C2 and C3 are all functions ofDt. The equation willprobably be executed as floats! (Or very special care must be taken

with scaling.


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Assignment

Complete CAN message demo

Turn in course portfolio by 5:00 PM Wednesday Dec.

8th

Documents

PID Implementation