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一种基于DMC的新型预测PID控制器及其整定

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本文提出一种基于动态矩阵控制(DMC)算法预测特性的新型PID控制方法.在考虑将来的输出期望偏差罚函数最小的前提下,由DMC计算出控制变量的值.继而构造基于DMC的预估器用以预测将来时刻的系统输出.根据将来时刻的多步预测偏差,PID控制器产生当前时刻的实际控制增量.文中也给出了基于DMC的预估器及PID控制器的参数整定方法.仿真结果表明,与常规的PID控制和DMC控制相比,所提方法具有良好的控制性能,扰动抑制尤其优良.

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控制理论与应用

Control

Theory&Applications

No．12

v01．27

第27卷第12期

2010年12月

Dec．2010

Alrtide

ID：1000-8152(2010)12—1743—0r7

_predictivePID controller

and

novel DMC—based

^itstuning

LUOYun—huil，一，LIU

Leil，ZHANG

Xu-guanga

Hong—bel，JIA

ofControlScience and

(1。School

Engineering，ShandongUniversity,Jinan Shandong250061，China；

Instituteof

2．School of

Chemical and Environmental

Light

3．School of Electronic InformationandControl

Engineering．Shandong

Engineering，Shandong

Ligllt Industry，Jinan Shandong 250353，China；

lrmtimte of

Lightindusu'y,Jinan Shandong 250353，China)

Abstract：Tllis

novel PDcontrol scheme

with

basedon

matrix

future

paperproposes

equipped

predictive property

dynamic

expected

the

variable

through minimizing

a COSt function

manipulated

control(DMC)algorithm．DMC computes

errors．Next。a DMC．based_predictoris constructed

tlle

values at thefuture time instant．1．tle

output predicted

predict

future errors are used in

PIDcontroller to

theactual centrelactions．ne DMC．based

witII

and thePIDcon=

predictor

generate

troller arc

well tuned to

the

the conventional PIDand DMCcontr01．simulation

rejection performance．

provide

design parameters．Compared

resultsdemonstratethe better

in disturbance

output responses，particularly

control；Pm

matrix

control(DMC)；controller tuning

Keywords：predictive

CLCnumber：1’王，273

control；dynamic

Document code：A

一种基于DMC的新型预测PID控制器及其整定

罗运辉1,2，刘红波1，贾磊1，张绪光3

(1．山东大学控制科学与工程学院，山东济南250061；

2．山东轻工业学院轻化与环境工程学院。山东济南250353；3．山东轻工业学院电子信息与控制工程学院。山东济南250353)

摘要：本文提出一种基于动态矩阵控制(DMC)算法预测特性的新型PID控制方法。在考虑将来的输出期望偏差罚

函数最小的前提下，由DMC计算出控制变量的值．继而构造基于DMC的预估器用以预测将来时刻的系统输出．根

据将来时刻的多步预测偏差，PID控．制器产生当前时刻的实际控制增鼋．文中也给出了基于DMC的预估器及PID控

制器的参数整定方法．仿真结果表明，与常规的PID控制和DMC控制相比，所提方法具有良好的控制性能，扰动抑制

尤其优良．

关键词：预测控制：比例一积分—微分控制；动态矩阵控制；控制器整定

call

used

practice。

Introduction

bustness

not

they

extensively

_{control，the}PID

Predictive centrel

is one of the advanced

In industrial

control

algorithm

that have had

process

widely

algo—

control

rithmis the most

usedeven

up^to

strategies

significant impact

the

percentages．

the

industrial contr01．It

elror values of

ref-

algorithm ^is

Theconventional PID

predicts

simple，and easily

erence

and the

SO as to calculate

process output

with three

input

implemented．Although only

tuning pa-

the actual

variable．Due to

a1．

manipulated

predictive

differentiating

meets the con—

rameters(proportional，integrating，and

are

internal modelbased and Can

_{coefficients)，the}PID control

generally

gorithms

intrinsically

Can

essentially

dead

times of

process．they

the

welltll．However

^trolperformancespecifications

very

compensate

ever in case of

dead

caseof

dead time in the

model。the

system

provide goodperformance

long

output response

time when_consideringthe same

process

combination ofPID and

will be slower than that with no dead

controller

timel61．Consequently,the

pre．

obtain their botll

dictive

^controlmaybe

PID

ofdead time

properties：good

tuning

parameters

parame—

and

PID，and

tersl2,31．The

easily

presence

performance

impairs closed．100p

are some dead time

time

characteristics and eas-

control[7“101．In

dead

good

compensation

performancell,4，51．There

compen-

as Smith

call

predictor'which

because of their ro-

ilv constraints

tackling

sation

predictive

strategies[51，such

dead time

long

case

systems containing

significantly

provide good performances．But

Received date：2010-05—0r7：Revised date：2010—07一03．

in the for

Foundation

found

and

scientists of

Shandong Province(2007BS01009)．

item：Supported

part by

bounty

outstanding

middle—age

young

万方数据

V01．27

1744

Control

Theory&Applications

of no model

Fig．1．In case

nominal

mismatching，the

faster control

can be achieved with

performance

than

pre·

dictive control

with PID

model is same as the actual

model，that is‰ o(s)=

contr01．Also

case

of known future

is to

the future

reference

control

trajectory predictive

predictor

provide

夕m(s)，Lm=L．ne

utilize

better

value ahead ofthe dead time L．Ifwe^can

it is

output

future _ormore _errorvalues it

several

provides

tracking properties．Nevertheless

difficult to introduce

results

advanced control

also work

the

inthe better

maybe

algorithms

P1D

practice，as

algorithms

well，and gen—

process output performance．

control

Call be solved with them．In re．

erally

cent

problems

some workon

PID has been inves—

predictive

years

new _predictivePID control

tigated．Miller

law which is

proposed

mathematically equivalent

generalized

weighting

state

predictive control(GPC)with

steady

term[7，81．Tllle idea of

PID controllers was

predictive

initiated

Katebi and Moradi0l】and

systematically

utilized the

knowl．

future

Johnson and

MoradiB01．They

of the reference and

based on the _pro—

and tune PID

quality

Smith

block

diagram

edge

cess

prediction

Fig．1

predictor

the control

modelto

improve

PID controller considers

it can

predictive

predicted

faster

provide

controllers．E Arousi

PI control

and

applied

proposed

algorithms

valueofthe error

signal．Therefore

to an

with

equipped

predictive properties

than the traditional PID controller in case

performance

dead

first order model

aperiodic process approximated by

^{with dead time[12】．All these methodsneed to}design

ofthe

time．An extension

PID

long

predictive

controlleris when a series of the

taken

error values

series of PID _{controllers，and}the control structures are

predicted

are

also

are

into

controller

calcu-

account，the

outputs

very complex．

lated from the difference of the

reference

sig—

TIlis

novel PID control scheme

based on

predicted

values ofthe

paper provides

with

hal values and the

signal

output

predicted

equipped

matrix

predictive property

dynamic

horizon．

provides

the

given prediction

control(DMC)algorithm．DMC computes

Dueto

the

variable

cost func—

DMCcall

val-

predictive

output

manipulated

through minimizing

ues ahead of

value

tion

future errors．Next

DMC·

the current

test

considering expected

output

using

step

based

constructed

the

model，we can constructa

block

based on the DMC

predictor^is

predictor

ofthe

predict

output^val—

ues of

times．硼1e

future errors

gather

future

structure

proposed

diagram

predicted

principle．The

the actualcontrol vari-

and thePID_controller

are tuned to

shown

into

PDcontroller to

that we

employee descrip-

produce

Fig．2．Note

able．The DMC—based

tion in

discrete

the

predictor

form．Here芭(％+引七)denotes

with

value ofthe error

ahead over the

predicted

signal ⁱstep

two．degree-of-freedom(2DOF)form

the suitable

current time

the reference

design parameters．11le appropn-

control

provide

ate

^ofk．r(k+iI七)is

signal，

can

the

provide good

perfor-

tuning parameters

and雪(尼+{I七)is

predicted output signal

step

manceand

robustness．

ahead over the current time of

high

k．(For

simplicity,in

will be omit-

the rest

the current time mark k

_predictivePIDcontrol

paper

in the

Proposed

ted

for all

values．)And

expressions

predicted

2．1

Controlstructure

is the

predictive output

i=1，2，，M，where

the

has

the

predicting

Smith

property

predictor

time

horizon．The error

factors is

weighting

presented

sumofthe

which ahead ofthe actual

process．So

output response

the controller can excited

the

with伽t(i=1，2，，M)．e(k)denotesthe

the control action ahead of

errors at the current time k．ne

weighted predictive

controller needs all

captured by Fig．1。

system output．The principle

model

in advance

of an

operation

predic-

which shows

go(s)e—L5 containing

given by

process

tion toeliminate the error andthe

oscillation of the out．

dead time L．The controller

ge(S)，usually

loop involving

gm0(S)e—L4。．

with

there is aninternal

error is

not

PID

put responses．Namely,the

the error in

form，and

model_{representation}

predicted

only

control

but also the difference

9m(s)2

period

and the reference

output

process

The

on锄internal modeIis shown in

betweenthe

based

model

at the

input

predictor

万方数据

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一种基于DMC的新型预测PID控制器及其整定

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