Model Reference Learning Approach with Predictive PI for Higher … · 2014-06-27 · Parameters . Abstract — In this paper model reference learning approach with predictive PI

Abstract—In this paper model reference learning approach with

predictive PI (PPI) control strategy for higher order has been

introduced. Due to this approach reaching time is minimized in

higher order systems. The proposed control structure is presented and

their performance compared with other PPI control methodologies.

This controller has good tracking performance than other PPI

controllers with minimum reaching time

Keywords— Model Reference control, Predictive PI, Dead Time,

Higher order system

INTRODUCTION

REDICTIVE control is used to control processes with

long dead time. The control performance of proportional-

integral- derivative (PID) controller is limited for long

dead time. When the process has a long dead time then the

performance of the system can be improved by using a

predictor structure. These controllers are known as dead time

compensators (DTC). The prediction can be performed by an

internal simulation of the process inside the controller.

Smith predictor is one of the dead time compensating

methods and they require a model of the process, typically

consisting of a gain, a time constant, and a dead time. The

following process model structure is commonly used for

Smith Predictor,

(1)

i.e., a first order system with static gain Kp, time constant T

and dead time L. Combined with a PI-control algorithm, this

means that they contain five parameters. i.e , PI controller

parameters K and Ti and the process model parameters Kp, T,

and L. These controllers are therefore difficult to tune by

"trial and error" procedures. The advantage of the Predictive

PI controller compared with the other dead time compensating

controllers is that although it also contains five parameters,

only three are adjusted by the operator. i.e., the parameters K,

Ti, and L are determined by the operator.

Dipali Shinde is with AISSMS’s, IOIT, University of Pune, Maharashtra,

India as a Asst. professor in Instrumentation and Control Engineering

Department. (e-mail: [email protected]).

Laxman Waghmare, is with S.R.T.M.University, Nanded, India as a

professor in Instrumentation and Control Engineering Department.

Satish Hamde is with S.R.T.M.University, Nanded, India as a professor in

Instrumentation and Control Engineering Department.

Parameters Kp and T are calculated as functions of the K

and Ti in the following way:

(2)

Where, κ and τ are constants

The predictive controller can be expressed as,

(3)

Where p is the differential operator d/dt.

The open loop system has a pole at s= -1/T.W ith PI control

the closed loop system is of second order. The design criterion

is chosen so that the closed loop system has a double pole at

s= -1/T. This gives the following values of κ and τ

(4)

Equation (3) is simplified as,

(5)

The PPI controller is a compromise between MPC and PID,

and is based on a first-order plus dead-time model of the real

industrial process, which is representative of the majority of

process dynamics in industry. This controller consists of two

parts: a standard PI controller and a predictive term with

which its dynamics depend on the system time delay.PPI

controller has good Robust stability and control performance

than PID . The controller is also suited for processes with

varying dead times. [3]

Fig.1 Structure of Predictive PI controller

Model Reference Learning Approach with

Predictive PI for Higher Order Systems

Dipali Shinde, Laxman Waghmare, and Satish Hamde

P

International Journal of Computer Science and Electronics Engineering (IJCSEE) Volume 2, Issue 1 (2014) ISSN 2320-401X; EISSN 2320-4028

1

Advantages of predictive PI (PPI) control:

Much simpler to use than a Smith Predictor

Uses same structure as a Smith Predictor, but needs no

process model to be specified

It creates its own process model from gain, integral

time

and dead time

Ideal where the dead time is more than double the

dominant time constant

Manually tuned using a simple step response test.

II. DIFFERENT TUNNING METHODOLOGIES

A. Open loop method

The identification techniques based on an open-loop

experiment generally derive the FOPDT transfer function

parameters based on the evaluation of the process step

response (often denoted as the process reaction curve). This

can be done in many ways. Some techniques proposed in the

literature are explained hereafter with the aim of highlighting

their main features.

The tangent method consists of drawing the tangent of the

process response at the inflection point. Then, the process gain

can be determined simply by dividing the steady-state change

in the process output y by the amplitude of the input step A.

Then, the apparent dead time L is determined as the time

interval between the application of the step input and the

intersection of the tangent line with the time axis. Finally, the

value of T +L is determined as the time interval between the

application of the step input and the intersection of the tangent

line with the straight line y = y∞ where y∞ is the final steady

state value of the process output. Alternatively, the value of T

+ L can be determined as the time interval between the

application of the step input and the time when the process

output attains the 63% of its final value y∞. From this value

the time constant T can be trivially calculated by subtracting

the previously estimated value of the time delay L. The

method is sketched in Figure (1). It is worth stressing that the

method is based on the fact that it gives exact results for a true

FOPDT process. The main drawback of this technique is that

it relies on a single point of the reaction curve (i.e., the

inflection point) and that it is very sensible to the

measurement noise. In fact, the measurement noise might

cause large errors in the estimation of the point of inflection

and of the first time derivative of the process output. [4]

K = 1/Kp, Ti = T63%, L = Lp.

B. Analytical method

There are several analytical tuning methods like

1) λ-Tuning

2) The Haalman Method

3) Controller based on the internal model principle.

Where, the controller transfer function is obtained from the

specifications by a direct calculation. Let Gp and Gc be the

transfer functions of the process and the controller. The

closed-loop transfer function obtained with error feedback is

then,

(6)

Solving this equation for Gc we get

(7)

If the closed-loop transfer function Go is specified and Gp

is known, it is thus easy to compute Gc. The key problem is to

find reasonable ways to determine Go based on engineering

specifications of the system. It follows from Equation (7) that

all process poles and zeros are canceled by the controller. This

means that the method cannot be applied when the process has

poorly damped poles and zeros. The method will also give a

poor load disturbance response when slow process poles are

canceled. [5]

III. MODELREFERENCE LEARNING APPROACH WITH PPI

Fig.2. Block diagram of model reference learning approach with

predictive PI control

The proposed control algorithm basically consist of two

stages

A. Design of predictive PI control

Identify the FOPDT (First order plus dead time) model

FOPDT (First order plus dead time) Systems.The great

majority of PID tuning rules actually assume that a FOPDT

model of the process is available, namely the process is

described by the following transfer function

Where, K is the estimated gain, T is the estimated time

constant and L is the estimated (apparent) dead-time. This is

motivated by the fact that many processes can be described

effectively by this dynamics and, most of all, that this suits

well with the simple structure of a PID controller. Different

methods have been therefore proposed in the literature to

estimate the three parameters by performing a simple

experiment on the plant. They are typically based either on an

open-loop step response or on a closed-loop relay feedback

experiment.

Frequency response based method. Consider the frequency

response of a first-order model

The ultimate gain Kc at the crossover frequency ωc is

actually the first intersection of Nyquist plot with the negative


2

part of the real axis, i.e.The ultimate gain Kc at the crossover

frequency ωc is actually the first intersection of Nyquist plot

with the negative part of the real axis, i.e.,

(8)

Where k is the steady-state value or DC gain of the system

which can directly be evaluated from the given transfer

function.Define two variables χ1 = L and χ2 = T satisfying

(9)

The Jacobian matrix is that

So, (x1, x2) can be solved using any quasi-Newton

algorithm.

In transfer function based method, consider the first order

model with delay given by .Taking

the first and second order derivatives of with respect to

s, one can immediate find that,

,

Evaluating the values at s=0 yields

Where, Tar is also referred to as the average residence time.

From the former equation, one has L=Tar-T. Again the DC

gain 𝑘 can be evaluated from Gn(0). If the transfer function of

the plant model is known, use the actual G(s) to replace Gn(s)

so as to identify the parameters of the equivalent first-order

plus delay model. This method may not be suitable for

systems with unknown mathematical models. In the automatic

tunning techniques, the frequency based method is more

useful. After identifying parameters such as process gain, time

constant and dead time from actual plant model (Higher

order/ Linear/ Nonlinear) and tune the control setting

parameters such as proportional gain and integral time.[1]

Kp = 0.5*L

Ti = (1.5 – γ)*L

B. Design of model reference learning approach

Define switching surface

Here, (10)

Consider delay free first order plant model which is given

as

(11)

Differential equation of plant model

(12)

Taking the derivative of switching surface

(13)

From equation (18), we can write

Overall control action can be written as,

We can write,

[21]

IV. EXAMPLE

Following parameter values are consider Higher order

process model

Reference model is

Here,

Identified delay free first order plant model

(Process Gain) K= 0.4167, (Time Constant) T= 2.3049 sec

& (Dead Time) L= 0.7882 sec

Parameters involved in reaching law are


3

Control Settings of predictive PI are,

Kp (Proportional gain) = 0.5*L

Ti (Integral Time) = (1.5 – γ)*L

Choose value of γ = 0.5 [1]

The results of the simulations are presented in Figs.3-5 .

The figures show responses to a set-point change from 10 to

15 at time t = 50. The design goal for MRACPPI, Analytical

tuning method (Astrom) and PPI (Hagglund ) controller has

been to obtain fast robust control without any overshoot. Figs.8-10 clearly demonstrate that the MRACPPI controller is

superior to the another two controller for these dead-time

dominated processes of higher order.

V. SIMULATION RESULTS

Fig.3 Process output of model reference learning approach with

predictive PI control

Fig. 4 Comparison of MRACPPI and Analytical tuning method

Fig. 5 Comparison of MRAC PPI , Analytical tuning, PPI (Proposed

by Hagglund) method

VI. CONCLUSION

In this paper MRAC with Predictive PI control strategy for

higher order system have been introduced. Because of the

combined control action reaching time in set point tracking

response is minimized. In model reference control, PI type

switching surface is employed with exponential reaching law

for fast action purpose, while in PPI control method, Integral

– Proportional type control structure is used for eliminating

the effect of proportional kick off problem and tuning

procedure is simple based on process reaction curve method.

Control Settings of predictive PI are taken, Kp (Proportional

gain) = 0.5*L, Ti (Integral Time) = (1.5 – γ)*L and γ = 0.5.

Here, proposed control strategy is tested on process models

are delay dominant models, higher order plant. The proposed

control structure is presented and their performance compared

with various PPI control methodologies. Simulated results

show excellent tracking performance than other PPI

controllers with minimum reaching time and less oscillations.

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Dipali Shinde born in 1980, received her master degree from Shri

Ramananded Tirth Marathwada University, Nanded in 2004.

Professor in the department of instrumentation and control at AISSMS’s,

IOIT, University of Pune, Maharashtra, India. Her research interests include

Predictive control, Process Dynamics and Control and Industrial automation.

Laxman Waghmare Professor in the department of Instrumentation

Engineering at S.G.G.E&Tech, S.R.T.M.U, Nanded, Maharashtra, India.

His research interests include Model Predictive Control, Neural Network

and Advance process control.

Satish Hamde Professor in the department of Instrumentation Engineering at

S.G.G.E&Tech, S.R.T.M.U, Nanded, Maharashtra, India.

His research interests include Advance process control, Automation,

Biomedical Instrumentation.


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Model Reference Learning Approach with Predictive PI for Higher … · 2014-06-27 · Parameters . Abstract — In this paper model reference learning approach with predictive PI