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