# Fuzzy Coordinated PI Controller: Application to  the Real-Time Pressure Control Process

Authors: N. Kanagaraj; P. Sivashanmugam; S. Paramasivam
Journal: Advances in Fuzzy Systems
 (2008)

---

## Abstract

This paper presents the real-time implementation of a fuzzy coordinated classical PI control scheme for controlling the pressure in a pilot pressure tank system. The fuzzy system has been designed to track the variation parameters in a feedback loop and tune the classical controller to achieve a better control action for load disturbances and set point changes. The error and process inputs are chosen as the inputs of fuzzy system to tune the conventional PI controller according to the process condition. This online conventional controller tuning technique will reduce the human involvement in controller tuning and increase the operating range of the conventional controller. The proposed control algorithm is experimentally implemented for the real-time pressure control of a pilot air tank system and validated using a high-speed 32-bit ARM7 embedded microcontroller board (ATMEL AT91M55800A). To demonstrate the performance of the fuzzy coordinated PI control scheme, results are compared with a classical PI and PI-type fuzzy control method. It is observed that the proposed controller structure is able to quickly track the parameter variation and perform better in load disturbances and also for set point changes.


---

## Body

## 1. Introduction

The
classical controllers like PI or PID controllers are widely used in process
industries because of their simple structure, assure acceptable performance for
industrial processes and their tuning is well known among all industrial operators.
However, these controllers provide better performance only at particular
operating range and they need to be retuned if the operating range is changed.
Further, the conventional controller performance is not up to the expected
level for nonlinear and dead time processes. In the present industrial scenario, all the processes require automatic
control with good performance over a wide operating range with simple design
and implementation. This provides the motivation for online tuning, where the
focus is on the automatic online synthesis and tuning of the conventional
controller parameters, that is, using the online data, the adopted intelligent
system can continually learn which will ensure that the performance objectives
are met. The online tuning of a conventional controller through an intelligent
technique is one of the ways to automate the operator’s task and to obtain the
better controller performance over a wide operating range. Among the various
intelligent control techniques, fuzzy logic provides a formal methodology for
implementing humans’ heuristic knowledge and it will be considered as an
obvious solution for tuning the conventional controllers. The fuzzy logic
control (FLC) in various forms is being designed and implemented for several
control applications [1–3]. FLC usually embeds the intuition and experience of
a human operator, recently it has been used in the form of supervisor for a
number of applications [4–7]. Specifically, a fuzzy inference system is used to tune the PI controller gains depending on the current operating conditions of
the controlled system.In
industrial environments, the control algorithm development and its
implementation cost should be feasible for real-time control application. In
this context, the use of embedded microcontrollers seems to be particularly
suitable, since the cost of the microcontroller nowadays is very low-, high-processing
speed with lesser amount of power consumption and also suitable to industrial
environments. Further developing the
application program and downloading into the microcontroller is very simple.
Successful application of microcontroller-based real-time control has been
reported [8–10]. Moreover, the embedded microcontroller can be used for remote
monitoring and control through a network-based control structure [11].Pressure
control is one of the primary task in areas-like steam generation in industrial
power plants, reaction control in chemical industry, heating, ventilating, and
air conditioning (HVAC) system, oil well drilling, automobile emission control, and
so on, [12–15]. In general, the pressure
control is a dynamic and nonlinear process, frequent controller tuning is
necessary based on the process operating conditions [16]. This paper reports
the design and implementation of a fuzzy-PI hybrid controller structure in
which the fuzzy controller is adapted to track error and process input of a
feedback system and tune the classical PI controller for set point changes and
load disturbances. The performance of the proposed control algorithm is
compared to conventional feedback controllers. The controller parameters for
the conventional method were computed via the Cohen and Coon (CC) tuning
method, from an open loop process reaction curve experiments.


## 2. Design of a Fuzzy Coordinated PI Controller

The prime
objective of the controller design is to achieve better control performance in
terms of stability and robustness for the set point changes and load
disturbances. Paramasivam and Arumugam [17] and Ketata et al. [18] have proposed
different methods of designing a hybrid control structure using fuzzy logic
system. He et al. [19] and Visioli [20] have used the fuzzy system in such a
way to modify the parameters of the conventional controller. The hybrid control
structure consists of a simple upper-level intelligent controller and a lower-level
classical controller. The upper-level controller provides a mechanism to the
main goal of the system, whereas the lower-level controller should deliver the
solutions to particular situation. In the proposed control structure, a rule-based
mamdani-type fuzzy controller is used in the upper level and a conventional PI
controller is selected for the lower level. The structure of the fuzzy-coordinated
PI controller is shown in Figure 1. In usual practice, the error (e) and error
change (Δe) parameters were preferred whereas designing the antecedent of the
fuzzy rules for control applications. But in the present application, a
modified control structure has been applied in which the fuzzy system utilize
the error (e) and process input (u) and detects the possible deviation from a
prescribed course so that it can able to tune the conventional controller for
set point changes and load disturbances.Figure 1
Fuzzy-coordinated PI controller structure.


### 2.1. Fuzzy Tuning of PI Controller

In the
hybrid control structure, the fuzzy system is used to modify either the system
set point or scaling factor of a conventional controller. The present method
focuses the input scaling factor modification of a classical PI controller. The
PI controller is usually implemented as follows:(1)uPI=Kpe(t)+TKi∑n=0te(n)e(t)=yr(t)−y(t), where Kp,Ki are the proportional andintegral gains. The
controller output, process output, and the set point are denoted as μPI,y,yr, respectively. In the conventional PI controller, the values
of Kp and Ki in (1) are adjusted by the operator
according to the changes in process condition. By developing a rule-based
intelligent fuzzy coordinate hybrid controller structure, these parameters can
be modified online according to the changes in process condition without much
intervention of operator and further it will enhance the conventional
controller performance over a wide operating range.


### 2.2. Rule Base and Membership Functions of the Fuzzy Controller

The upper-level
fuzzy system of the proposed control structure contains operator knowledge in
the form of IF-THEN rules to decide the gain factors according to the current
trend of the controlled process. In this
proposed hybrid controller structure, the control rules of the fuzzy system have
been developed using the general domain knowledge about the conventional
controller tuning [21]. The effect of variation in gain parameters on rise time,
overshoot, and settling time of a PI controller are illustrated in Table 1.Table 1
Effects of the gain parameters.
Gain parameterEffects of increasing gainRise timeOvershootSettling timeKpDecreaseIncreaseSmall
changeKiDecreaseIncreaseIncreaseIn the
proposed method, the control rules are developed with the error and process
input as a premise and the proportional and integral gains are consequent of
the each rules. The structure of the fuzzy rule is written as(2)IFeisNSanduisLOWTHENKpisHIGandKiisMID.Table2 shows the fifteen linguistic fuzzy rules which have been used in the fuzzy
coordinated PI control structure. The linguistic values of each input and
output fuzzy variables divide their universe of discourse into adjacent
intervals to form the membership functions. Each membership function of a fuzzy
variable is assigned with an abbreviated linguistic value-like MED (medium),
VHIG (very high), and so on. The membership function converts the degree of
fuzziness into the normalized interval (0,1). The triangle membership
functions are selected in the present controller and its degree of fuzziness is
expressed as (3)μδ(x)={0,forx<ax−ab−afora≤x<bc−ab−aforb≤x≤c0,forx>c. The
triangle shape membership functions with 50% of overlapping for the input and
output fuzzy variables are shown in Figures 2 and 3. The scaling coefficients
of each fuzzy variable are initially selected from the earlier experimental
data in [22], and their values have been fine tuned during the implementation
in order to obtain the desired results. In the present system, the measured
pressure signal is converted into a 10-bit binary equivalent and the binary number is mapped with the universe discourse.Table 2
Rule base for fuzzy-coordinated PI controller.
InputOutputError(e)Process input(u)KpKiNBLOWVHIGHIGMEDHIGMEDHIGMEDMEDNSLOWHIGMEDMEDMEDLOWHIGLOWVLOWZELOWMEDLOWMEDLOWLOWHIGVLOWVLOWPSLOWLOWVLOWMEDLOWMEDHIGVLOWHIGPBLOWMEDVLOWMEDHIGVLOWHIGHIGMEDFuzzy output membership functions (a) error (b) process input.
(a)(b)Fuzzy output membership functions (a) proportional gain (b) integral gain.
(a)(b)For the
fuzzy implication, the intersection minimum operation has been used, the center
average defuzzification [23] has been selected to find the crisp value of
outputs. The center average defuzzification is defined as (4)μ(KpKi,)=∑i=1Rbiμi∑i=1Rμi, where μ(Kp,Ki) are the gain outputs,  bi denotes the center of the
membership function of the consequent of ith rule and μi denotes
the membership value for the ith rule’s premise.To
demonstrate the performance of the proposed control technique, the performance
of the PI-type fuzzy and the conventional PI controllers have been studied and
compared for the pressure process. The
rule base and membership functions of PI-type fuzzy controller have been
designed using the operative knowledge about pressure process. The controller
parameters for the conventional PI controller were obtained through CC
controller tuning method, from an open loop process reaction curve experiments.


## 2.1. Fuzzy Tuning of PI Controller

In the
hybrid control structure, the fuzzy system is used to modify either the system
set point or scaling factor of a conventional controller. The present method
focuses the input scaling factor modification of a classical PI controller. The
PI controller is usually implemented as follows:(1)uPI=Kpe(t)+TKi∑n=0te(n)e(t)=yr(t)−y(t), where Kp,Ki are the proportional andintegral gains. The
controller output, process output, and the set point are denoted as μPI,y,yr, respectively. In the conventional PI controller, the values
of Kp and Ki in (1) are adjusted by the operator
according to the changes in process condition. By developing a rule-based
intelligent fuzzy coordinate hybrid controller structure, these parameters can
be modified online according to the changes in process condition without much
intervention of operator and further it will enhance the conventional
controller performance over a wide operating range.


## 2.2. Rule Base and Membership Functions of the Fuzzy Controller

The upper-level
fuzzy system of the proposed control structure contains operator knowledge in
the form of IF-THEN rules to decide the gain factors according to the current
trend of the controlled process. In this
proposed hybrid controller structure, the control rules of the fuzzy system have
been developed using the general domain knowledge about the conventional
controller tuning [21]. The effect of variation in gain parameters on rise time,
overshoot, and settling time of a PI controller are illustrated in Table 1.Table 1
Effects of the gain parameters.
Gain parameterEffects of increasing gainRise timeOvershootSettling timeKpDecreaseIncreaseSmall
changeKiDecreaseIncreaseIncreaseIn the
proposed method, the control rules are developed with the error and process
input as a premise and the proportional and integral gains are consequent of
the each rules. The structure of the fuzzy rule is written as(2)IFeisNSanduisLOWTHENKpisHIGandKiisMID.Table2 shows the fifteen linguistic fuzzy rules which have been used in the fuzzy
coordinated PI control structure. The linguistic values of each input and
output fuzzy variables divide their universe of discourse into adjacent
intervals to form the membership functions. Each membership function of a fuzzy
variable is assigned with an abbreviated linguistic value-like MED (medium),
VHIG (very high), and so on. The membership function converts the degree of
fuzziness into the normalized interval (0,1). The triangle membership
functions are selected in the present controller and its degree of fuzziness is
expressed as (3)μδ(x)={0,forx<ax−ab−afora≤x<bc−ab−aforb≤x≤c0,forx>c. The
triangle shape membership functions with 50% of overlapping for the input and
output fuzzy variables are shown in Figures 2 and 3. The scaling coefficients
of each fuzzy variable are initially selected from the earlier experimental
data in [22], and their values have been fine tuned during the implementation
in order to obtain the desired results. In the present system, the measured
pressure signal is converted into a 10-bit binary equivalent and the binary number is mapped with the universe discourse.Table 2
Rule base for fuzzy-coordinated PI controller.
InputOutputError(e)Process input(u)KpKiNBLOWVHIGHIGMEDHIGMEDHIGMEDMEDNSLOWHIGMEDMEDMEDLOWHIGLOWVLOWZELOWMEDLOWMEDLOWLOWHIGVLOWVLOWPSLOWLOWVLOWMEDLOWMEDHIGVLOWHIGPBLOWMEDVLOWMEDHIGVLOWHIGHIGMEDFuzzy output membership functions (a) error (b) process input.
(a)(b)Fuzzy output membership functions (a) proportional gain (b) integral gain.
(a)(b)For the
fuzzy implication, the intersection minimum operation has been used, the center
average defuzzification [23] has been selected to find the crisp value of
outputs. The center average defuzzification is defined as (4)μ(KpKi,)=∑i=1Rbiμi∑i=1Rμi, where μ(Kp,Ki) are the gain outputs,  bi denotes the center of the
membership function of the consequent of ith rule and μi denotes
the membership value for the ith rule’s premise.To
demonstrate the performance of the proposed control technique, the performance
of the PI-type fuzzy and the conventional PI controllers have been studied and
compared for the pressure process. The
rule base and membership functions of PI-type fuzzy controller have been
designed using the operative knowledge about pressure process. The controller
parameters for the conventional PI controller were obtained through CC
controller tuning method, from an open loop process reaction curve experiments.


## 3. Description of the Experimental Setup

The
schematic diagram of a pilot pressure regulating system is shown in Figure4.
It consists of a miniature pressure tank inlet of which is connected to an air
compressor through a 50 mm control valve. At the bottom of the tank, an outlet
is provided with a manually operating gate valve to allow the air flow at a constant
rate. A pressure transmitter attached to the pressure tank is used to measure
tank pressure and provides an output current in the range of 4 to 20 mA. In this closed loop pressure regulating
system, the inlet air flow rate is manipulated by changing the control valve
position in order to reach the desired set pressure. A decreasing sensitivity
type equal percentage electropneumatic control valve characteristic shown in
Figure 5 is used for inlet air flow manipulation.Figure 4
Schematic
diagram of the pilot pressure regulating system.Figure 5
Control
valve characteristics.


## 4. Implementation of the Fuzzy Coordinated PI Controller

The
proposed fuzzy coordinated PI control algorithm source code has been developed
and downloaded into the target ARM7 microcontroller. The host (PC) machine and
the target microcontroller were interfaced usingμLINK programming device for
downloading the application code. A subminiature embedded microcontroller
target board with a 32-bit advanced RISC architecture (ATMEL AT91M55800A) has
been selected to implement the proposed control algorithm and is shown in
Figure 6. Its features are one MByte onboard flash memory, network application
capable processor (NCAP) facilities, 32 MHz operating clock frequency, RS-232
transreceiver for three serial interfaces, and onboard ADC and DAC for real-time
interfacing [24]. The photograph of the experimental setup is shown in Figure 7. Flow chart for the various steps
involved in the development of fuzzy-coordinated PI control algorithm is shown
in Figure 8.Figure 6
The ATMEL (AT91M55800A)-embedded microcontroller target board.Figure 7
Photograph of the experimental system.Figure 8
Flow chart of the various steps in
the development of fuzzy-coordinated PI control
algorithm.


## 5. Experiments and Results

To start
with the compressor, it has been switched on and the air flow from the
compressor was allowed continuously to the pressure tank to reach the set
pressure. The pressure transmitter
measures the tank pressure and gives an output current signal (4–20 mA) which will be converted to 0–5 volts using a current to voltage converter. The inbuilt 10-bit ADC of ARM7
microcontroller converts this analog voltage signal into the corresponding
binary equivalent. The error value is computed by comparing the process output
and the set point. The outlet valve was
set at a fixed opening to allow a constant air flow rate from the pressure tank
during the test period. By using error and process input, the hybrid control
algorithm provides the controller output which will manipulate the inlet air
flow rate to maintain tank pressure at the set level. The sampling rate has
been fixed at 0.5 second for pressure measurement.An
ARM7 microcontroller-based real-time experiments have been conducted for
pressure regulation in a pilot air tank system using PI, PI-type fuzzy, and
fuzzy-coordinated PI control algorithms. The controller parameters of the
conventional PI controller are obtained through CC tuning method. The system output response of the fuzzy-coordinated PI controller, PI controller, and PI-type
fuzzy controller for the set pressure level of 3 bar and 4 bar are
shown in Figures9 and 10. From the output response, it is observed that the
fuzzy-coordinated PI control algorithm makes the system to reach the set
pressure quickly without any overshoot and steady-state error. On the other
hand, the conventional-type PI control algorithm needs much time to reach the
set pressure. However, the PI-type fuzzy control algorithm consumes lesser time
than the PI controller, but having a small steady-state error. It is concluded
that fuzzy- based hybrid controller performance is better in terms of settling
time and steady-state error than the conventional PI and PI-type fuzzy control
methods for pressure control process.Experimental results, output responses of different controllers for the set pressure level of 3 bar.
(a)
Fuzzy-coordinated PI controller(b)
Conventional PI controller(c)
PI-type fuzzy controllerExperimental results, output responses of different controllers for the
set-pressure level of 4 bar.
(a)
Fuzzy-coordinated PI controller(b)
Conventional PI controller(c)
PI-type fuzzy controllerFigure 11
Experimental results of fuzzy-coordinated PI controller, control input, and PI
gains tuning for the set pressure level of 4 bar.The
performance of the proposed control algorithm has been tested for set-point
variation at steady-state condition by varying the set pressure. The response
of the set-point variation from 3 bar to 4 bar and 4 bar to 3 bar of different
controllers is shown in Figures12 and 13. From the results, the fuzzy-based
hybrid controller instantly responds to the set point changes and makes the
system to settle within a short time than the PI and PI-type fuzzy controller.Experimental results, output responses of different controllers for set point change from 3 bar to 4 bar.
(a)
Fuzzy-coordinated PI(b)
Conventional PI controller(c)
PI-type fuzzy controllerExperimental results, output responses of different controllers for set point
change from 4 bar to 3 bar.
(a)
Fuzzy-coordinated PI controller(b)
Conventional PI controller(c)
PI-type fuzzy controllerIn
order to compare the performance of different control algorithms, the integral
of the square of the error (ISE), integral of the absolute value of the error
(IAE), integral of time-weighted absolute error (ITAE), and root mean square
error (RMSE) criteria have been used. The ISE, IAE, ITAE, and RMSE are given as(5)ISE=∫0∞e2dt,IAE=∫0∞|e|dt,ITAE=∫0∞|e|tdt,RMSE=∑K=1N(yr−y(k))2N, where e is
the usual error (i.e., yr−y), yr is the reference
pressure in bar, y is the actual output pressure in bar, and N is the number of
samples (N=100). The performance comparison of different control algorithms for
the set pressure level of 3 bar and 4 bar are presented in Table 3.Table 3
Performance comparison of different control algorithms.
Type of controlISEIAEITAERMSESettling time(ts) sec3 bar4 bar3 bar4 bar3 bar4 bar3 bar4 bar3 bar4 barPI control28.3636.9717.6320.1254.6564.230.5290.61842.350.6PI-type fuzzy control26.4135.1416.2618.4752.0657.210.5160.61140.747.4Fuzzy-coordinated PI control17.0428.3811.9714.5736.7145.350.4270.53633.239.1The comparison table indicates that the proposed fuzzy- coordinated PI controller
has small value for all types of error criteria (ISE, IAE, ITAE, and RMSE) than
the conventional controllers. By considering the settling time, the proposed
algorithm demonstrates the improved performance than the other methods. To
study the robustness of the controllers for load disturbances, a disturbance
has been applied in such a way to increase and decrease the process input at
steady-state condition. The system
output responses for load disturbances are shown in Figures14 and 15. The
results of conventional-type PI and PI-type fuzzy controllers are not good
enough for load disturbances because of the poor tracking performance for
parameter variation. It is also observed that the system output cannot reach
steady state even after long time.
However, in the case of fuzzy- coordinated PI controller, the results
are better for load disturbances. Since the fuzzy system can be able to track the input disturbances instantly by using its input parameters e and u, thereby necessary modification is made in the conventional controller part to bring the system output quickly to the set value.  From the results of load disturbances, it is
obvious that the disturbance rejection ability of the proposed technique is
superior to conventional techniques.Experimental results, load disturbance response of controllers for increasing the process input.
(a)
Fuzzy-coordinated PI controller(b)
Conventional PI controller(c)
PI-type fuzzy controllerExperimental results, load disturbance response of controllers for decreasing
the process input.
(a)
Fuzzy-coordinated
PI controller(b)
Conventional PI controller(c)
PI-type fuzzy controller


## 6. Conclusion

In this
paper, the stability, fast tracking capability for parameter variation, and
robustness of different controller algorithms were studied experimentally for a
pilot pressure control system. The experimental analysis proved that the
proposed fuzzy-coordinated PI control scheme maintains the tank pressure at set
level without any steady-state error unlike PI-type fuzzy controller. By
keeping the merits of PI and FLC, the proposed control scheme makes the system
output to reach the set level faster than PI and PI-type controllers. From the
results of the load disturbances and set point changes, the proposed hybrid
controller proves its robustness with aid of fast parameter tracking
capability. However, the performance of the PI and PI-type fuzzy controller was
not good enough for load disturbances because of the poor tracking
capability. It was found that from the
demonstrated results, the proposed fuzzy logic-based hybrid control scheme is
well suited to pressure control and other types of dynamic processes. Further,
the microcontroller-based embedded controller proved to be better tool for
implementing the hybrid control algorithm with low cost and simple design
technique.



---

*Source: 691808-2008-05-22.xml*