Draft Paper Itrec 2019.docx

Improvement of Linear Distillation Column Control Performance Using Fuzzy Self-Tuning PI Controller Abdul Wahid1, a), Albert Harazaki Mendrofa2, b), Muhammad Fathi Fadlian2, c), and Shafira Anandita1, d) 1 2

Department of Chemical Engineering, Faculty of Engineering University of Indonesia, Depok, West Jawa, 16424 Department of Electrical Engineering, Faculty of Engineering University of Indonesia, Depok, West Jawa, 16424 a)

Corresponding author: [email protected] b) [email protected] c) [email protected] d) [email protected]

Abstract. PID controller still plays an important role in industrial processes due to the structure’s simplicity and the ability to be implemented in industrial scale. However, PID controller is unable to give a satisfactory control performance in controlling nonlinear and multiple input and multiple output (MIMO) systems with strong loop interactions. To improve the control performance, PID controller is made to be adaptive by adding fuzzy controller. Fuzzy controller will calculate the values of ΔKp, ΔKi, dan ΔKd, so that the values of Kp, Ki, and Kd in PID controller will always be updated based on the error input in both PID and fuzzy controller. Hence, the controller is named as fuzzy self-tuning PID, due to the ability of calculating the optimum values of Kp, Ki, and Kd based on the system’s current condition. With the potentials aforementioned, this controller will be implemented in one of the multivariable systems in chemical processes, which is distillation column. The distillation column model used in this simulation is linear distillation column 2 × 2 by McAvoy and Weischedel as mentioned in Marlin. The simulation will be done with the MATLAB/Simulink software and the program routines are made with C (C MEX Sfunction). Verification of the control performance improvement will be reviewed from three parameters, which are overshoot, settling time, and IAE (integral absolute error). Keywords: Fuzzy, fuzzy self-tuning PID, C MEX, distillation column

INTRODUCTION The fuzzy logic control has proved its broad potential in industrial applications because of its good performance for controlling nonlinear and uncertain systems that could not be controlled satisfactorily by using conventional controllers, such as a conventional PID controller [1]. With the addition of self-tuning to the fuzzy logic control, it advances the fuzzy logic PID controller to overcome problems such as multiple-input and multiple-output (MIMO) systems with strong loop interactions. One of the most common multivariable system in industrial applications is the distillation column. There are a lot of researches regarding the distillation column, including the areas of process synthesis, process dynamics, and process control. Various process control methods, including optimization (tuning), have been studied and applied to various distillation column systems. However, with the potentials aforementioned, the application of fuzzy self-tuning PID controller for controlling distillation columns has not been studied further. The only paper found to study this subject is by Almeida and Coelho [1]. With a Wood and Berry 2 × 2 distillation column, they have proven that a fuzzy self-tuning PID controller results in a better controlling than using a conventional PID controller (with Ziegler-Nichols tuning method). However, the simulation method proposed in the paper is found to be unclear and unpractical due to the lack of a detailed discussion. To create a clear understanding about the subject, this essay will discuss in detail the simulation method proposed for implementing a fuzzy selftuning PI controller for distillation column with MATLAB/SIMULINK. The distillation column used as a case study

in this paper is a 2 × 2 linearized distillation column model by McAvoy and Weischedel (1981) as shown in Marlin [2].

LITERATURE REVIEW Here we provide some basic advice for formatting your mathematics, but we do not attempt to define detailed styles or specifications for mathematical typesetting. You should use the standard styles, symbols, and conventions for the field/discipline you are writing about.

Structure of Fuzzy Self-Tuning PID Controller According to Si and Wang [3], the fuzzy-PID controller takes conventional PID as the foundation, which uses the theory of fuzzy reason and variable discourse of universe to on-line regulate the parameters of PID automatically. The structure of fuzzy self-tuning PID controller is shown below.

Fig. 1. Structure of fuzzy self-tuning PID controller.

Here, e denotes the system error and ec denotes the system error changing rate. The error and error changing rate are used as the input variables in control system, and the output variables are the parameters of PID control, those are ΔKp, ΔKi, and ΔKd. The fuzzy sets of e, ec, ΔKp, ΔKi, and ΔKd are { NB, NM, NS, 0, PS, PM, PB }, where NB, NM, NS, 0, PS, PM and PB are linguistic values, which represent “negative big”, “negative medium”, “negative small”, “0”, “positive small”, “positive medium”, and “positive big” respectively. The regions of e and ec are described by the following method. 

PB = error tolerance 1*set point





PM = error tolerance 2*set point



PS = error tolerance 3*set point





ZO = 0





NS = -PS



NM = -PM



NB = -PB



By describing the e and ec region this way, it is allowed to determine the system’s error tolerance. Meanwhile, the regions of ΔKp, ΔKi, and ΔKd are described by the following method. PB = PB / rescaler



PM = PM / rescaler



PS = PS / rescaler





NS = NS / rescaler





NM = NM / rescaler



NB = NB / rescaler





Which Microsoft Word Equation Editor Should I Use? (Second Level Heading) The essential part of the fuzzy logic controller is a set of linguistic rules. In many cases, it is easy to translate an expert’s experience into such rules. Any number of rules can be created to define the actions of the fuzzy controller. In this paper, the fuzzy control rules design is based on the medical robot that can approach the target quickly and stable. The application of conventional fuzzy conditions and fuzzy relations “If e is A and ec is B, then ΔKp is C, ΔKi is D, and ΔKd is E” can establish fuzzy rules. The finally determined fuzzy rules are shown below. TABLE I.

FUZZY RULE FOR ΔKP

TABLE II.

FUZZY RULE FOR ΔKI

TABLE III.

FUZZY RULE FOR ΔKD

After constructing the table of fuzzy control rule (ΔKp, ΔKi, and ΔKd), the adaptive correction is made by the following method.  

Kp = Kp’ + ΔKp



Ki = Ki’ + ΔKi



Kd = Kd’ + ΔKd



Based on the above analysis, according to the principles of self-tuning parameters of PID, the model of fuzzy selftuning PID controller is shown below.

Fig. 2. Model of fuzzy self-tuning PID controller.

C MEX According to Yusivar and Wakao [4], C MEX is an add on feature of SIMULINK that enables S-function to be written using C. A simple C MEX S-function can be composed of a S-function block with one input port and one output port configuration. The number of I/O elements can be multiplexed or demultiplexed using the Mux or Demux block. S-function is identified by a name that is actually same as the C program’s file name so that MATLAB can recognize and link each other. There are three simple basic structures of C MEX, where each structure consists of program routines that are meant to do specific tasks. The initialization routine is dealt with setting of I/O port width number, sample time, number of states (discrete, continuous, or none), and initialing the values of those states. A state is a calculated value that will be used in the next iteration. The mdlOutputs is the area for formulating outputs, usually in a simple math equation. The mdlUpdate routine is used to express the algorithm. Usually, the structure with a mdlUpdate routine is a discrete function. The mdlDerivatives is required by a continuous system. In this routine, SIMULINK integrates the differential equations using variety methods that can be chosen. In the Termination routine, may be performed any actions that are necessary at the termination of a simulation, such as for free the memory that has been allocated. Structure A is used for a function that has only feed through calculations for outputting data from inputs. The sample time for a function with structure A can be discrete or continuous, but it has no state. Therefore, structure A has no mdlUpdate nor mdlDerivatives routine. Structure B is usually for a discrete system. All algorithms are written in the mdlUpdate routine that may also consist a discrete integration created by the user. This routine is only for updating data or states every time the sample time is hit. SIMULINK doesn’t do any integration process. Structure C is used for a continuous system. SIMULINK will automatically process the integration of any differential equations written down in the mdlDerivatives area. The integration results will update the states automatically. Then, by combining the simple C MEX S-functions with any structures, we can simulate dynamic systems such as motor drive system and distillation process with a constant and scope blocks additions for parameter setting and data displaying purposes.

Fig. 3. Simple C-MEX S-function configuration.

Fig. 4. Simple structure of C-MEX file.

PROCESS DESCRIPTION AND MODEL The fuzzy self-tuning PID controller is implemented on a 2 × 2 linearized distillation column model by McAvoy and Weischedel (1981) as shown in Marlin [2]. The model is based on a two-product distillation column separating a binary feed as shown in Fig. 5 with the initial conditions for the model is shown in Table 6.

Fig. 5. Example of a distillation column. TABLE IV.

INITIAL CONDITIONS OF THE MODEL

Parameters Relative volatility Number of trays Feed tray Analyzer dead times Feed light key (XF) Distillate light key (XD) Bottoms light key (XB) Feed flow (FF) Reflux flow (FR) Distillate flow (FD) Reboiler flow (FV) Tray holdup (H) Holdup in drums (HD)

Value 2.4 17 9 2 min 0.50 0.98 mole fraction 0.02 mole fraction 10.0 kgmole/min 8.53 kgmole/min 5.0 kgmole/min 13.53 kgmole/min 1.0 kgmole 10.0 kg mole

The transfer functions are derived based on the schematic diagram of binary distillation column and the linearized equation is shown below.

  Based on Fig. 5 and Eq. 17, the manipulated variables are reflux and reboiler flow rates, the controlled variables are distillate and bottoms compositions, and the disturbance is the feed composition. Meanwhile, other parameters such as pressure and levels are controlled tightly. The control configuration used in the distillation column is a two-point PI control with LV-configuration. A twopoint PI control means that both distillate and bottom compositions are controlled, especially when both distillate and bottom products are valuable, so that the effect of disturbances will be small at low frequencies. While LVconfiguration means that the reflux flow (FR) and boil-up flow (FV) are the variables used to control both distillate and bottom compositions, whereas the distillate flowrate (D) and the bottom flowrate (B) are used for level control [5].

SIMULATION Figures, tables, and equations must be inserted in the text and may not be grouped at the end of the paper. Important: A miscount of figures, tables, or equations may result from revisions. Please double check the numbering of these elements before you submit your paper to your proceedings editor.

A. Open Loop Simulation The open loop simulation is done without any controller with the Simulink structure example and how the changes are performed given in Giwa et al. [6]. The aim of the open loop simulation is to understand the effect of the manipulated variables and disturbance towards the controlled variables. The open loop simulation is done by giving a positive step of 10% for both manipulated variables and disturbance. For FR, the value is changed from 8.53 to 9.383. For FV, the value is changed from 13.53 to 14.883. For XF, the value is changed from 0.4 to 0.44.

Fig. 6. Open loop / dynamic simulation of the system.

If you need to arrange a number of figures, a good tip is to place them in a table, which gives you additional control of the layout. Leave a line space between your figure and any text above it, like this one:

(a)

(b)

FIGURE 1. To format a figure caption use the Microsoft Word template style: Figure Caption. The text “FIGURE 1,” which labels the caption, should be bold and in upper case. If figures have more than one part, each part should be labeled (a), (b), etc. Using a table, as in the above example, helps you control the layout

Cite all figures in the text consecutively. The word “Figure” should be spelled out if it is the first word of the sentence and abbreviated as “Fig.” elsewhere in the text. Place the figures as close as possible to their first mention in the text at the top or bottom of the page with the figure caption positioned below, all centered. Figures must be inserted in the text and may not follow the Reference section. Set figure captions in 9 point size, Times Roman font.

Type the word “FIGURE 1.” in bold uppercase, followed by a period.

B. Closed Loop Simulation The closed loop simulation is done with the controller scheme purposed in this paper as shown in Fig. 7. To have a clear understanding whether the controller scheme purposed in this paper has a better performance, a closed loop simulation with the PI controller is also done as shown in Fig. 8. The tuning constants used for the PI controller are calculated by the MATLAB auto tuner. The performance of each controller is analyzed from various parameters such as overshoot, settling time, and IAE (Integral Absolute Error). Smaller overshoot, smaller settling time, and smaller IAE value are desired from a controller.

Fig. 7. Closed loop simulation of the system with fuzzy self-tuning PI controller.

Fig. 8. Closed loop simulation of the system with PI controller.

C. Simulation Testing Simulation testing is done by setpoint changes and disturbance rejection testing to see the aggressiveness (how aggressive the controller behaves towards new setpoint value) and the robustness (how robust the controller behaves to handle disturbance) of the controllers. Setpoint change testing is done by two methods: (1) changing ±5% of the XD setpoint to see the changes in both XD and XB and (2) changing ±5% of the XB setpoint to see the changes in both XD and XB. Changing the XD setpoint will result in a disturbance for XB, while changing the XB setpoint will result in a disturbance for XD. By changing the XD and XB setpoint in different simulations and not done simultaneously, the simulation results will show pure effect of the XD setpoint change towards XB and pure effect of the XB setpoint change towards XD respectively. Disturbance rejection testing is done by changing ±10% of the XF value to see the changes in both XD and XB.

Due to the wide range and complexity of tables, we simply offer an example for guidance. Please follow the style for table (and figure) captions. TABLE 1. To format a table caption, use the Microsoft Word template style: Table Caption. The text “TABLE 1,” which labels the caption, should be bold and all letters capitalized. Center this text above the Table. Tables should have top and bottom rules, and a rule separating the column heads from the rest of the table only. Column Header Goes Here Column Header Goes Here Column Header Goes Here

Row Name Here Row Name Here Row Name Here

x x x

x x x

RESULTS AND DISCUSSION Here are the main points you need to follow (the AIP author template packages contain comprehensive guidance):

A. Open Loop Simulation Fig. 9 and Fig. 11 show the dynamic response of the system to positive steps in reflux flow rate (FR) and feed composition (XF) for distillate and bottom composition respectively. Fig. 10 and Fig. 12 show the dynamic response of the system to positive steps in reboiler flow rate (FV) and feed composition (XF) for distillate and bottom composition respectively. The results show that when the reflux flow rate and feed composition are increased, both distillate and bottom composition are increased. Meanwhile, when the reboiler flow rate and feed composition are increased, both distillate and bottom composition are decreased. The results are in accordance with the transfer functions model given by the case study used in this paper.

Fig. 9. Dynamic response of the system to positive steps in reflux flow rate (FR) and feed composition (XF) for distillate composition (XD).

Fig. 10. Dynamic response of the system to positive steps in reboiler flow rate (FV) and feed composition (XF) for distillate composition (XD).

Fig. 11. Dynamic response of the system to positive steps in reflux flow rate (FR) and feed composition (XF) for bottom composition (XB).

Fig. 12. Dynamic response of the system to positive steps in reboiler flow rate (FV) and feed composition (XF) for bottom composition (XB).

B. Closed Loop Simulation Fig. 13 and Fig. 14 show the comparison of the system’s response between PI and fuzzy PI controller for both distillate and bottom compositions respectively. From Fig. 13, the fuzzy PI controller shows better control performance for XD because it can reach the setpoint on a much faster rate (at around t = 600 s) than the PI controller (at around t = 1500 s). From Fig. 14, the fuzzy PI controller also shows better control performance for XB because its overshoot is three time less than the PI controller. From Fig. 13 and Fig. 14, the IAE values are evaluated based on the area under the setpoint graph. The calculation result can be seen on Table V, where the fuzzy PI controller has smaller IAE values for both XD and XB, or in other words, has a better control performance.

Fig. 13. Comparison of the system’s dynamic response between PI and fuzzy PI controller for XD.

Fig. 14. Comparison of the system’s dynamic response between PI and fuzzy PI controller for X B. TABLE V. AE of Fuzzy PI Controller XD XB 68.5967 15.2723

IAE VALUES FOR FUZZY PI AND PI CONTROLLER

IAE of PI Controller XD XB 105.6351 107.4742

C. Setpoint Change Testing Fig. 15 and Fig. 16 show the dynamic response of the system towards +5% XD setpoint change at t = 2000 s and 5% XD setpoint change at t = 3200 s for XD and XB respectively. Fig. 17 and Fig. 18 show the dynamic response of the system towards +5% XB setpoint change at t = 2000 s and -5% XB setpoint change at t = 3200 s for XD and XB respectively.

Fig. 15. Dynamic response of the system towards +5% XD setpoint change at t = 2000 s and -5% XD setpoint change at t = 3200 s for XD

Fig. 16. Dynamic response of the system towards +5% XD setpoint change at t = 2000 s and -5% XD setpoint change at t = 3200 s for XB

Fig. 17. Dynamic response of the system towards +5% XB setpoint change at t = 2000 s and -5% XB setpoint change at t = 3200 s for XD

Fig. 18. Dynamic response of the system towards +5% XB setpoint change at t = 2000 s and -5% XB setpoint change at t = 3200 s for XB

D. Disturbance Rejection Testing Fig. 15 and Fig. 16 show the dynamic response of the system towards +10% disturbance at t = 2000 s and 10% disturbance at t = 3200 s for XD and XB respectively.

Fig. 19. Dynamic response of the system towards +10% disturbance at t = 2000 s and -10% disturbance at t = 3200 s for XD

Fig. 20. Dynamic response of the system towards +10% disturbance at t = 2000 s and -10% disturbance at t = 3200 s for XB

CONCLUSION Ut wisi enim ad minim veniam, quis nostrud exerci eliton ullamcorper suscipit lobortis nisl ut aliquip ex en commodo consequat. Duis te feugifacilisi per suscipit lobortis nisl ut aliquip ex en commodo consequat.Lorem ipsum dolor sit amet, consectetuer adipiscing elit, sed diem nonummy nibh euismod tincidunt ut lacreet dolore magna aliguam erat volutpat.

REFERENCES 1.

2. 3.

4. 5. 6.

Almeida, O. D. M. and Coelho, A. A., 2002. A fuzzy logic method for autotuning a PID controller: SISO and MIMO systems. In 15th IFAC World Congress on Automatic Control. Marlin, T. E. 1999. Process Control: Designing Processes and Control Systems for Dynamic Performance, 2 nd Edition, New York: McGraw-Hill Si, X. and Wang, J., 2010, November. A Vector-control System Based on Fuzzy Self-tuning PID controller for PMSM. In E-Product E-Service and E-Entertainment (ICEEE), 2010 International Conference on (pp. 1-4). IEEE. Yusivar, F. and Wakao, S., 2001. Minimum requirements of motor vector control modeling and simulation utilizing C MEX S-function in matlab/simulink. IEEE journal. M. Thone, M. Potters and S. Baldi, "Control configurations in distillation columns: A comparative study," 2016 European Control Conference (ECC), Aalborg, 2016, pp. 37-42. Giwa, A., Owolabi, J.O. and Giwa, S.O., 2017. System identification and IMC-based PID control of a reactive distillation process: a case study of n-butyl acetate production. In International Journal of Engineering Research in Africa (Vol. 31, pp. 104-119). Trans Tech Publications.