EFFICIENT CONTROL OF LEVEL IN INTERACTING CONICAL
TANKS USING REAL TIME CONCEPTS
V. Karthikeyan
Department of Electrical and Electronics Engineering, Dr. M.G.R. Educational and Research Institute, University, Chennai, India E-Mail: [email protected]
ABSTRACT
In this research work an effort is made to design a real time control system for a non linear system and the performance is compared with existing methods. Level control in conical tank is a difficult task considering its non linear design. The proposed controller algorithm is implemented in LPC 1768 processor board along with µ cos –II real time operating system for controlling level in the interacting conical tanks. The algorithm is written in keil ‘C’ Platform. Process reaction curve method is used to design a mathematical model for first order process having dead time for each tank. The designed PID controller Algorithm is tested in real time with conical tanks system. On comparing the work done with existing ones it is found that interaction factor is very less in the proposed method. The results obtained shows negligible steady state error and very high stability compared to conventional methods.
Keywords: conical tanks, PID control, LPC 1768, µ cos –II, interaction factor.
INTRODUCTION
Flow and level are the main variables that need attention in process industry. The way of representing processes mathematically is called mathematical modeling. Mathematical modeling of conical tanks is very complex compared to linear tanks. The use of conical tanks plays pivotal role in various process industries like petro chemical, waste water treatment, food processing, concrete mixing industries etc. The main characteristic of conical tanks is its change in cross sectional area at each point of the tank. Conventional PID control algorithms produce best results in controlling the level of the linear tank , but it shows decline in performance due to the non linearity present in the Conical tanks. If the level of liquid rises in the tank, the corresponding area of the tank also increases. The existing decentralized controllers are not suited when there is a large interaction present between the Loops. In the proposed method a PID controller is designed and implemented in real time. The following table describes various process variables related to the work.
Literature survey
Feed forward controller is a good concept since the process variable is getting controlled before the disturbance has an effect on the process variable, but it has a drawback that all the disturbances cannot be identified and measured [2]. A model of PID controller for conical tanks was designed and comparison between the performance of internal model controller tuning with Particle swarm optimization tuning is done and found that PSO method is superior over heuristic PID tuning [6].Two centralized PI controller tuning methods davison method and Tanttu and Liestehto method are used for the control of interacting conical tanks and their performances are tested for both servo and regulator problems. Tanttu method gives better results [3]. A controller was designed based on skogestad tuning method .The designed controller performs effectively in the minimization of error [9].
Table-1. Process variable description.
S. No. Process
Variable Description 1 Pressure Force /Area
2 Absolute Pressure
Gauge pressure + Atmospheric Pressure
3 Flow Square root of Differential Pressure
4 Flow Rate
Amount of flow that flows in a given period of time
M = ρ x Q
5 Level
Length of liquid column or Pressure the column exerts over a Datum level
A neural estimator for non linear Interacting process was designed and implemented it in python language and its performance is compared with fuzzy estimator [10]. The characteristics of the non linear spherical tanks is studied and performance comparison is made using four types of controllers and found FO PI controller reduces the error to good effect compared to other methods [1].
REAL TIME PLANT
transmitter output will be 4- 20 mA. It measures the differential pressure from the bottom and top of the tank. Out of three tanks which may be connected in non interacting mode when tank 1 and 3 are sequentially
connected with no connection to tank 2 or in interacting mode when tank 1 is connected sequentially with tank 2.
Figure-1. Real time plant.
Control loops interact when movement of actuator of one control loop affecting both its own process variable and also of other loops. The corrective action of one controller affecting the other process variable as well. It is called interaction between the loops
Tank level can be measured by the hydrostatic pressure measurement of the tank
P = Height of the liquid X Specific gravity
Non linearity to linearity conversion
Non linearity to linearity conversion is done at different operating regions of the conical tanks. Volume Calculation of Conical Tank is done as follows
Let
R - Radius of the tank at 100 % H - Height of the tank at 100 % r - Radius of the tank at “x “point h - Height of the tank at “x” point R/r = H/h
r = R * h/H Volume at x point V = 1/3 * 𝜋 * r2 * h
Interacting control mode operation
The various steps involved in the Interacting conical mode operation is as follows:
a) Keep the hand valves MV 1, MV 4, MV 5, MV 7, MV 9, MV 10 AND SV 1 in open condition b) Valves MV 2 and MV 11 are in partially open
condition
c) Remaining hand valves and solenoid valves are in closed condition
d) Power on the pump
e) Run the controller algorithm with desired set point f) Based on the control valve movement reservoir tank
starts filling tank 1 and tank 2
g) When process variable = set variable , levels in tank 1 and tank 2 are equal
h) Introduce disturbance in tank2 by adjusting MV 11 i) Disturbance in tank 1 affects tank 2 ( interaction)
HARDWARE SETUP
In this study the controller is implemented with the combination of LPC 1768 hardware alongwith µ C/OS-II kernel are used to minimize the interaction present in the system. The LandTiger V2.0 NXP LPC1768 ARM development board is a 32 bit Microprocessor used for real time applications. The Board has following features of 512KB on chip flash program memory, Color LCD display interface, USB 2.0 interface, 64KB SRAM for high performance CPU, Two CAN bus communication interfaces, RS 485 communication interface, SD/MMC card (SPI) interface, Two RS 232 serial interfaces, RJ45-10/100M Ethernet network interface, DAC o/p interface and ADC i/p interface, Standard JTAG test/debug interface.
LPC 1768 is a high performance and Low power consumption Microprocessor. µC/OS-II is a real time multi tasking operating system kernel version 2. It is used for inter task communication and synchronization and it has superior features compared to other RTOS. The various features are:
a) Portable, preemptive, multitasking kernel b) It can handle 64 tasks
c) It supports processors up to 64 bit d) It has deterministic execution times
e) µC/OS-II is simple to use and simple to implement KERNEL
An real time operating system (µC/OS-II) fulfills the requirements of events that happens in real time.
USB cable of the LPC 1768 Board is connected to USB port of the system and Serial port of the LPC 1768 Board is connected to Serial port of the system The PID Controller algorithm is programmed, compiled and downloaded to the LPC 1768 board by resetting the
board, the control action for the conical tank starts. The experimental setup is shown in Figure-3.
Figure-3. Experimental setup 1. USB Cable of LPC 1768(Connected to USB Port of PC), 2. Serial port of LPC
1768(Connected to PC Serial port) (Karthikeyan et al, 2014).
CONTROLLER DESIGN
The function of controller is based on measurement of process variables. Input/output data are measured from the conical tank plant. The main function of Controller is to produce control inputs which in turn depend on error value. The controller function is implemented in LPC Board and RTOS and tested in Real time non linear system. The efficiency of designed controller is tested using various time domain specifications like rise time, Peak overshoot and settling time.
The mathematical model for level of tanks h1 and h2 are derived from the mass balance equation.
The transfer function of the conical tank 1 and 2 can be approximated with transfer function of first order process with dead time
Where td = Dead time, K = static gain, = Time constant Mathematical model gives the mathematical relationship between input and output of the system which is an important factor in the design of controller. The process reaction curve method of controller tuning is used for tuning the PID controller for selecting best values for
KP = Proportional gain, KI = Integral gain, KD = Derivative gain
RESULTS AND DISCUSSIONS
Figure-4. Response of Tank 1 and 2.
The results are obtained in C Language which is worked in µ Cos -II operating system with LPC 1768 Hardware board. The screen captured image of error is shown in Figure-5, which clearly shows that error value is reduced at each instant.
Figure-5. Error value at each instant.
The Process output (variable) controlled by PID Algorithm is shown in Figure-6. It is very clear that the response is stable in nature. The variation of error with respect to time is plotted in Figure-7.
Time
Figure-6. Response of process output with time.
Time
Figure-7. Variation of error with time.
CONCLUSIONS
A PID controller algorithm is implemented in LPC 1768 board with µ cos - II in keil C platform for the interacting conical tanks. The main objective of minimizing the interaction factor is achieved in this paper. Process reaction curve method is used for tuning the designed PID controller. On comparing the results the proposed method works efficiently in minimizing the error compared to conventional algorithms and the algorithm satisfies various time domain specifications like Rise time, Peak overshoot, settling time. The future scope of study will be designing the controller algorithm for three tank interacting system.
0 2 4 6 8 10 12 14 16 18
0 50 100
Process output (cm)
Process output (cm)
-5 0 5 10 15 20
0 50 100
Error
REFERENCES
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