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1 International Conference on Engineering Innovations and Solutions DESIGN OF CASCADE CONTROL BASED FPID TUNING FOR NON-LINEAR PROCESS N.Jayaprakashnarayanan ( PG Scholar) Dept of Electronics and Instrumentation Bannari Amman Institute of Technology Sathyamangalam,Erode. I.Aravindaguru (PG Scholar) Dept of Electronics and Instrumentation Bannari Amman Institute of Technology Sathyamangalam,Erode. Abstract - This paper evaluates the performance of cascaded FPID design for the level and flow control of non-linear tank system. The level control of nonlinear tank is the massive challenge in process industry and it cannot be effectively controlled by means of conventional linear PID controller. FPID controller in cascaded architecture is the best choice compared to conventional single loop control system for controlling these non-linear process. Based on consideration about the expected operating modes of both FPID controller, the tuning of both inner and outer loop controllers are selected accordingly. Here the Spherical tank system is taken as non-linear system and their mathematical modelling is developed to show the system dynamic performance. The output response of cascade based FPID controller is simulated using LabVIEW and compared with conventional PID controllers. Keywords - Cascade, Conventional PID, FPID,DAQ card, LabVIEW, Spherical tank system I. INTRODUCTION Measurement of level, temperature, pressure and flow parameters are very vital in all Process Industries. Real time systems provide many challenging control problems due to their dynamic behaviour, uncertainty and time varying parameters, constraints on manipulated variables, dead time on input and measurements, interaction between manipulated and controlled variables and unmeasured frequent disturbances. Because of the inherent nonlinearity, most of the chemical process industries are in need of modern control techniques. Level control of spherical tank is one of the requirements in industries, where the storage of large volumes of highly pressurized liquids takes place. The level control in spherical tank is cumbersome due to variation of cross sectional area with respect to its height. The nonlinearities may also due to the saturation-type introduced by maximum or minimum allowed level in tanks, valve geometry, flow dynamics, pumps and valves. The most basic and pervasive control algorithm used in the feedback Derivative (PID) control algorithm. A PID controller attempts to correct the error between a measured process variable and a desired set point by calculating and then providing a corrective action that can adjust the process accordingly. Level and flow are the process measurement of spherical tank system, in which level can be controlled using flow of process known as cascade control.it is widely used in process industries and is particularly useful when the disturbances are associated with the manipulated variable or when final control element exhibits nonlinear behaviour. A simulation of cascade based PID control of spherical tank system to control level is done with LabVIEW software. Cascade Control is an advanced application of the PID that can improve control of systems that are subject to significant lag. Since such systems are slow to respond to disturbances their performance can suffer with each upset. The Cascade architecture can be applied effectively to such sluggish processes when a related and faster responding loop is available. When applied in concert the faster loop serves as an early warning mechanism that buffers the impact on its slower counterpart, allowing for smoother control and enhanced performance. Cascade control should always be used if you have a process with relatively slow dynamics (like level, temperature, composition, humidity) and a liquid or gas flow, or some other relatively-fast process, has to be manipulated to control the slow process. The calibration of modern transmitters is done using HART. Its most notable advantage is that it can communicate over legacy 4-20 ma analog instrumentation wiring. Calibrating the level transmitter means that the instrument must show an output of 4mA when there is no level and 20mA during full level. Before calibrating, the height between bottom tank and transmitter (LRV) and height between top tank from the transmitter (URV) are noted. To get an effective and accurate mathematical model, the spherical tank level is controlled in closed loop and step is given in open loop, then it is allowed for self regulation to get the E-ISSN :
2 International Conference on Engineering Innovations and Solutions International Conference on Engineering Innovations and Solutions process reaction curve. The selection of the model could be from the open-loop step response. The open loop step response is obtained by providing a step change in VFD frequency which will increase or decrease the inflow rate. LabVIEW developed by National Instruments (NI) is a graphical development with built in functionality for simulation, data acquisition, instrument control, measurement, analysis and data presentation it gives the flexibility of a powerful programming language without the complexity of traditional development environments. Data acquisition is the process of gathering and generating information in an automated fashion from analogue and digital measurement sources such as sensors and software to provide a flexible, user defined measurement system. The Data Acquisition (DAQ) system is used to pass a conditioned electric signal to a computer for software analysis and data logging. level values initially then signal is converted to current signal in the range 4 to 20mA. pressure signal acts on a control value which controls the flow of water in to the tank there by controlling the level. II. PROCESS MODELING The level process station was used to conduct the experiments and collect the data. The computer acts as a controller [3].It consists of the software used to control the level process station. The setup consists of a process tank, reservoir tank, control valve, I to P converter, level sensor and pneumatic signals from the compressor. When the set up is Switched on, level sensor senses the actual Fig. 1. Level Control of Spherical Tank System E-ISSN :
3 International Conference on Engineering Innovations and Solutions A. Description of the Spherical Tank Level Process The tank is made up of stainless steel body and is mounted over a stand vertically. Water enters the tank from the top and leaves the bottom to the storage tank. are as follows, The inlet pipe has a Rotameter, Electromagnetic type flow meter called as Flow Transmitter (FT1), air-to-open type pneumatic Control Valve (CV) and a hand valve to monitor and control the flow rate. The outlet has a hand valve, Electromagnetic type flow Spherical tank system The real time system consists of one input (inflow) and one output (level of the tank). The inflow is taken from a reservoir tank through a centrifugal pump with single phase motor. Table 1. Specifications of Spherical Tank System S.No. Parts/Field Description instruments Material: Stainless Steel, Diameter: 43 cm, 1. Spherical Tank (LRV= mmh2o, URV=866.5 mmh2o, Volume: 42 liters VFD: ABB-ACS350, 3Φ 4-20 ma to 0 to Pump and VFD Hz.Pump: Grundfos- JP5 centrifugal pump, 3Φ. DPT for level 3. measurement (LT) 6200T Series, Range:0 to6500mmh2o, DPT for level Output: 4 to 4. measurement (FT) 20mA+HART 5. Control valves Linear, Air to open, Body :1, Trim1/2 6. Rotameter 150 to 1500 lph 7. E/P converter Input:4-20 ma, 20 psi Output: 3 to 15 psi Analog input: 8, Analog output:2, Resolution: NI USB bits, Sampling rate: DAQ 250kS/s input & output voltage: -10V to +10V E-ISSN :
4 3 3 ( ) A (Re) +1 3 ( ) +1 ti me delay ] International Conference on Engineering Innovations and Solutions International Conference on Engineering Innovations and Solutions meter called as Flow Transmitter (FT2) and airto-open type pneumatic CV. The tank level is measured using a DPT, called as Level transmitter (LT). The level in the tank is directly proportional to the pressure created by liquid in it. LT measures the level by measuring pressure at bottom of the tank with reference to the atmosphere and coverts into an electrical quantity (4 to 20 ma). The LT is energized with 24V DC source and Lower Rage Value (LRV) & Upper Range Value (URV) are set using a Highway Addressable Remote Transducer (HART) communicator. The system is interfaced to the computer through NI USB 6211 data acquisition card (NI DAQ) and it can handle a maximum of 10 V, so the DPT outputs (4 to 20 ma) are converted into 2 to 10V using a 500Ω resistances and scaled up using LabVIEW. The controller signals (0 to 10V) from computer via NI DAQ is converted into 4 to 20 ma using a voltage to current convertor and given to current to pressure (E/P) convertor. The pneumatic line from the compressor is connected to an air regulator and its output is given as constant inputs (20 psi) for two different E/P converters. The CVs are operated based on the pneumatic outputs from E/Ps B. Mathematical model for Spherical tank system In order to design any control system the value of its transfer function should be known. To get the transfer function, mathematical modeling of the system needs to be done.the spherical tank in figure 5.3 is essentially a system with nonlinear dynamics. The nonlinear dynamics described by first-order differential equation. Fig.2.Schematic Diagram of Spherical Tank Area [A] = 4 π( h ) (3) Differentiating with respect to time = 8 π( ) 2 h h 1 h [A +8π 2 ] h = ( = ) =A h [Mass Balance Equation] Fin-Fout = A h Fout = h = h Fin = A h + h = Fin-Fout (1) Where V is the volume of the tank, Fin is the inlet flow and fault is the output flow. Volume of sphere (V) = 4 3π 3 Area of sphere (A) = 4 π 2 Taking Laplace Transform Fin(s) = As ( ) + ( ) (4) ( ) = Re (5) Thus, it is the first order system. Practically there will be a time delay. So, the equation becomes V= 1 [AR] = 1 [Ah] (2) ( ) Ke τds = [τd= Differentiating with respect to time E-ISSN : = 1 [A h +h ] 3
5 International Conference on Engineering Innovations and Solutions From the diagram, = h III.EXISTING SYSTEM A. Conventional PID Controller The Proportional-plus-Integral-plus- Derivative (PID) controllers have found wide acceptance and applications in the industries for the past few decades. It has a simple control structure E-ISSN :
6 International Conference on Engineering Innovations and Solutions International Conference on Engineering Innovations and Solutions which was understood by plant operators and which they found relatively easy to tune. In spite of the simple structures, PID controllers are proven to be sufficient for many practical control problems and hence are particularly appealing to practicing engineers. controller is the level controller using the level setpoint and measurement to determine the setpoint for the slave controller driving the input flow valve. Measurements of input and output flow are taken into account, enabling the system to faster respond to output flow disturbances. IV.PROPOSED SYSTEM Fig.3. PID Loop Control An abundant amount of research work has been reported in the past on the tuning of PID controllers. Ziegler Nichols step response, Ziegler Nichols ultimate cycling, Cohen Coon, Internal model control, and error-integral criteria tuning formulae are to mention only a few. "PID" means Proportional-Integral-Derivative, referring to the three terms operating on the error signal to produce a control signal. Since many control systems using PID control have proved satisfactory, it still has a wide range of applications in industrial control. Defining u(t) as the controller output, the final form of the PID algorithm is: A.Cascade FPID An alternative approach and one that can significantly improve the dynamic response to disturbances, employs a secondary measurement and a secondary feedback controller. The secondary measurement point is located so that it recognizes the upset condition sooner than the controlled variable, but the disturbance is not necessarily measured. This approach, called cascade control, is widely used in the process industries and is particularly useful when the disturbances are associated with the manipulated variable or when the final control element exhibits nonlinear behavior. The Self-tuning fuzzy PID controller, which takes error "e" and rate of change-in-error "ec" as the input to the controller makes use of the fuzzy control rules to modify PID parameters on-line. The self-tuning of the PID controller refers to finding the fuzzy relationship between the three parameters of PID,Kp,Ki, and Kd and "e" and "ec", and according to the principle of fuzzy control modifying the three parameters in order to meet different requirements for control parameters when "e" and "ec" are different and making the control object produce a good dynamic and static performance. Selecting the language variables of "e","ec", Kp, Ki, Kdby choosing seven fuzzy values (NL,NS,ZE,PS,PL). The region of these variables, in this case, is taken to be {-2,-1, 0, 1, 2}. S d u e d Fuzzy PID controller Plant P Where: Pout : Proportional term of output Kp : Proportional gain, a tuning parameter Ki : Integral gain, a tuning parameter Kd : Derivative gain, a tuning parameter E : Error = SP PV T : Time or instantaneous time (the present) MV : Manipulated variable The PID controller output determines the E-ISSN :
7 International Conference on Engineering Innovations and Solutions state of the feed valve. The system has limitations in reacting to variations in output flow, which is to be regarded as a system disturbance. The cascade control uses two PID controllers for a better performance of the level control. The master Fig.4. Basic structure of a fuzzy PID controller Here (NL,NS,ZE,PS,PL) is the set of linguistic values which respectively represent Negative Large, Negative Small, Zero, Positive Small, Positive Large.The following E-ISSN :
8 International Conference on Engineering Innovations and Solutions International Conference on Engineering Innovations and Solutions figure is the block diagram of a fuzzy self-tuning PID controller. As it can be seen from the block diagram, the fuzzification takes two inputs (e ande c) and gives three outputs ( K p, K i, K d). The set of linguistic rules is the essential part of a fuzzy controller. In the designed fuzzy system, conventional fuzzy conditions and relations such as If e is A and ec is B, then Kpis C, Ki is D andkd is E. are used to create the fuzzy rule tables Tab le 2. Fuzzy rules for kp = + = + = + e / ec NL NS ZE PS PL NL PVS PVL PVL PVL PVL NS PML PML PML PL PL ZE PVS PVS PS PMS PMS PS PML PML PML PL PVL HereKp,Ki and Kd refer to the previous value of the PID parameters whereaskp,ki andkd refer to the new corrected values of the parameters after a particular tuning step was completed. Therefore, with the help of Fuzzy sets (error and change in error) the above mentioned output variables K p, K i, K d fuzzy set values determined and fuzzy set rules framed. Totally 25 fuzzy set rules framed which is mentioned n table 2, table 3 and table 4 along with the error and change in error various values (NB,NM,NS,ZO,PS,PM,PB). The self-tuning of the PID controller refers to finding the fuzzy relationship between the three parameters of PID,Kp,Ki, and Kd and "e" and "ec". B. Simulation of Cascade PID PL PVL PVL PVL PVL PVL Table 3. Fuzzy Rules for Ki e / NL NS ZE PS PL ec NL PM PM PM PM PM NS PMS PMS PMS PMS PMS ZE PS PS PVS PS PS PS PMS PMS PMS PMS PMS PL PM PM PM PM PM Table 4.Fuzzy Rules for Kd e / ec NL NS ZE PS PL NL PM PM PM PM PM NS PMS PMS PMS PMS PMS ZE PS PS PVS PS PS PS PMS PMS PMS PMS PMS PL PM PM PM PM PM Fig.5. Front Panel of Cascade PID in LabVIEW V.RESULTS & DISCUSSION Open loop test is conducted for 200mm of height and then it is allowed to settle at 250mm height by giving a step change in flow. The response of open loop test is shown in the below figure. Process parameters such as Process gain, Time constant and dead time are calculated from the Process Reaction Curve. Kp = τ = 570 Td = 5.4sec Adaptive corrections can be made by the following methods, E-ISSN :
9 International Conference on Engineering Innovations and Solutions International Conference on Engineering Innovations and Solutions response method for PID control, Journal of Process Control, Vol. 14, pp AnandanatrajanR, ChidambaramM and Jayasingh T (2005), Design of controllers using variable transformations for a nonlinear process with dead time, ISA Transactions, Vol. 44, no. 1, pp Fig.6. Process Reaction Curve Obtained transfer function for the height of 200 mm, 3. Nithya, S., G. Abhay Singh, N. Sivakumaran, T. Balasubramanian and N. Anantharaman,, (2008), Design of intelligent controllers for non-linear processes,asian J.Applied science 1,pp ( ) ( ) = Table 5.Comparison between PID and Cascade FPID Controller Rise Settling Set Controller time time point tr ts (cm) (sec) (sec) 20 PID Cascade 4 11 FPID VI.CONCLUSION In this paper, the experimental setup of spherical tank system have studied and level control measurement was done. Calibration of level and flow transmitter was done using HART communicator. The process reaction curve of the spherical tank system was obtained through open loop test and dynamic performance was obtained from the transfer function. Simulation of cascade control for level and flow measurement have been done using LabVIEW software. The three parameters of conventional PID control need to be adjusted constantly in an online by Fuzzy controller to achieve better control performance. Thus the settling time, rise time, and other parameters of the system had been achieved with better dynamic performance. 4. Truong Nguyen Luan Vu, Moonyong Lee (2010), Independent design of multi-loop PI/PID controllers for interacting multivariable processes,journal of Process Control 20 (2010) D.Dinesh Kumar, B.Meenakshipriya (2012), Design and implementation of Non Linear System Using Gain Scheduled PI Controller,journal of process control (Elsevier), Procedia Engineering 38 ( 2012 ) K.Hari Krishna, J SatheeshKumar and MahaboobShaik, Design and Development of Model Based Controller for a Spherical Tank, International Journal of Current Engineering and Technology,Vol.2, No.4(Dec. 2012),ISSN Selvaraj S.P and Nirmalkumar A (2014), Implementation of GA based online parameter tuning of the Conical tank system, International Journal of Applied Engineering Research, Vol. 9, no. 22, pp PradeepKannan.D, Sathiyamoorthy,(2012) Design and Modelling of State Feedback with Intergal Controller for a Non-Linear spherical tank Process., International Journal of Emerging Technology and Advanced Engineering, 2(11), REFERENCES 1. Astrom K.J and Hagglund T (2004), Revisiting the Ziegler Nichols step E-ISSN :
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