Implementation of Direct Synthesis and Dahlin Control Algorithms on Data Driven Models of Heater System

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1 Implementation of Diret Synthesis and Dahlin Control Algorithms on Data Driven Models of Heater System Mr. R. G. Datar Sanjay Ghodawat Group of Institutes, Atigre Mr. A. N. Shinde Sanjay Ghodawat Group of Institutes, Atigre Mr. A. B. umbhar Sanjay Ghodawat Group of Institutes, Atigre ABSTRACT The orthodox methods like PID ontrollers have been universally aepted for the ontrol of different types of proesses and are still work horses of industrial ontrol. The digital ontrollers provide better handles to tune losed loop response than the onventional PID ontrol. The objetive of this work is the implementation of the advaned digital ontrol algorithms like Diret Synthesis PID and Dahlin Controllers for linear SISO system through easily available hardware platforms. The effiay of these algorithms is tested through a Heater System whih is temperature ontrol proess with heater and fan. The system identifiation of the proess is done by using data driven or blak box modeling. So we proposed to develop and evaluate the performane of digital ontrollers for data driven model of heater system. The performanes of individual ontrollers are studied through various performane measures. The analysis of the ontrol algorithms is done using LabVIEW and Matlab. eywords Diret Synthesis PID, Dahlin, First Order plus Time Delay Model, Output Error Model, System Identifiation 1. INTRODUCTION: The immense literature on PID ontrollers onsists of a vast variety of design and tuning methods based on various performane riteria. The very popular design methods were reported by Cohen and Coon (CC) and Ziegler-Nihols (ZN) earlier. In Diret Synthesis design methods, we usually use the speifiation of the desired losed loop transfer funtion. In this method, the alulation of parameters of the feedbak ontroller is determined from a system and a desired losed loop response [1]. The Dahlin-Higham design method was popular in early digital proess ontrol design beause the alulations required for the design are very simple. It was introdued by Eri Dahlin in He proposed a method for developing the ontroller by defining the losed-loop transfer funtion to be FOPTD equal to that of the system [2]. The SISO system here is Heater System, in whih the temperature is the only output and its ontrol is theonly objetive. The ontrol law is to maintain temperature at desired value by ontrolling urrent through heater oil and the disturbane to the system is fan speed whih is ontrolled using PWM. The system identifiation plays a key role in health monitoring, predition of output, simulator design and ontroller design. In this ase, the data driven or empirial system identifiation is used to implement design advaned digital ontrol algorithm [3][4]. The latter part of the paper is arranged in the following sequene. Setion 2 presents system identifiation of temperature ontrol system. The digital ontrol algorithms like Diret Synthesis PID and Dahlin Controllers are presented in Setion 3. The results of hardware implementation of ontrollers are presented in Setion 4. The main onlusions are reahed through analysis of results. 37 Mr. R. G. Datar, Mr. A. N. Shinde, Mr. A. B. umbhar

2 2. HEATER SYSTEM AND DATA DRIVEN MODELLING: The Fan-Heater System under onsideration is a multiple input single output (with one heater and one fan) temperature ontrol system. It is shown in the Figure 1. Miroontroller ATmega16, RS232 and USB are used for ommuniation. SBHS is interfaed with omputer through LabVIEW software. The temperature of the thin metal plate modifies aording to the urrent flowing through the heater oil. The fan is fixed near to the heating metal plate. It might at as a disturbane to the heater system. The supply of urrent passing through the heater oil determines the temperature of the plate. The transfer of heat takes plae through onvetion. A temperature sensor AD590 whih is very heap senses the temperature of this plate. LCD onneted to the miroontroller displays the perentage values of Heat and Fan and temperature of the plate [4]. Figure 1: Shemati of Temperature Control System The system identifiation is done through data driven model identifiation whih uses input and output data. It has four steps: Experimental Design Data Generation and Data Colletion Data Proessing Model Development and Validation In the experimental design, the aurate representation the dynamis of the systemis apturedby hoosing proper input signal generation. Generally,we give a step to find out First Order with time delay (FOPTD)model and Pseudo Random Binary Sequene (PRBS) to find the disrete time transfer funtion.high frequeny disturbanes, oasional burst, outliers, drifts must be removed before further tasks. The general objetive is to build a deterministi-plus-stohasti model. In model development, the model struture and order seletion is involved. Time series model, State Spae model, Proess model, Nonlinear ARX model struturesan be identified by using system identifiation toolbox in MATLAB. Model validation inludes heking the model output for different datasets [3][6].The transfer funtion between the input to the system and output from the system is determined by using System Identifiation tehnique. Any system an be expressed in different forms of time series modeling but ARMAX model an be expressed as written in Eq.(1). The heater urrent is input, temperature is output and fan speed is disturbane whih is kept onstant. Here, y(k) is output signal from system, u(k) is ontrol effort or input signal to the system and e(k) onsists of measured and unmeasured disturbanes, noise and measurement errors A()()()()()() y k B u k e k (1) Output Error Model between Temperature and Heater Current is given by G() as given below: 38 Mr. R. G. Datar, Mr. A. N. Shinde, Mr. A. B. umbhar

3 G() B1 () A() FOPTD Model between Temperature and Heater Current is given by G(s) as: s G() s e (3) s (2) 3. DIGITALCONTROL ALGORITHMS: Figure 2: Disrete-time system Usually, for designing a digital ontroller, the blok diagram shown in Figure 2 an be used. In this figure, R() isthe referene input, E() is the error, U() is the ontrol effort or output of the ontroller and Y() is the output of the system. G() represents the digital proess transfer funtion with the ero-order hold [7].The losed-loop response of system shown in Figure 2 is designed by losed-loop transfer funtion of the system and the required ontroller and it is written as shown below. If we know the model of the proess, the ontroller D() an be designed shown in Eq. (5). The ontroller D() must be hosen suh that it should be stable and realiable pratially. T() D() D()() G (4) 1()() D G 1() T G()1() T (5) 3.1 Diret Synthesis-PID Controller for FOPTD model: If we onsider FOPTD model of SBHS then the Diret Synthesis PI ontroller for set-pointtraking is designed by following way. A feedbak ontrol system with the standard blok diagram is shown in Figure 3. G(s) is Transfer Funtion of SBHS and G(s) is Designed Controller. The losed-loop transfer funtion for set-point hanges is derived as the Overall Transfer Funtion v(s): Y() s G()() s G s v() s U() s 1()() G s G s (6) G () s 1() v s G()1() s v s (7) 39 Mr. R. G. Datar, Mr. A. N. Shinde, Mr. A. B. umbhar

4 Figure 3: General Control Strategy The desired losed-loop transfer funtion for set-point hangeis speified as v(s) whih is having unity gain and expeted time onstant Tl. As the harateristis of v(s) have a diret impat on the resulting ontroller, v(s) should be hosen so that the losed-loop performane is satisfatory and the resulting ontroller is physially reliable. T p 1 G () s 1 () T T T s p l So it an be ompared with PI ontroller as shown in Eq.(9) and the ontroller parameters an be found out. Where T i Tp () T T T p p l d d p G () PI s (9) T s 3.2 Diret Synthesis-PID Controller for time series model: The designing of PID ontroller inludes typially a time domain or frequeny domain performanes. Diret Synthesis design methods are dependent on the desired losed loop transfer funtion speifiation. In DS method, an analytial expression for the PID ontroller is alulated from the desired losed loop response and a system model [1]. The Desired Closed loop response is given as T() in Eq. (10 ). The Output Error model identified is G() as indiated in Eq. (11) and the overall transfer funtion of ontroller is G() as alulated in Eq. (12 ). The PID ontroller in Bakward Euler form is given as Eq. (13 ). By using Diret Synthesis method for alulation of PID gains with suitable values of N and Ts, we get proportional gain, integral gain and derivative gain as mentioned in Eq. (13): i T() (8) 1 1 p (10) G() 1 1 d 1 1 (11) 1 a b 40 Mr. R. G. Datar, Mr. A. N. Shinde, Mr. A. B. umbhar

5 G () 1() T G()1() T (12) ITs DN 1 GPID P 1 1 NT 1 s (13) Where P I D 3ak 5bk k 4p k ak bk 4p k 3ak 9bk 4p 3.3 Dahlin s Control Algorithm for time series model: A modified dead-beat ontroller is alled as the Dahlin ontroller. It produes an exponential response whih is smoother than that of the dead-beat ontroller. It was introdued by Eri Dahlin (1968) and used in paper and pulp industries in He introdued an algorithm to develop the ontroller by giving the losed loop transfer funtion T() to be FOPTD onverted to disrete as shown in Eq. (14) and it should be equal to that of the system and is having unity steady-state gain [2][7][8].In it, T is the sampling interval, τ is the time onstant of the losed loop response and k = time delay/t. From FOPTD model in equation G() and T(), the typial feedbak ontroller of the form D() designed in Eq. (15) is found to be: D T 1 e 1 e T / 1k T / 1 41 Mr. R. G. Datar, Mr. A. N. Shinde, Mr. A. B. umbhar T / 1k 1 1 e G 1() e 1 e T / 1 T / 1k The speed of the response is adjusted by using the time onstant τ used as a tuning parameter. In Dahlin ontroller, the eros of the plant G() might exist outside unit irle then the transfer funtion between referene and input to the plant is unstable. There will be problem if there are eros lose to -1. To overome these problems, the eros at origin has been substituted for the unstable eros of plant G(). This is Modified Dahlin Control algorithm as shown in Eq. (16) [2][7]. Where T / 1 1 e G X 1() e 1 e X MDC T / 1 T / 1k P1... Pn m Ak 1 An 1 A1 Ak (14) (15) (16)

6 - and + are used here to represent the eros inside the unit irle and outside the unit irle respetively. P1 to Pnare poles and A are eros whih are onverted into good and bad polynomials. m indiates the number of eros to be disarded. 4. HARDWARE IMPLEMENTATION OF DIRECT SYNTHESIS PID AND DAHLIN CONTROLLERS: 4.1 Hardware Results of DS-PID Controller for FOPTD model: The FOPTD of the SBHS system is generated form step test test as written in Eq. (3). The Controller parameters are: G DS PI s 8:9412 T I s s (17) These ontroller gains are given to the system with LabVIEW interfaing and results are obtained as shown in Figure 4. Figure 4: DS-PID Controller for FOPTD model 4.2 Hardware Results of DS-PID Controller for Time Series model: The identified output error model of the SBHS system is generatedform PRBS test as written in Eq. (2).The alulation of PID gains is done for desired losed loop transfer funtion. The PID gains alulated from Diret Synthesis method as follows: , , P I D These ontroller gains are given to the system with LabVIEW interfaing and results are obtained as shown in Figure Mr. R. G. Datar, Mr. A. N. Shinde, Mr. A. B. umbhar

7 Figure 5: DS-PID Controller for OE model 4.3 Hardware Results of Modified Dahlin Controller for Time Series model: The ontroller transfer funtion for identified model of SBHS is obtained. The results of modified Dahlin ontroller are as shown in Figure 6. Figure 6: Modified Dahlin Controller for OE model CONCLUSIONS: Diret Synthesis PID Controller for FOPTD model gives good response to set point hange. But the ontrol signal i.e. heater urrent is not smooth enough. It requires more ontrol efforts and overheads the limit of heater urrent. Diret Synthesis PID Controller for OE model perform better than earlier one. Modified Dahlin Controller responds better for set-point hange and has smoother ontrol signal than diret synthesis PID Controller.Modified Dahlin ontroller is best among all of the ontroller. It attains the set-point faster and rejet disturbane suessfully and quikly. The analysis of all ontrollers is done below in Table Mr. R. G. Datar, Mr. A. N. Shinde, Mr. A. B. umbhar

8 Table 1: Analysis of Designed Controllers altogether with Performane Measures Sr. No. Type of Controllers Rise Time (se) Settling Time (se) IAE 1. DS-PID for FOPTD Model DS-PID for OE Model Modified Dahlin REFERENCES [1] Dan Chen and Dale E. Seborg, (2002), PI/PID Controller Design Based on Diret Synthesis and Disturbane Rejetion, Ind. Eng. Chem. Res., Vol. 41, No. 19,. [2] E. Zafiriou, and M. Morari, (1985), Digital Controllers for SISO Systems: A Review and a New Algorithm, Int. J. Control 42, 885. [3] Patwardhan S. C, "Advaned Proess Control Leture Notes", Dept. of Chemial Engineering, Indian Institute of Tehnology, Mumbai. [4] I. Arora,. M. Moudgalya, and S. Malewar, A low ost, open soure, single boardheater system, in E-Learning in Industrial Eletronis (ICELIE), th IEEE International Conferene on. IEEE, 2010, pp [5]. J. Åström and B. Wittenmark, (1995), Adaptive Control, Addison-Wesley, 2nd edition,. [6] Arun. Tangirala, (2015), Priniples Of System Identifiation Theory and Pratie, CRC Press, Taylor & Franis Group,. [7] Dogan Ibrahim, (2006),"Miroontroller Based Applied Digital Control, John Wiley & Sons Ltd. [8] Xia Hong, Xia Tao, (Ot. 2009), Implementation of the Dahlin Digital Controller by IIR Network Method, Intelligent Computation Tehnology and Automation, ICICTA '09. Seond International Conferene on, [9]. J. Åström and B. Wittenmark, Computer-Controlled Systems: Theory and Design, Prentie Hall Information and System Siene Series, 3rd Edition. 44 Mr. R. G. Datar, Mr. A. N. Shinde, Mr. A. B. umbhar