Online Tuning of Adaptive-Optimal PID Controllers via Artificial Neural Networks

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1 International OPEN ACCESS Journal Of Modern Engineering Research (IJMER) Online Tuning of Adative-Otimal PID Controllers via Artificial Neural Networks Hilton S. S. Santos. 1, Madson C. Machado 1, João V. Fonseca Neto. 2 *(Deartment of Electrical Engineering- UFMA) ( hiltonseheres@hotmail.com) ** (Deartment of Electrical Engineering- UFMA) ABSTRACT: This research resents a methodology for online tuning of artificial neural network arameters that are in the context model redictive control (MPC). This MPC system design is comosed of anadative-otimal PID controller. The Artificial Neural Network RBF reresents the algebraic structure of the PID, in order to meet not only the design requirements, but also to resent roerties of adatability and otimality at each instant of samling. Also in this article, the roosal of an adative PID control structure based on the redictive neural network model for controller tuning is resented. The artificial neural networks guarantee a satisfactory incororation of dynamics of the rocess to be controlled, being a one-ste neural network to redict the outut of the rocess. The roosal is evaluated in hotovoltaic anel, the adative-otimal PID controller results are comared to the classic PID model. Keywords: tuning, online, Neural Networks, controller, PID, Radial Basis Function and Adative. I. INTRODUCTION Online alications have bottlenecks that require an investigation of their imlementation so as not to comromise real-time roects.for examle, otimization methods require large comutational efforts, which often tend to fail with the comlexity of the dynamic system.the motivation for emloying bio-insired stochastic otimization algorithms as comutationally efficient alternatives to the deterministic aroach [1]. Frequently, otimal control theory rovides the suort to solve automation roblems in electrical, mechanical, and industrial rocesses. Often, the hysical nature of these rocesses introduces time delays. In engineering systems delays are often resent due to measurement, transmission and transort lags, comutational delays, or unmanaged inertia of the system comonents [2]. In control systems, it is known that time delays can undermine system erformance and even cause [3]. At the beginning of the millennium, the PID controller remains a key comonent in the control of industrial rocesses. During the last century many different combinations of structures have been roosed to overcome the limitations of PID controllers.due to its simlicity and use it has roven to be a owerful solution for the control of a large number of industrial rocesses [4]. This control model is quite oular and used in the industrial field due to the ease of design and imlementation at low cost [5]. However, the otimal tuning for controller gain is still challenging and motivating. In a number of books and articles, such as PSO evolution algorithms [6], DE [7], GA [8], among others have been used to tune PID controllers. The adative control aroaches in [9], [10], [11] and the references [12][13]contribute to the alication framework. The otimal control aroaches contribute to the degree of freedom of the designer to meet and systematically insert energy consumtion constraints. The demand for high erformance control systems is a ressing need of the contemorary world as can be seen in references that show alications in industrial, ower and aeronautical systems.in this way, the demand for new architectures and toologies that surass or add value to the closed-loo control system design in the classical sense is erceived. These new systems must satisfy the randomness of the oeration (human errors), cost reduction in the roduction of added value of the final roduct and rocess variations.the develoment of intelligent control systems with the roerties of adatability, rediction and learning associated to comutational intelligence and rediction aroaches within a control horizon with the classic arametric estimation methodologies in order to obtain the tuning of gains of transfer functions of the Adative and otimal control meshes. The union of these aroaches has shown to be an attractive alternative for real-time tuning of the arameters of estimators and controllers in real-world systems. IJMER ISSN: Vol. 6 Iss. 11 November

2 The resent article resents the rocedure for imlementing an adative - otimal PID controller in a osition control of a solar anel. Then comared to a classical PID tuning method.the imlementation is associated to the online algorithm that is develoed for arameter adustments in control systems with adativeotimal PID architecture. In terms of hardware, indoor erformance is used for erformance tuning method of arameters. The reduced model of real-world lant such as: osition control of a Solar Panel.The article is organized in sections that resent the roosed methodology and its develoment, the adative and otimal algorithms, the embedded system and the evaluation test. II. PROBLEM CHARACTERIZATION AND SOLUTION In this section we resent the roblem-solving characterization that consists of the descrition of the roblem of the online tuning of PID controllers and their formulation. The following is the resentation of the mathematical formulation of the solution method that develos algorithms online via comutational intelligence for online tuning of the PID-otimal controllers. A descrition of the online tuning method ofpid controllers. Generally, it is imossible to obtain a hysically aroriate model of dynamic industrial automation and electrical ower systems due to the comlexity of the underlying rocesses or the lack of knowledge of critical arameters (such as mass transfer coefficients, Heat, or viscosities deendent on temerature and ressure) of the models. One way to overcome these roblems of rocess modeling, it is to use neural networks as nonlinear black box models of the dynamic rocess behavior [14]. As described in the article we demonstrate, the measurements of inut and outut variables of the rocess oerated with the linear controller can rovide very good training data for the redictive neural network. II.1. MATHEMATICAL FORMULATION OF THE PROBLEM The mobile target roblem consists of the stes of detecting the resence of the crawled obect and the second ste consists of ositioning devices to extract information that characterizes the target in question. The characterization of the rocess allows the extraction of arameters, such as time constants, gains and stability, that allow to establish restrictions or secifications to meet the control requirements. Mathematical modeling of the dynamic rocess, inut and outut, in discrete form: (1) Modeling the PID Controller in equations the difference in the form of Euler, For the definition of Δe(k) = e (k) -e (k-1). Structure of the Prediction RBF network, Fig. (1), given by (2) Figure 1: Structure of Neural RBF Predictive The inut of the network is comosed of six sensory units, the current outut of the system and two oututs being delayed, the other three being formed by the current inut of the system with the two delayed ones. The inut reresented by vector x [ x1, x2, x3, x4, x5, x6 ] and the outut of the rediction network is IJMER ISSN: Vol. 6 Iss. 11 November

3 y ( 1) k. The inut and outut of the RBF Predictive Neural Controller. Inut of the control RBF network is defined by the vector xc [ x1, x2, x3 ] and the outut of the controller is uk. The RBF Artificial Neural Network is used for adative neural PID controller architecture. The RNA is designed with three layers (3-5-1) in consideration of the real-time requirement of the control system. The structure of the neural PID controller is develoed by the direct method, in order to abort the outut of the controller through the inuts of the neural network RBF Fig. (2). Figure 1:Proosed controller scheme. The structure of the neural network can be written in function of J that is given by 1 2 J r ( k 1) y ( k 1) (3) 2 d The steeest descent method is used to adust the network weights to reach the goal of J.In this way e( k 1) rd( k 1) y ( k 1).The criterion of Eq. (3), the outut of the controller uk already defined the inut vector of the neural network RBF, has the inut of the hidden layer hc cc xc. The xc reresents the inut and cc reresents the center of the RBF. And for the inut of the controller's neural network RBF is defined as: k ek x1 e( k), x2 T e( k) and x 3. i 0 T II.1. PID-Adative-Otimum Control System The structure of the neural PID controller is develoed by the direct method, in order to abort the outut of the controller through the inuts of the neural network RBF.The neural network consists of three sensory units in the inuts, five neurons in the hidden layer and one neuron in the outut layer, (3-5-1). The outut of each neuron from the hidden layer is Oc frbf ( Ih), The inut of neuron I h and Oh of the hidden layer, IO Wf RBF ( Ih) (4) The outut of the RBF network rovides the control action uk. u( k) fo( IO) (5) The function of the network outut layer f o is linear. The udate of the RBF neural network arameters of control is used the descending gradient method,which is used Eq. (3), 1 E( k) r( k 1) y ( 1) 2 k (6) 2 With the following conditions met, E y( k) w( k) e( k)( y( k) y( k)) h (7) w u( k) E y( k) u( k) b ( k) e( k) b u( k) b E y( k) u( k) c ( k) e( k) b u( k) c To udate the weights w, b and c of the control network. w ( k) w ( k 1) w ( k) w ( k) (10) (8) (9) IJMER ISSN: Vol. 6 Iss. 11 November

4 b ( k) b ( k 1) b ( k) ( b ( k 1) b ( k 2)) (11) ci ( k) ci ( k 1) c i ( k) ( ci ( k 1) ci ( k 2)) (12) Where and are the learning rate and moment factor, resectively. For the next udates of the b and c arameters.where yk is the Jacobian value that exresses the outut and inut sensitivity of the system. This uk yk value can be obtained by the signal of. uk III. TRACKER DESIGN AND IMPLEMENTATION Within a context of ossessing roerties of adatability and otimality. The roosed control system is based on adative-otimum PID controllers. III.1. Tracking Control System The block diagram of Fig.(2) reresents control system for hotosensitive tracking. The block diagram reresents the rocess, a gearmotor and sensors that are modeled by means of ordinary differential equations for the urose of equiment secification and develoment of the control algorithms.the urose of the control is to track Luminous Intensity (IL) variation, in this case not by the aarent rotation of the sun, but to track IL caused by a circular artificial light system at a rate of 1m / s. The dynamic system receives the IL by the sensor set formed by the two LDRs and sends it to the control unit. The actual system is shown in Fig. (3). Figure 2:Block diagram of the hotosensitive tracking system In the summation a second-order mathematical model is used, which is the controlled model. The RBF neural PID controller with a structure and for the redictive neural network is used a structure network. Figure 3:Photosensitive tracking system IJMER ISSN: Vol. 6 Iss. 11 November

5 III.2. Mathematical Modeling of the Tracking Control System The transfer function Gs () of the actuator (motor) and the rocess (anel). The moment of inertia 6 2 ( Jm 3, 2 10 kgm ) and the coefficient of friction to the moment of inertia 2 ( J 100 kgm ) 6 ( b m 5,5 10 ) of the motor are negligible with resect and the coefficient of friction ( b 1) of the anel. Thus, the moment of inertia and the coefficient of friction of the motor are relaced by that of the anel in the modeling of the lant. m Figure 4:Mathematical modeling of the solar anel Thus, the system transfer function, taking into account the relation between the angle of the axis a m of the motor and the anel angle ( a ) according to Fig.(4), is: () s 10 K V s RJ s Rb s K K s K M 2 c () [( ) b M ] 10 M 6 6 The motor arameters Ra 4, L 2.75*10, b m *10 and Km were obtained by means of the datasheet sulied by the manufacturer. However, for many DC motors, in relation to their modeling for control uroses, the effect of armature inductance is disregarded. For this situation the system is stable, it has no oles on the right side of lane s. Alying a ste inut in the system to verify its behavior. III.3. Elements of the Control System Following a conventional taxonomy, the elements of the control system of Fig. 2 are classified as rocess, load, sensors, actuators and control unit. III.3.1 Process and Load For control uroses, the tracking rocess of the moving body (Sol) is comosed of loads distributed in fixed and varied loads. The fixed load is the sum of the frictional forces of the sliding bearings. The varied load is comosed by the moment of inertia and natural and normal reactions. III.3.2 Sensors The rocess consists of two sensors: sensor for tracking, LDR, a assive electronic comonent of variable resistor tye, whose resistance varies according to the intensity of the light that falls on it. Resonsible for the location of the mobile body (Sol) and has the imortant role of reference of the control system. Locating sensor, Linear Potentiometer, with curve of constant resistance variation (linear) in relation to the angle of rotation of the axis. The osition of the movable table is verified by the otentiometer and sent to the control system. III.3.3 Actuators The 12V / 75RPM gearmotor, Celeron gear, sliding bearing at gear unit outut, insulation class of 180 C, model CEP 9 and manufacturer BOSCH. It is couling on the axis of the turntable and has the function of moving the movable set of the turntable, comosed of axis, solar anel and sensors. (13) IJMER ISSN: Vol. 6 Iss. 11 November

6 III.3.4 Control Unit It consists of an 8-bit Atmel ATmega328 microcontroller with modified Harvard architecture. It belongs to the AVR family of Atmel. It has a basic architecture and set of instructions, articularly the tinyavr (ATtiny microcontrollers), megavr (the ATmega) and XMEGA (the Atxmega ). IV. DISCUSSION OF THE RESULTS For the analysis of the classic PID controller we have the values of K, K, and i K d that satisfy the requirements of the roect are resectively , and Using these values and analyzing their behavior. The tuning of the PID controller using the method roosed by Ziegler-Nichols. For the behavior of the system the transient resonse of the system, one has the rise time, 1.75 s, accommodation time, s and Overshoot Figure 5:Ste resonse The rediction of dynamic system outut is based on an online training RBF network. The inut of the neural network is comosed of six sensory units, the current outut of the system and two oututs delayed, the other three is formed by the current inut of the system with the two delayed ones. From the redictive neural network Fig. (1).For the rediction of the outut of the dynamic system at the instant of ( k 1) is acquired, using the function aroximation tool an RBF neural network with structure Where the red line reresents the behavior of the obect and the dashed black line reresents the rediction in a ste ahead of the rocess. Figure 5:Prediction of system behavior IJMER ISSN: Vol. 6 Iss. 11 November

7 The Adative PID-RBF controller has a structure, the J function is described in (3). The inut of the network is a linear combination according to the error, described in detail in Section II. The inut vector of the network xc and the outut of the neural network being the signal of the controller. Figure 6:Resonse to the system ste with the PID controller with online tuning The adusted RBF neural network arameters are only the momentum hotometer (0.12) and the learning coefficient (0.35). The other factors (RBF centers and length) are adusted online and adatively. V. CONCLUSION This article resented a new design methodology to attend the new technological demands that require the action of systems of high oerational erformance. The roosed method has characteristics of adatability that is reresented by the adative control and the otimality that is served by the otimal control aroaches. Acknowledgements The authors are indebted to the Federal University of Maranhão (UFMA), the Graduate Program in Electrical Engineering (PPGEE), the Embedded Systems and Intelligent Control Laboratory (LABSECI), the Coordination of Undergraduate Personnel Imrovement (CAPES), and the National Council for Scientific and Technological Develoment (CNPq) for the develoment infrastructure and financial suort. REFERENCES [1] Binitha, S., and S. Siva Sathya. "A survey of bio insired otimization algorithms." International Journal of Soft Comuting and Engineering(2.2), 2012: [2] VINTER, Richard. Otimal control. (Sringer Science & Business Media, 2010) [3] BEVRANI, Hassan. Robust ower system frequency control. (New York: Sringer, 2009). [4] ÅSTRÖM, Karl J.; ALBERTOS, Pedro; QUEVEDO, Joseba. PID control. Control Engineering Practice, v. 9, n. 11, , [5] Yaghoobi, Saber, and Hamed Moallali. "Tuning of a PID controller using imroved chaotic Krill Herd algorithm." Otik-International Journal for Light and Electron Otics (2016): [6] Solihin, Mahmud Iwan, Lee Fook Tack, and Moey Lea Kean. "Tuning of PID controller using article swarm otimization (PSO)." International Journal on Advanced Science, Engineering and Information Technology 1.4 (2011): [7] Bingul, Zafer. "A new PID tuning technique using differential evolution for unstable and integrating rocesses with time delay." International Conference on Neural Information Processing. Sringer Berlin Heidelberg, [8] Herreros, Alberto, Enrique Baeyens, and José R. Perán. "Design of PID-tye controllers using multiobective genetic algorithms." ISA transactions 41.4 (2002): [9] Camacho, Eduardo F., and Carlos Bordons. Model redictive control in the rocess industry. (Sringer Science & Business Media, 2012). [10] Camacho, Eduardo F. "C. Bordons Model redictive control." (2004). [11] Findeisen, Rolf, and Frank Allgöwer. "An introduction to nonlinear model redictive control." 21st Benelux Meeting on Systems and Control. Vol. 11. Technische Universiteit Eindhoven Veldhoven, IJMER ISSN: Vol. 6 Iss. 11 November

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