Journal of applied science in the thermodynamics and fluid mechanics Vol. 4, No. 2/2010, ISSN 1802-9388

COMPARISON OF ADVANCED CONTROL METHODS WITH CLASSICAL PID CONTROL FOR USING IN HEATING PROCESS CONTROL BASED

ON OUTDOOR TEMPERATURE COMPENSATION*Ivana LUKÁČOVÁ, **Jana BORŽÍKOVÁ

*Technical University of Košice, Faculty of Mechanical Engineering Park Komenského 9, 041 27, Košice, Slovak Republic

Email: ivana.lukacova@avl.com

**Technical University of Košice, Faculty of Manufacturing Technologies with the seat in PrešovBayerova 1, 080 01, Prešov, Slovak Republic

Phone:+ 421 948 800 648 Email: jana.borzikova@tuke.sk

The aim of this paper is to analyse the dynamic properties of a Model Free Adaptive (MFA) Control, Model Predictive Control (MPC) and Proportional–Integral–Derivative (PID) Control. Usually the PID-Control as standard control method is still used in industry. From more advanced control methods MPC is used the most frequently. Properties of the MFA controller, MPC controller and the classic PID controller were compared mutually by simulation experiments with model of heating process control based on the outdoor temperature compensation with room influence. The design of MFA and MPC controller was implemented in MATLAB environment.

Keywords: PID controller; MPC controller; MFA controller

1 INTRODUCTIONMultilayer feed-forward neural network with sufficient number of hidden neurons are universal approximators and therefore they are able to accomplish input-output behaviour of any continuous function with the required accuracy. Therefore we can consider them as a universal resource of regression analysis of the functions defined by training set, where the shape of model function will be predetermined by UNS architecture (topology and interconnection of neurons by setting the weight coefficients and threshold values for certain values). This ability can be used in control of the complex systems, where conventional methods usually fail. Model Free Adaptive (MFA) controllers, based on the neural networks, enable control of system, whose parameters change over time. MFA controllers can also be used for hardly identifiable systems without knowledge of complex mathematical model of system or for manually tuning of controller parameters.

Nowadays, predictive control methods represent a large group of modern control techniques with an increasing number of applications. The group of methods, called Model Predictive Control (MPC), consists of such methods that use control process mathematical model obtained from the measured process data for calculation appropriate control action.

Modern algorithms and control methods using artificial intelligence techniques are applying in the increasing number of successful applications in practice, especially in the heating process control. Latest control methods are of benefit for several reasons. One of them is the fact that optimization of control actions is part of these methods and in consequence of this there is a presumption of economical manufacturing plant in which these methods are implemented. Another important feature of these methods is ability to include constraints of process variables in control algorithms without changing the structure. It is not possible in the classical PID structures. The paper deals with the analysis of the dynamic properties of MFA (Model Free Adaptive) controller, MPC (Model Predictive Control) controller and their comparison with classical PID controller for optimization of heating process control based on the outdoor temperature compensation.

2 MFA CONTROLLERUsing of artificial neural networks for systems identification requires a feed-forward neural model of the system, while their using as a feedback neural controller requires the creation of inverse model of controlled system.

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Journal of applied science in the thermodynamics and fluid mechanics Vol. 4, No. 2/2010, ISSN 1802-9388

Let's consider system, which input-output behaviour can be described by the relationship y = f(u), where y is output of system, u is input of system and function f(.) is unknown nonlinear function. The control objective for the controller is to produce an output u(t) to force the process variable y(t) to track the given trajectory of its setpoint r(t) under variations of setpoint, disturbances and process dynamics. Task is to find and train such artificial neural network to generate such approximation function which adequately approximates the unknown function f(.) using input-output data of process. Identification of the systems is based on the standard closed-loop circuit (Fig. 1).

Figure 1: Block diagram of closed-loop with MFA controller

Discrete MFA controller is designed as a 3-layer neural network Φ with proportional term. To ensure good control, trained neural network must be exact inversion of system feed-forward model, which we get as the expression of u(t) as the control action of controller in the form:

u(t) = e t ,e t−T ,e t−2T , ... ,e t−N−1T ;w Kc e t , (1)

where e - control error,T - sample time,N - number of last samples,w - weight vector of neural network,Kc - gain of controller.

In 1986 Dr. Rumelhardt with co-workers proposed a simple algorithm of adaptation of the weight coefficients of multilayer feed-forward networks with non-linear neurons - backpropagation or backwards propagation of error method (BP). The name of the method was divided from the method of calculation of the partial derivatives recurrently, from the highest to the lowest layer. That method was a generalization of Widrow-Hoff rule for multilayer artificial neural networks with nonlinear transfer functions, weights and bias change in the direction of negative change in the gradient of objective function. The goal of this method is to train to recognize and repeat certain patterns in iterative process, in which will also be adjusted such weights, to minimize chosen nonlinear objective function:

Es t =12

e2t =12[ r t −y t ]2 . (2)

Adaptative process of the neural network is realized by minimizing the objective function E with respect to the threshold and weight coefficients. We suppose that the activation function is nonlinear and differentiable. Partial derivative of the objective function with regard to the weight coefficients and with using rules for derivation composite functions can be written in the form:

w tT =w t − .g w t , (3)

g w t ≈∂Es t ∂w t , (4)

∂Es t ∂w t

=e t ∂e t ∂w t . (5)

Learning step η > 0 was calculated analytically in Matlab/Simulink to assess the stability of MFA controller. Fig. 2 shows dependence of learning step on the sampling period T graphically.

For design and training of the MFA controller was used NETLAB Toolbox in MATLAB. To MFA controller was designed, there was used three-layer neural network, which has one hidden layer with the same number of neurons as the input layer. Output layer has only one neuron. With increasing number of hidden neurons adaptation process of NN still provides better results (value of objective function for the testing set will be asymptotically close to zero).

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Journal of applied science in the thermodynamics and fluid mechanics Vol. 4, No. 2/2010, ISSN 1802-9388

Figure 2: Graphical dependence η(T)

3 MPC CONTROLLERPredictive control is a calculation of the sequence of control actions, which minimize the criterion of control, at a given constraints of control and controlled variables. Basic features of predictive control are:

• Specification of the reference trajectory and its prediction for the chosen horizon (Fig. 3).• Prediction of the system output based on the mathematical model of the system on the chosen

horizon.• Calculation of new control actions based on the minimizing the objective function and knowledge of

mathematical model of the system.• Correction of the predicted output based on the last measured outputs.

Basic elements of predictive control are: model of the process, objective function with constraints and optimization procedure. Input user parameters are: predictive and control horizon, the parameters of minimization function and constraints.

Mathematical expression of the problem of predictive control:

minuk /k , ... ,ukm−1/k

=l=1

p l

y∥y k l / l −r k l∥2l=1

m l

u∥u kl−1∥2 , (6)

where p - is horizon of output prediction, m - is horizon of control prediction,

r - reference trajectory.

u and y are weight matrices and marginal conditions are u∈⟨ulow ,uhigh⟩ ,u∈⟨u low ,u high⟩ , y∈⟨y low , yhigh⟩

One of the predictive control methods is the Dynamic Matrix Control (DMC). For calculation of control actions DMC uses mathematical model based on the transient response, which is obtained from measured process data.

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Journal of applied science in the thermodynamics and fluid mechanics Vol. 4, No. 2/2010, ISSN 1802-9388

Figure 3: Basic principle of predictive control

Let the system state in time k is defined as follows:

Y k = [ y 0 k y 1 k ⋮

y n−1k ] (7)

where y ik ≃y ki for u k j =0 ; j0 .

Described state contains full relevant information needed to predict the new state. Prediction of the future state:

[y k1/ky k2/k

⋮⋮

y kp /k] = [ y1k

y2k ⋮

y p k ] + [

s1u 0 ⋯ 0

s2u s1

u ⋯ 0⋮ ⋮ ⋯ ⋮sm

u sm−1u ⋯ s1

u

⋮ ⋮ ⋯ ⋮sp

u sp−1u ⋯ sp−m1

u] [

u k /k u k1/k

⋮⋮

u km−1/k ] + [

w y k1/k w yk2/k

⋮⋮

w y kp /k ] , (8)

where the vector y represents predicted state, vector y represents the effect of past inputs on the system, matrix of coefficients si

u of transient response is matrix of dynamics, vector w y represents the effect of un-modelled dynamics on process and vector u represents future control actions, which are results of optimization procedure.

Estimation of w y :

w y k /k ≈y mk − y 0k , (9)

where y m k - is measured value of output from process,y 0k - is first element of output vector prediction.

After definition of matrix M and lp.

M = [0 1 0 ⋯ ⋯ 00 0 1 0 ⋯ 0⋮ ⋮ ⋮ ⋮ ⋮ ⋮0 0 ⋯ ⋯ 0 10 0 ⋯ ⋯ 0 1

] , lp = [11⋮⋮1] , (10)

previous relations can be written into compact formY k =M Y k−1Su k−1lp ym k−1− y0k−1 . (11)

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Journal of applied science in the thermodynamics and fluid mechanics Vol. 4, No. 2/2010, ISSN 1802-9388

4 RESULTS AND CONCLUSIONThe design of MFA and MPC controller was implemented in simulation environment MATLAB. Properties comparison between these two controllers and PID controller was realized by simulation on the heating system control model based on the outdoor temperature compensation with room influence. The comparison criterion was the speed and accuracy of temperature control Ti in reference room at set-point steps Tid. The simulation results are shown in Fig. 4 and 5, where Tid is set-point of desired temperature in the reference room, Ti-PID is the actual value of temperature controlled by PID controller, Ti-MFA is the actual value of temperature controlled by MFA controller and Ti-MPC is actual value of temperature controlled by MPC controller.

Figure 4: Simulation results of PID and MFA controller

Figure 5: Simulation results of PID and MPC controller

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Journal of applied science in the thermodynamics and fluid mechanics Vol. 4, No. 2/2010, ISSN 1802-9388

Simulation results show that the MPC controller was slower than MFA controller, but room temperature control by MPC was with lower overshooting. PID controller was the fastest, but also less accurate. The best control results however can be achieved by tuning of parameters of PID controller. It follows that one of the possibilities of improving the heating process control based on outdoor temperature compensation is the combination of using classical PID algorithm with advanced artificial intelligence algorithms. Advanced control algorithms from the field of artificial intelligence can be used for tuning of parameters of classical PID controller if the controlled system parameters change in time. Generally, it is applicable for all other processes, in which there are the changes of static and dynamic characteristics of the controlled system in time.

For obtaining the best results, complex optimization procedures are required, which have also some limitation of these methods because they are relatively computing time consuming. But research is still active in this area. One of these optimization procedures is the procedure based on the genetic algorithms. This procedure is one of those very computing time consuming, but its contribution is that it gives suboptimal solution in the case of earlier termination of algorithm as boundary condition fulfils and can get out of the local extremes.

In spite of these problems, modern control algorithms for heating control based on the artificial intelligence combined with advantages of outdoor temperature compensation can contribute to improving of control of heating processes. Especially it is in the most modern control systems, which by their hardware and software support development of applications based on the artificial intelligence.

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ACKNOWLEDGEMENTSThe research work is supported by the Project of the Structural Funds of the EU, Operational Programme Research and Development, Measure 2.2 Transfer of knowledge and technology from research and development into practice. Title of the project: Research and development of intelligent control systems for biomass based heat production and supply. ITMS code: 26220220030

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