Design of Model Predictive Controller for Pasteurization Process

This research paper is about developing a better type of controller, known as MPC (Model Predictive Control) for pasteurization process plant. MPC is an advanced control strategy that uses the internal dynamic model of the process and a history of past control moves and a combination of many different technologies to predict the future plant output.. The dynamics of the pasteurization process was estimated by using system identification from the experimental data. The quality of model structures like ARX, ARMAX, BJ and CT model structures was checked based on best fit with validation data, residual analysis and stability analysis. Auto-regressive with exogenous input (ARX322) model was chosen as a model structure of the pasteurization process dynamics and fits about 79.75% with validation data. Finally MPC control strategies were designed using ARX322 model structure.


Introduction
In a modern world the economic and quality issues become more and more important, efficient control systems have become indispensable.Therefore the process industries require more reliable, accurate, robust, efficient and flexible control systems for the operation of process plant.In order to fulfill the above requirements there is a continuing need for research on improved forms of control.[1] Control of temperature plays an important role in pasteurization plants.High temperature short time (HTST) is keeping milk or other food stuffs at 72 0C for 15 seconds in insulated holding tube.The pasteurization process consists of three stages like regeneration, heating and cooling sections.The crucial stage is heating process using heat exchanger to ensure unpasteurized product achieve desired pasteurization temperature before pass through holding tube and cooling sections.Prior to pasteurize milk sample, the equipment must have adequate controller to control the outlet temperature in order to maintain at standard value.[2] The proportional integral (PI) and proportional integral derivative (PID) controllers are widely used in many industrial control systems because of its simple structure.These controllers are designed without process constraints only use mathematical expression based on error from a set point.In these circumstances, conventional controllers (PI and PID) are no longer to provide adequate and achievable control performance over the whole operating range.Thus designing a controller considering the process constraints and optimize the control performance is essential.[3] Model Predictive Control also known as receding horizon control, is an advanced strategy for optimizing the performance of multivariable control systems.MPC generates control actions by optimizing an objective function repeatedly over a finite moving prediction horizon, within system constraints, and based on a model of the dynamic system to be controlled.[4]

Process Description
The plant PCT23, manufactured by Armfield (UK), is a laboratory version of a real industrial pasteurization process.It consists of a bench-mounted process unit to which is connected a dedicated control console.An interface card DT2811 is used for monitoring and controlling the process through a computer.

Experimental Setup 3.1. Input-Output Data
The input-output data was generated by introducing step input in milk flow rate, hot water flow rate and power input, then by recording pasteurization temperature response.The experiment was repeated two times for model estimation and validation purpose.

System identification
The input-output data was analyzed by the System Identification toolbox in MATLAB.The continuous and discrete model structures were tried to select the model structure that have best fit with validation.Then the selected model structure is tested for residual analysis and pole-zero analysis to check the model stability.The continuous time (CT) model, Autoregressive with exogenous input (ARX) model structures, ARMAX (auto regressive with moving average and exogenous (or extra) input model, and state space model structures were tried get best model structure in terms of best fit with validation data and model stability for further controller design.[6] Best fit is calculated as: where: y is validation data, ̂ is estimated data and ̅ is mean of validation data After selection of best fit model structures model quality analysis like residual and pole zero location should be checked to select a nice and simple model for further controller design.The prediction error or residual is the key quantity.
It is defined as: The stability of a system can be easily inferred by examining the pole locations of the transfer function.[7].

Controller Design
Controllers are basically employed in a closed loop control system.Closed loop control system is one that automatically changes the output based on the difference between the feedback signals to the input signal.Controller is an element used to produce manipulated variable from error variable, for Control action.

Model Predictive Control
The model predictive uses quadratic minimization problem defined as: Subject to: input and output constraints of the system.Where is the set point, Q1 is output weight and Q2 is input weight.The size of this minimization function and weight matrixes are depend on prediction and control horizon.[10][11]

Results and Discussions 4.1. Model Structure selection
First step input was introduced at different time on milk flow rate, water flow rate and heater power to collect pasteurization temperature data with those three inputs.Two different experiments were done to collect the data for model estimation and validation purpose until it reaches to stability.The continuous time model fits 82.77% with the validation data better than the others.ARX422 (81.03% fit), ARMAX3202 (80.9% fit).The continuous time model doesn't mean a good model rather further analysis will be needed to select best model.

Model Quality Analysis 4.2.1. Residual Analysis
For different model structures the auto corelation of residuals for the output (whitness test) and cross correlation of residuals with the input (independence test) were analyzed.From the graphs the horizontal scale is the number of lags, which is the time difference (in samples) between the signals at which the correlation is estimated.The upper and lower bounds on the plot represents the confidence interval of the corresponding estimates.Any fluctuations within the confidence interval are considered to be insignificant.A good model should have residuals uncorrelated with past inputs (independence test) and past outputs (whitness test).For poor models either auto and cross corelation residuals or two of residuals is out of the confidence region.In our case 99.9% confidence interval is taken.From Figure 3, the BJ10021 model is failed the analysis because both of auto and cross correlation residual analysis is out of the confidence region.The continuous time (CT) model also failed the analysis due to its auto correlation is out of the limit.ARMAX3202 and ARX422 models pass the residual analysis, but further analysis should be taken to select best model structure.

Stability Analysis
The pole-zero location on the unit circle can tell as the stability of the process model.Poles are detrimental for the process stability.If all poles are inside a unit circle, the process model is stable.If one or more of its poles on unit circle, it is marginally stable.If one of its poles out of a unit circle, it is unstable.When we see Figure 5 one of its pole is on a unit circle, this means the process model is marginally stable.The process model is not selected because it has the chance to become unstable.

Model Reduction
When the model order reduced ARX gives slight decrease of fit..When the ARX422 is reduced to ARX322 the final prediction error is 0.035.Therefore ARX322 can represent the model.Further reduction below this order deteriorates the fit percent with validation data.The reduced model also passes the model quality analysis.Therefore the ARX322 model represents the pasteurization process dynamics.

Conclusions
Maintaining the temperature at a constant value is a critical issue in many of the Industries.MPC fulfills these types of difficulties by bringing the process variable to the desired set point as early as possible.MPC controller is more suitable for complex process control like milk pasteurization processes.From the simulation results, the MPC controller removes overshoot, but the control action is sluggish.to track set point immediately.This controller performance may be best, if it is used for real time pasteurization process environment.

Figure 2 .
Figure 2. Percent fit of different model structures with validation data (zv).

Figure 3 .
Figure 3. Residual analysis of model structures