Stanislav Talas

Multivariable gain scheduled control of two funnel liquid tanks in series

This paper presents a concept of the continuous-time gain scheduled 2DOF control for the nonlinear system of two funnel liquid tanks in series, based on linearization of nonlinear equations of the system about selected operating points. Discussed technique extends the idea of design via linearization approach. In order to achieve desired stability and performance requirements, a linear feedback controller is designed at each point. Based on this strategy, polynomial method is taken into account. Specifically, the exact pole placement method as well as weighting matrix, dividing weights among numerators of transfer function matrices of subcontrollers guarantee control quality. The parameters of the resulting family of linear controllers are scheduled as functions of reference variables, resulting in a single feedback matrix controller. The derived gain scheduled controller is implemented and applied on the illustrative nonlinear model of two funnel liquid tanks in series.

LQ Control Of Heat Exchanger - Design And Simulation.

Heat exchangers are devices whose primary responsibility is the transfer (exchange) of heat, typically from one fluid to another. However, they are not only used in heating applications, such as space heaters, but are also used in cooling applications, such as refrigerators and air conditioners. Heat exchange processes often contain time-delay. This paper deals with design of universal and robust digital control algorithms for control of great deal of processes with time-delay. These algorithms are realized by the digital Smith Predictor (SP) based on polynomial approach – by minimization of the Linear Quadratic (LQ) criterion. For a minimization of the LQ criterion is used spectral factorization with application of the MATLAB polynomial Toolbox. The designed polynomial digital Smith Predictors were verified in simulation conditions. Simulation model for a verification of the designed control algorithms was realized using experimental measured data on the laboratory heat exchanger. The program system MATLAB/SIMULINK was used for simulation of the designed algorithms.

Measurable Error Compensation with GPC in a Heat-Exchanger with a Traffic Delay

This paper demonstrates use of Model Predictive Control (MPC) to system control with delay. Generalized Predictive Control (GPC) method was selected to demonstrate the ability to both control the system and compensate the measurable disturbance while bot the system and the disturbance are delayed. For the realization the MATLAB/SIMULINK program environment was used with system parameters based on the laboratory system. GPC method was chosen and its ability to compensate the outer disturbance with delay was verified by simulation of system control based on real laboratory model. Control algorithm and simulation were realized in MATLAB/SIMULINK program environment. Results have proven capabilities of GPC method to control and compensate error in stable, oscillatory and non-minimum phase systems with traffic delay. Additionally, real model parameters were selected to test a possibility of realization.

Nonlinear Gain Scheduled Controller For A Sphere Liquid Tank.

In this paper, we develop a gain-scheduled controller for a nonlinear plant of the sphere liquid tank. The proposed strategy is based on linearization of the nonlinear state equation around selected operating points. This methodology allows to apply any linear control design method. In particular, we discuss a polynomial method to achieve desired stability and performance requirements. Following this idea, both 1DOF and 2DOF control configurations are considered. The linear design methods are applied at each operating point in order to arrive at a set of linear control laws. Additionally, the parameters of the resulting family of linear controllers are scheduled as functions of reference variable, resulting in a single controller. Nonlocal performance of gain scheduled controller for the nonlinear model is checked by mathematical simulation.

Use of Dynamic Matrix Control in Simulation of Heat System.

This paper demonstrates the use of Model Predictive Control (MPC) to system control. Dynamic Matrix Control (DMC) method was chosen and its functionality was verified by a simulation of system control based on a real laboratory model. A control algorithm and the simulation were realized in MATLAB/SIMULINK program environment. Results have proven capabilities of DMC method to control stable oscillatory and nonminimum phase systems. Additionally, real model parameters were tested with a demonstration of a possibility of tuning by a ratio of weighting values form objective function. INTRODUCTION Considering the scientific area of process control, it targets at present tendency of satisfying demands of the maximal productivity of the highest quality products at the lowest cost possible. With the power of the modern computing technology an approach of finding optimal results in reasonable time was made possible. Advanced methods popular in industries with slow and large dimensional systems are predictive control methods (Qin & Badgwell, 2003). These techniques commonly contain an internal model for system behavior predictions. Gained information is further used to calculate a sequence of control inputs by minimizing a sum of squares between the desired and predicted trajectories. Therefore an optimal output is received in reference to the minimal error, eventually to the change of control inputs. Development in this area started in 1980s with the publication of DMC method (Cutler & Ramaker, 1980). Original purpose of DMC was focused on multivariable constrained control problems, mainly occurring in chemical and oil industry. The influence of DMC caused its widespread use in world’s major industrial companies (Morari & Lee, 1999). Over the time there was a vast development of the DMC algorithm, its modifications and possibilities of application. (Garcia & Morshedi, 1986) provided a utilization of a quadratic algorithm for an efficient handling of constraints, tuning and robustness. (Shridhar & Cooper, 1997) suggested a tuning strategy of DMC parameters for SISO systems, followed by an approach in case of MIMO systems (Shridhar & Cooper, 1998). (Dougherty & Cooper, 2003) described an approach to tune the parameters of the basic DMC algorithm for the case of integrating processes. In occurrence of nonlinear processes (Dougherty & Cooper, 2003) suggested a new adaptive control strategy using the output of multiple linear DMC controllers to maintain the performance over a wide range of operational levels. The purpose of this paper is to give an insight on abilities of DMC options for the control of stable processes, primarily in the area of tuning its performance by changing the weight ratio of the optimization process between the output error and a demand of action value. The paper is organized in the following way. General principles of MPC are presented first, followed by the description of specific properties of the DMC method. Basic functionality and characteristics are introduced. The final section presents the implementation of the simulation into the MATLAB/SIMULINK program environment and its results. MODEL PREDICTIVE CONTROL Predictive control is an approach to control a process trough optimization. The main principle is in the prediction of future process outputs based on the inner model of the process. The goal of the control algorithm is to find such a vector of input values that the output of the model is optimal along the defined time area called horizon. To ensure robustness and stability an approach using feedback called the receding horizon strategy is often applied. From the vector of input values only the first value is used as an increment ∆u(k) added to the previous input giving the current input value u(k). In the next step the entire procedure is repeated with new process output values. The area of the optimization is defined by values of horizons representing the amount of sampling periods from the current time into the future. Values of horizons N1 and N2 limit the area, where the divergence between the desired and the output value is minimized. The horizon Nu limits the distance of steps where the action value is minimized. Proceedings 28th European Conference on Modelling and Simulation ©ECMS Flaminio Squazzoni, Fabio Baronio, Claudia Archetti, Marco Castellani (Editors) ISBN: 978-0-9564944-8-1 / ISBN: 978-0-9564944-9-8 (CD) Figure 1: Receding horizon strategy Calculation of the optimal output consists of a free response prediction describing the system behavior in the case of a constant input and the forced response with a reaction on a suggested series of inputs. Based on the superposition principle, the sum of these responses results in the future output prediction. Several methods of MPC are used in practice; the main differences are in the description of the controlled process and in the objective function. The Figure 2 shows a layout of the predictive control and a data transfer. Figure 2: Basic structure of model predictive control The optimization process is based on the minimization of values involved in control. Their mutual relations are formed by an objective function. The general expression of an objective function is     , ) 1 ( ) ( ) ( ) ( ˆ ) ( 1 2 2 2 1             u N

Predictive Control Adapting to Fractional Values of Time Delay

A combination of identification and control procedures is presented which is aimed at precise control of systems with any value of time delay. Suggested strategy allows the predictive controller to adapt its parameters to a value of the time delay identified during the control process. The system flexibility resides in the ability to work precisely even with time-delay values that are not integer multiples of the sampling period. Overall, the designed approach presents a more precise method to control systems with both static and variable cases of time delay.

State-Space Predictive Control Of Inverted Pendulum Model.

This paper presents a possible way to control the a very fast nonlinear systems. The system of the inverted pendulum was chosen as an exemplar process. This is an example of the nonlinear single-input multi-output process with a sampling period in order of milliseconds. The state-space predictive control was chosen as a control method and the system is described by CARIMA model. The whole process of the controller design is described in this paper. That includes a description of the inverted pendulum nonlinear mathematical model and its linearization, the inference of the output values prediction and the control signal calculation. The control signal is calculated by predictor-corrector method. The results compare several optimization methods to achieve the fastest calculation of the control signal. All of the simulation was done in Matlab. INTRODUCTION In real life we can come across with many types of processes. Many of them are nonlinear and their mathematical models are very complex. Even the sampling period can be very different. This paper focuses on the very fast processes with a sampling period in the order of milliseconds. The basic control methods may not handle with this situation with required precision so we need a more advanced method. The predictive control is a great example of the modern control method that can be used to solve the complex control problems (Bobál 2008). This method belongs to the model based control methods and the mathematical model is used for the output values prediction. This prediction is determine on the chosen time horizon that should be long enough to cover the step response of the controlled system. The model of the inverted pendulum is described by the state-space CARIMA mathematical model for the single-input multi-output (SIMO) system (Bars et al. 2011; Wang 2009). The control signal calculated by the predictive control ensures the desired output values in the near future time horizon. This is achieved by minimization of the cost function that usually has a quadratic form and it minimize the differences between the reference value and the output value and the control signal increments. If the process require some kind of the process variable constraints, several method such as quadratic programming method, fast-gradient method, predictorcorrector method etc. can be used to minimize the cost function (Camacho and Bordons 2004; Maciejowski 2002; Rossiter 2003). However, the chosen CARIMA mathematical model used to the prediction of the output values works only for the linear models so the nonlinear mathematical model of the inverted pendulum needs to be linearized. This paper is divided into the following sections. The model of the inverted pendulum is described in the first section. The predictive control and the calculation of the control signal are described next. The final sections shows the results of the research and the conclusion (Albertos Peréz and Sala 20014; Hangos et al. 2004). MATHEMATICAL MODEL OF THE CONTROLLED SYSTEM The Amira PS600 inverted pendulum system was used as the exemplar model. The photo of this system is shown at figure 1. The main parts of the system are cart driven by servo amplifier and the pendulum rod attached to the cart (Amira 2000; Chalupa and Bobál 2008). Figure 1 : Amira PS600 Inverted Pendulum system The inverted pendulum system is an example of the single-input two-output system. The force produced by the DC motor that moves with the cart is the input variable and the cart position and the angle of the pendulum rod are the output variables. The figure 2 shows the analysis of the forces acting in the system (Amira 2000; Chalupa and Bobál 2008). Proceedings 31st European Conference on Modelling and Simulation ©ECMS Zita Zoltay Paprika, Péter Horák, Kata Váradi, Péter Tamás Zwierczyk, Ágnes Vidovics-Dancs, János Péter Rádics (Editors) ISBN: 978-0-9932440-4-9/ ISBN: 978-0-9932440-5-6 (CD) Figure 2 : Analysis of the inverted pendulum The variables in the figure 2 are following. The angle of pendulum rod is φ, M0 and M1 stands for the weight of the cart and pendulum respectively, lS is a distance between centre of gravity of the pendulum and the centre of rotation of the pendulum and g is the gravity acceleration constant. Symbol F represents the force produced by the DC motor. The affect of the pendulum on the cart can be expressed as a horizontal and a vertical forces described by the equations (1) and (2)

Predictive Control Of A Series Of Multiple Liquid Tanks Substituted By A Single Dynamics With Time-Delay.

The article focuses on control of a system consisting of a series of liquid tanks. Accumulation of individual dynamics causes, that the overall system exhibits high order behaviour. Another effect is a summation of slow responses of individual systems on an input signal leading to a significant time gap in reaction time of the whole system. In order to make control operations more straightforward and increase calculation speed, the mathematical description of gathered dynamics was approximated into a simplified form containing timedelay. The resulting form of the system is regulated by a predictive controller with time-delay compensation. The whole process is simulated in the Matlab environment.

1DOF Gain Scheduled PH Control Of CSTR.

Motivated by the rich dynamics of chemical processes, we present a gain scheduled control strategy for a pH neutralization occurring inside continuously stirred tank reactor built on a linearization of a nonlinear state equation about selected operating points. Firstly, we address the problem of a selection of scheduling variable. Based on this, an extra scheduling mechanism is presented to simulate the behavior of a nonlinear process using a linear model. Specifically, the proposed step aims at extending the region of validity of linearization by introducing a parametrized linear model, which enables to construct linear controller at each point. Finally, the parameters of resulting family of linear controllers are scheduled as functions of the reference variable, resulting in a single scheduling controller.

State-Space Predictive Control of Two Liquid Tanks System

This paper presents a process control method called the predictive control used to control a nonlinear process about a selected operating point. The system of the two funnel liquid tanks in series is chosen as an exemplar process. The predictive control is used in its state-space modification for CARIMA mathematical model. This paper describes the linearization process of the nonlinear system at the operating point and a process of a control signal calculation. The designed controller is verified on the process without and with a time-delay.