Identification And LQ Digital Control Of A Set Of Equal Cylinder Atmospheric Tanks - Simulation Study

Time-delays (dead time) are found in many processes in industrial practice. Time-delays are mainly caused by the time required to transport mass, energy and information. In many cases time-delay is caused by the effect produced by the accumulation of a large number of low-order systems. One of possibilities of control of such processes is their approximation by lower-order model with time-delay. The contribution is focused on the design of an algorithm for digital control of highorder process that is approximated by a second-order model with time-delay. The controller algorithms use the digital modification of the linear quadratic (LQ) Smith predictor (SP). The LQ criterion was combined with pole assignment principle. These algorithms were applied to the control of a set of equal liquid cylinder atmospheric tanks. INTRODUCTION Some technological processes in industry are characterized by high-order dynamic behaviour or large time constants and time-delays. For control engineering, such processes can often be approximated by the FOTD (first-order-time-delay) model. Timedelay in a process increases the difficulty of controlling it. However using the approximation of a high-order process by a lower-order model with time-delay provides simplification of the control algorithms. Let us consider a continuous-time dynamical linear SISO (single input ( ) u t – single output ( ) y t ) system with time-delay L. The transfer function of a pure transportation lag is Ls e where s is a complex variable. Overall transfer function with time-delay is in the form ( ) ( ) Ls L G s G s e = (1) where ( ) G s is the transfer function without time-delay. Processes with time-delay are difficult to control using standard feedback controllers. When a high performance of the control process is desired or the relative time-delay is very large, a predictive control strategy must be used. The predictive control strategy includes a model of the process in the structure of the controller. The first time-delay compensation algorithm was proposed by (Smith 1957). This control algorithm known as the Smith predictor contained a dynamic model of the time-delay process and it can be considered as the first model predictive algorithm. Historically first modifications of time-delay algorithms were proposed for continuous-time (analogue) controllers using various approaches. In industrial practice, the implementation of the timedelay compensation algorithms on continuous technique is difficult. One of possible approaches to control of process with time-delay is digital Smith predictor based on polynomial theory. Polynomial methods are design techniques for complex systems (including multivariable), signals and processes encountered in control, communications and computing that are based on manipulations and equations with polynomials, polynomial matrices and similar objects. Systems are described by input-output relations in fractional form and processed using algebraic methodology and tools (Šebek and Hromčík 2007). Controller design consists in solving polynomial (Diophantine) equations. This paper is oriented to design of a robust LQ control using polynomial theory. The Diophantine equations can be solved using the uncertain coefficient method – which is based on comparing coefficients of the same power. This is transformed into a system of linear algebraic equations (Kučera 1993). The digital pole assignment Smith predictor was designed using a polynomial approach in (Bobál et al. 2011). The design of this controller was extended by a method for a choice of a suitable pole assignment of the characteristic polynomial. Because the classical analogue Smith predictor is not suitable for control of unstable and integrating time-delay processes, the polynomial digital LQ Smith predictor for control of unstable and integrating time-delay processes has been designed in (Bobál et al. 2014). Proceedings 30th European Conference on Modelling and Simulation ©ECMS Thorsten Claus, Frank Herrmann, Michael Manitz, Oliver Rose (Editors) ISBN: 978-0-9932440-2-5 / ISBN: 978-0-9932440-3-2 (CD) It is obviou industrial pra uncertainties implementati Some adaptiv Smith predic 1993); Bobá controllers w (Bobál et al. The paper i general prob with regard Section 1. T predictor is system (a se tanks) is an description o of the prima components proposed in individual co in Section 6. PRINCIPLE The discrete are more su industrial pra (see Hang et function of th analogue ver