Control of Distributed Parameter Systems - Engineering Methods and Software Support in the MATLAB & Simulink Programming Environment
[chapter]
Gabriel Hulko, Cyril Belavy, Gergely Takacs, Pavol Bucek, Peter Zajicek
2011
MATLAB for Engineers - Applications in Control, Electrical Engineering, IT and Robotics
The first monographs in the field of DPS control have been published in the second half of the last century, where mathematical foundations of DPS control have been established. This mathematical theory is based on analytical solutions of the underlying PDE (Butkovskij, 1965; Lions, 1971; Wang, 1964) . That is the decomposition of dynamics into time and space components based on the eigenfunctions of the PDE. Recently in the field of mathematical control theory of DPS, publications on control
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... PDE have appeared (Lasiecka & Triggiani, 2000; ... ). An engineering approach for the control of DPS is being developed since the eighties of the last century (Hulkó et al., 1981 (Hulkó et al., -2010 . In the field of lumped parameters system (LPS) control, where the state/output quantities x(t)/y(t) -parameters are given as finite dimensional vectors, the actuator together with the controlled plant make up a controlled LPS. In this sense the actuators and the controlled plant as a DPS create a controlled lumped-input and distributed-parameter-output system (LDS). In this chapter the general decomposition of dynamics of controlled LDS into time and space components is introduced, which is based on numerically computed distributed parameter transient and impulse characteristics given on complex shape definition domains in 3D. Based on this decomposition a methodical framework of control synthesis decomposition into space and time tasks will be presented where in space domain approximation problems are solved and in time domain synthesis of control is realized by lumped parameter control loops. For the software support of modelling, control and design of DPS, the Distributed Parameter Systems Blockset for MATLAB & Simulink (DPS Blockset)www.mathworks.com/products/connections/ has been developed within the CONNECTIONS program framework of The MathWorks, as a Third-Party Product of The MathWorks Company (Hulkó et al., 2003-2010). When solving problems in the time domain, toolboxes and blocksets of the MATLAB & Simulink software environment such as for example the Control Systems Toolbox, Simulink Control Design, System Identification Toolbox, etc. are utilized. In the space relation the approximation t a s k i s f o r m u l a t e d a s a n o p t i m i z a t i o n p r o b l e m , w h e r e t h e O p t i m i z a t i o n T o o l b o x i s made use of. A web portal named Distributed Parameter Systems Controlwww.dpscontrol.sk has been created for those interested in solving problems of DPS control (Hulkó et al., 2003-2010). This web portal features application examples from different areas of engineering practice such as the control of technological and manufacturing processes, mechatronic structures, groundwater remediation etc. Moreover this web portal offers the demo version of the DPS Blockset with the Tutorial, Show, Demos and DPS Wizard for download, along with the Interactive Control service for the interactive solution of model control problems via the Internet. DPS -DDS -LDS Generally in the control of lumped parameter systems the actuator and the controlled plant create a lumped parameter controlled system. In the field of DPS control the actuators together with the controlled plant -generally being a distributed-input and distributedparameter-output system (DDS) create a controlled lumped-input and distributedparameter-output system (LDS).
doi:10.5772/20839
fatcat:7fgsuxgzz5hkxjk3xb5xci5peq