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H∞ CONTROL DESIGN OF A MULTITANK SYSTEM
Abstract
This paper considers MATLAB® modeling and simulation of H∞ controller and its realization on the Multitank System. The first task is to study the physical plant of the laboratory Multitank System and to apply a given mathematical model for optimal controller design. The general objective of the derived regulator is to reach and stabilize the level in the tanks by an adjustment of the pump operation or/and valves settings. Finally, it is necessary to simulate the obtained closed-loop system and to test its workability.
The recently introduced continuous-time perfect control algorithm has revealed a great potential in terms of the maximum-speed and maximum-accuracy behaviors. However, the discussed inverse model-originated control strategy is associated with considerable energy consumption, which has exceeded a technological limitation in a number of industrial cases. In order to prevent such an important drawback, several solutions could be considered. Therefore, an innovative perfect control scheme devoted to the multivariable real-life objects is investigated in this paper. Henceforth, the new IMC-related approach, strongly supported by the vital sensor-aided system, can successfully be employed in every real-time engineering task, where the precision of conducted processes plays an important role. Theoretical and practical examples strictly confirm the big implementation potential of the new established method over existing ones. It has been seen that the new perfect control algorithm outperforms the classical control law in the form of LQR (considered in two separate ways), which is clearly manifested by almost all simulation examples. For instance, in the case of the multi-tank system, the performance indices ISE, RT, and MOE for LQR without an integration action have been equal to 2.431, 2.4×102, and 3.655×10−6, respectively, whilst the respective values 1.638, 1.58×102, and 1.514×10−7 have been received for the proposed approach.
This article deals with the level controls in a laboratory two-tank system. The plant is strongly nonlinear due to the basic dynamic equations and the characteristics of the valves. We develop a nonlinear control law which achieves robust approximately time-optimal control over the full range of operation conditions. The development is based on ideas from fuzzy control, but in contrast to usual fuzzy controller designs, most of the rules are not derived from heuristics but rather are mathematical formulas which, together with the standard fuzzy quantization of the system's variables, approximate the time-optimal control law. This approximation is improved by heuristic rules which were gained from the observation of the behavior of the controlled plant. The resulting nonlinear control law exhibits a performance which is neither attainable with standard linear control nor with classical time-optimal control.< >
Simple state-space formulas are derived for all controllers
solving the following standard H <sub>∞</sub> problem: For
a given number γ>0, find all controllers such that the H
<sub>∞</sub> norm of the closed-loop transfer function is
(strictly) less than γ. It is known that a controller exists if
and only if the unique stabilizing solutions to two algebraic Riccati
equations are positive definite and the spectral radius of their product
is less than γ<sup>2</sup>. Under these conditions, a
parameterization of all controllers solving the problem is given as a
linear fractional transformation (LFT) on a contractive, stable, free
parameter. The state dimension of the coefficient matrix for the LFT,
constructed using the two Riccati solutions, equals that of the plant
and has a separation structure reminiscent of classical LQG (i.e. H
<sub>2</sub>) theory. This paper is intended to be of tutorial
value, so a standard H <sub>2</sub> solution is developed in
parallel
Design charts are given which permit the control engineer to select reasonable controller settings for liquid-level control loops by examining quantitatively the effects of these settings on damping coefficient, peak height, and rate of change of flow. The decrease in damping coefficient for a sequence of level tanks in series is quantified in an easy to use design chart.
Accurate control of the mold level in continuous casting is
believed to be a key factor in improving the quality of the cast
product. This paper describes an application of advanced control to this
problem leading to a complete recommissioning of the mold level control
system. Careful physical modeling identified smooth as well as nonsmooth
nonlinearities in the process. Three different control strategies were
implemented and evaluated. The article also describes some of the steps
necessary to bring advanced control to practical reality, including
safety, rapid prototyping, online tuning, and economic evaluation
Robust Control Systems: analysis and synthesis with MATLAB®, ABC Techniques
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User's Manual, inteco.com.pl
- Multitank Inteco
- System
INTECO, Multitank System, User's Manual, inteco.com.pl, 2008.
- R L Street
- G Watters
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