Emphasizing an Expanded Optimal Control Policy for a Coupled Tanks System with Random Disturbance | Chapter 5 | Theory and Practice of Mathematics and Computer Science Vol. 5

 An significant study in the control engineering and process industries is a coupled tank system, consisting of a joint of two tanks together via pipes in order to reserve water at the operating height level. An extended optimal control policy is proposed in this paper to research the system of coupled tanks, where random disturbance is applied to the system. Because the dynamics of the coupled tank system can be formulated as a nonlinear system, it is useful for operational decisions to assess the optimum water level in the tanks. In this respect, the dynamics of the coupled tank system are typically linearized to give the operating height of the steady state. In our strategy, to obtain the true operating height of the real coupled tank system, a model-based optimal control problem is considered, which is introduced with modified parameters. The variations between the real plant and the model used are calculated repeatedly during the computation process, where the optimal solution of the model used is modified. System optimization and parameter estimation are integrated on this basis. At the end of the iteration, despite model-reality variations, the iterative solution approximates the correct optimal solution of the original optimal control problem. In conclusion, the efficiency of the solution proposed is seen. With the use of filtering techniques, the optimal solution of the coupled tank method with random disturbance could be further improved. Therefore, in future studies, it is proposed to determine the optimal filtering solution of the coupled tank system with random disruption.

Author(s) Details

Sie Long Kek
Department of Mathematics and Statistics, Universiti Tun Hussein Onn Malaysia, Pagoh, Malaysia.

Sy Yi Sim
Department of Electrical Engineering Technology, Universiti Tun Hussein Onn Malaysia, Pagoh, Malaysia.

Chuei Yee Chen
Department of Mathematics, Universiti Putra Malaysia, Serdang, Malaysia.

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Study on Discrete-Time Nonlinear Stochastic Optimal Control Problem Based on Stochastic Approximation Approach | Chapter 4| Theory and Practice of Mathematics and Computer Science Vol. 5

 An fascinating research subject is the nonlinear optimal control problem, which is interrupted by random noises. In the presence of random sounds, it was not possible to calculate precisely the entire state trajectory. A theoretical approach for solving the discrete-time nonlinear optimal control problem is proposed in this paper, which is interrupted by a series of random noises. Since it is impossible to obtain the exact solution to such an optimal control problem, estimating the dynamics of the state is currently necessary. Here, it is believed that the output from the actual plant process can be calculated. In our strategy, in order to construct a linear model-based optimal control problem, where the model output is measurable, the state mean propagation is used. An output error that takes account of the differences between the actual output and the model output is defined on this basis. Then, applying the stochastic approximation approach, this output error is minimised. The stochastic gradient is defined during the computation process, in order to iteratively update the optimal solution of the model used. Once the convergence is reached, in spite of model-reality variations, the iterative solution approximates the true optimal solution of the original optimal control problem. An example of a continuous stirred-tank reactor problem is examined for illustration, and the result obtained shows the applicability of the proposed solution. The efficiency of the proposed solution is, therefore, strongly recommended.

Author(s) Details

Sie Long Kek
Department of Mathematics and Statistics, Universiti Tun Hussein Onn Malaysia, Pagoh, Malaysia.

Sy Yi Sim
Department of Electrical Engineering Technology, Universiti Tun Hussein Onn Malaysia, Pagoh, Malaysia.

Wah June Leong
Department of Mathematics, Universiti Putra Malaysia, Serdang, Malaysia.

Professor Kok Lay Teo
Department of Mathematics and Statistics, Curtin University of Technology, Perth, Australia.

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