State Estimation and Optimal Control of Four-Tank System with Stochastic Approximation Approach

Authors

• Xian Wen Sim Department of Mathematics and Statistics, Universiti Tun Hussein Onn Malaysia, Johor, Malaysia
• Sie Long Kek Department of Mathematics and Statistics, Universiti Tun Hussein Onn Malaysia, Johor, Malaysia
• Sy Yi Sim Department of Electrical Engineering, Universiti Tun Hussein Onn Malaysia, Johor, Malaysia
• Jiao Li School of Mathematics and Statistics, Changsha University of Science and Technology, Hunan, China

Keywords:

four-tank system, nonlinear optimal control, stochastic approximation, state estimation

Abstract

This study aims to optimally control the level of a four-tank system at the steady state in the random disturbance environment using the stochastic approximation (SA) approach. Firstly, the stochastic optimal control problem of an equivalent discrete-time is introduced, where the voltages to the pumps are the control inputs. By minimizing the sum of squared errors, the liquid levels are estimated. Then, first-order necessary conditions are derived by defining the Hamiltonian function. Thus, the optimal voltages are calculated based on the estimated liquid levels to update the gradient of the cost function. Finally, for illustration, parameters in the system are considered and a simulation is conducted. The simulation results show that the state estimation and control law design can perform well, and the liquid levels are addressed along the steady state. In conclusion, the applicability of the SA approach for handling a four-tank system with random disturbances is demonstrated.

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2023-04-01

How to Cite

[1]
Xian Wen Sim, Sie Long Kek, Sy Yi Sim, and Jiao Li, “State Estimation and Optimal Control of Four-Tank System with Stochastic Approximation Approach”, Adv. technol. innov., vol. 8, no. 2, pp. 150–161, Apr. 2023.

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