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

Xian Wen Sim, Sie Long Kek, Sy Yi Sim, Jiao Li
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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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四缸系统状态估计与最优控制的随机逼近方法
本研究旨在使用随机近似(SA)方法,在随机扰动环境下,将四缸系统的液位最优控制在稳态。首先,引入了等效离散时间的随机最优控制问题,其中泵的电压是控制输入。通过最小化误差平方和,可以估计液位。然后,通过定义哈密顿函数,导出了一阶必要条件。因此,基于估计的液位来计算最佳电压,以更新成本函数的梯度。最后,为了便于说明,考虑了系统中的参数,并进行了仿真。仿真结果表明,状态估计和控制律设计能够很好地执行,并且液位沿着稳态进行处理。最后,证明了SA方法在处理具有随机扰动的四箱系统时的适用性。
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来源期刊
Advances in Technology Innovation
Advances in Technology Innovation Energy-Energy Engineering and Power Technology
CiteScore
1.90
自引率
0.00%
发文量
18
审稿时长
12 weeks
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