Optimization of slosh suppression system through data-driven state feedback controller - Nurul Najihah, Zulkifli (2024)
The nature of the slosh motion phenomenon has commonly been found in various engineering applications. The phenomenon is present due to an oscillation liquid motion form in an open free-space container. For some events, the sloshing may cause functionality issues to the overall system due to the existence of unrestrained movement from the massive motion. It leads to overall system failure and eventually may give some changes to the dynamic system structure. Moreover, the slosh system is categorized as a nonlinear underactuated system. It is well-known for its complexities and controlling the system would be considered challenging. It is impossible to construct a global model, and the unmodelled system would make the model-based control approach difficult to apply. Thus, there is a growing interest in proposing objectives for constructing a suitable feedback controller design and developing a data-driven control algorithm to achieve stability. To reduce the dependency of the practical use on the mathematical model system in control theory as in model-based control, the data-driven control approach has demonstrated a promising result over the past few years. The general view of the data-driven control framework is to obtain the optimal solution of the controller’s parameter by only using the recorded input and output data system without any mathematical model system. The advantages of the closed-loop control are considered in the state feedback controller that promotes robustness and simplicity of the control structure. The implementation of the state feedback controller only would produce a large steady-state error. Hence, an integral term is added to eliminate such a signal. The state feedback controller with an integral term closed-loop control system is considered a control law action to be implemented and partial linearization is used to linearize the nonlinear system into a linear state space representation. Then, the linear system is discretized to be evaluated in the data-driven control approach. By performing a one-shot experiment, the initial input-output data is generated, recorded, and properly rearranged to be utilized to solve the control problem based on the Data-driven Linear Matrix Inequality (LMI), Data-driven Pole Placement, and Fictitious Reference Iterative Tuning-Particle Swarm Optimization (FRIT-PSO) to compute the control problem. The comparative assessment is investigated between the selected model-based control approaches and the proposed data-driven control approaches based on the numerical example of the state’s time response performance and performance evaluation assessment value of Integral Square Error (ISE), Integral Absolute Error (IAE), and Integral Time-weighted Absolute Error (ITAE). The analysis is carried out and evaluated using MATLAB Simulink software. Without any explicit mathematical dynamic system, the system performance after being tuned by data-driven LMI indicates a comparable response to model-based LMI control. The performance based on data-driven LMI generates values of 2.2365 ISE, 1.6654 IAE, and 2.9008 ITAE are smaller than model-based LMI and showcase an average improvement of 6.78%. Furthermore, the control problem based on Data-driven Pole Placement and FRIT-PSO improved the performance system and exhibited identical responses as the desired system. Data-driven pole placement has produced the values of 0.0038 ISE, 0.08 IAE, and 0.1806 ITAE with an average improvement of 3.31% compared to Model-based Pole Placement. Meanwhile, the FRIT-PSO produced values of 0.0039 ISE, 0.0844 IAE, and 0.1886 ITAE with an 11.96% average improvement compared to Model-based LQR-LMI. The results clarify that the data-driven control approaches are effective in repositioning the partially filled liquid container to its intended position following the desired responses while simultaneously maintaining the slosh angular motion at a minimum angle.