具有时变采样周期的水箱液位系统保性能控制

GUARANTEED-COST CONTROL OF A TWO-TANK SYSTEM WITH TIME-VARYING SAMPLING PERIODS

研究了具有控制输入饱和约束和时变采样周期的水箱液位系统保性能控制问题.首先,基于液体动力学对水箱液位系统进行建模,并用M序列激励水箱得到的实测数据进行模型验证.其次,根据采样周期的不同,将液位系统建模成一个具有多个子系统的离散时间切换系统.基于李雅普诺夫稳定性原理及平均驻留时间方法,给出具有控制输入饱和约束的最优保性能的状态反馈控制器存在条件,并将控制器增益的求解转化为一个凸优化问题.最后,将控制算法应用于水箱液位系统实验平台.实验结果验证了控制算法的有效性.

This paper is concerned with the guaranteed-cost control problem for a two-tank system with the time-varying sampling periods and control input saturation constraint. Firstly, by using the hydrodynamics theory, a mathematical model of the two-tank system is established. The effectiveness of the mathematical model is verified by the measurements of system exciting by an M sequence. Then, the closed-loop system is modeled as a discrete-time switching system according to the variations of different sampling periods. Based on the Lyapunov stability theory and the average dwell-time method, an optimally guaranteed-cost feedback control controller with control input saturation constraint is designed. The controller gain is obtained by solving a convex optimization problem. Finally, experiments on the real two-tank system are performed, which shows the effectiveness of the proposed control algorithms.