School of Engineering, Universidad Pontificia Bolivariana, Medellín 050031, Colombia.
Grupo de Investigación en Desarrollo Tecnológico GIDESTEC, Universidad Nacional Abierta y a Distancia, Carrera 45 # 55-19, Medellín 050012, Colombia.
Sensors (Basel). 2020 Nov 25;20(23):6738. doi: 10.3390/s20236738.
This paper addresses the observability analysis and observer design for a nonlinear interacting three-tank system. The plant configuration is first described using the process and instrumentation diagram (P&ID) and a state-space realization is derived; some insights about the behavior of the nonlinear system, considering equilibrium points and the phase portrait are provided. Then, observability in the Hermann-Krener sense is analyzed. A high-gain observer (HGO) is then designed, using the equivalence of the original state-space realization with its observability canonical form, in order to guarantee convergence of the state estimation. The performance was validated through simulation and experiments in a multipurpose plant equipped with real sensors; the HGO response was compared to a Luenberger observer (for a linear approximation of the plant) and the Extended Kalman Filter (for which convergence is not guaranteed), considering nonlinearities, interaction, disturbances and noise. Theoretical and experimental results show that the HGO can provide robust estimation and disturbance rejection, despite the sensitivity of HGOs to noisy variables in processes such as level of liquids.
本文针对非线性互扰三容水箱系统进行了能观性分析和观测器设计。首先利用过程和仪表图（P&ID）描述了系统结构，推导出了状态空间模型；提供了一些关于考虑平衡点和相图的非线性系统行为的见解。然后，从赫尔曼-克伦纳意义上分析了能观性。利用原始状态空间模型与其可观性规范型的等价性，设计了一个高增益观测器（HGO），以保证状态估计的收敛性。通过在配备实际传感器的多功能工厂中的仿真和实验验证了性能；将 HGO 的响应与线性化的 Luenberger 观测器（针对系统的线性近似）和扩展卡尔曼滤波器（其收敛性无法保证）进行了比较，同时考虑了非线性、交互、干扰和噪声。理论和实验结果表明，尽管 HGO 对液体水平等过程中噪声变量的敏感性，但 HGO 可以提供鲁棒的估计和干扰抑制。
