Full Information H2 Control of Borel-Measurable Markov Jump Systems with Multiplicative Noises

This paper addresses an H2 optimal control problem for a class of discrete-time stochastic systems with Markov jump parameter and multiplicative noises. The involved Markov jump parameter is a uniform ergodic Markov chain taking values in a Borel-measurable set. In the presence of exogenous white noise disturbance, Gramian characterization is derived for the H2 norm, which quantifies the stationary variance of output response for the considered systems. Moreover, under the condition that full information of the system state is accessible to measurement, an H2 dynamic optimal control problem is shown to be solved by a zero-order stabilizing feedback controller, which can be represented in terms of the stabilizing solution to a set of coupled stochastic algebraic Riccati equations. Finally, an iterative algorithm is provided to get the approximate solution of the obtained Riccati equations, and a numerical example illustrates the effectiveness of the proposed algorithm.

Design and Implementation of LMI-based H2 Control for Vertical Nonlinear Coupled-tank System

This paper presents the mathematical design and implementation of a robust H_2 output feedback controller for the vertical nonlinear coupled-tank system. Considering the growth of the complicated chemical processes in industries in the last decades, the necessity for the controllers with high robustness and proficiency is demanded. Therefore, to overcome some deficiencies of classical controllers such as Proportional Integral (PI), the robust H_2 output feedback controller is proposed to control the liquid level of the coupled tank system benchmark. Because of the nonlinearity of the system and the interactions between two tanks, the behavior of the controller in terms of the performance and disturbance rejection is on the main scene. The Linear Matrix Inequalities (LMI) is used to derive the design procedure. The effectiveness of the proposed approach in the setpoint tracking is highlighted in comparison with the PI plus feedforward controller and the acceptable results are achieved.

Design and Implementation of LMI-Based H2 Control for Vertical Nonlinear Coupled-Tank System

This paper presents the mathematical design and implementation of a robust H_2 output feedback controller for the vertical nonlinear coupled-tank system. Considering the growth of the complicated chemical processes in industries in the last decades, the necessity for the controllers with high robustness and proficiency is demanded. Therefore, to overcome some deficiencies of classical controllers such as Proportional Integral (PI), the robust H_2 output feedback controller is proposed to control the liquid level of the coupled tank system benchmark. Because of the nonlinearity of the system and the interactions between two tanks, the behavior of the controller in terms of the performance and disturbance rejection is on the main scene. The Linear Matrix Inequalities (LMI) is used to derive the design procedure. The effectiveness of the proposed approach in the setpoint tracking is highlighted in comparison with the PI plus feedforward controller and the acceptable results are achieved.

Piezo-based flexural vibration suppression for an annular rotor via rotating-frame H2 control optimization

Elastic vibration can arise in annular and thin-walled rotor structures, impacting on operating performance and the risk of failure. Feedback control to reduce flexural vibration can be realized using lightweight actuators and sensors embedded in the rotor structure. To design optimal controllers, rotating-frame models of both the structural dynamics and sources of excitation are required. This paper describes a solution to this problem for the case of an annular rotor equipped with piezo patch actuators and sensors. To account for space-fixed external excitation sources, a forcing function is considered involving specified spatial and frequency domain distributions. A model-based [Formula: see text] synthesis is used to compute optimal control solutions. These are tested experimentally on a thin-walled cylindrical steel rotor for cases with narrowband and broadband excitation sources, applied from the fixed frame. The results show that frequency-splitting within the rotating-frame dynamics plays a key role in predicting and controlling resonance. The effectiveness of the optimal control methodology in reducing circumferential vibration of the annular rotor is also confirmed.