Negative imaginary theorem with an application to robust control of a crane system

This paper presents an integral sliding mode (ISM) control for a case of negative imaginary (NI) systems. A gantry crane system (GCS) is considered in this work. ISM is a nonlinear control method introducing significant properties of precision, robustness, stress-free tuning and implementation. The GCS model considered in this work is derived based on the x direction and sway motion of the payload. The GCS is a negative imaginary (NI) system with a single pole at the origin. ISM consist of two blocks; the inner block made up of a pole placement controller (NI controller), designed using linear matrix inequality for robustness and outer block made up of sliding mode control to reject disturbances. The ISM is designed to control position tracking and anti-swing payload motion. The robustness of the control scheme is tested with an input disturbance of a sine wave signal. The simulation results show the effectiveness of the control scheme

Method and system to perform energy-extraction based active noise control

A method to provide active noise control to reduce noise and vibration in reverberant acoustic enclosures such as aircraft, vehicles, appliances, instruments, industrial equipment and the like is presented. A continuous-time multi-input multi-output (MIMO) state space mathematical model of the plant is obtained via analytical modeling and system identification. Compensation is designed to render the mathematical model passive in the sense of mathematical system theory. The compensated system is checked to ensure robustness of the passive property of the plant. The check ensures that the passivity is preserved if the mathematical model parameters are perturbed from nominal values. A passivity-based controller is designed and verified using numerical simulations and then tested. The controller is designed so that the resulting closed-loop response shows the desired noise reduction

A Survey of Riccati Equation Results in Negative Imaginary Systems Theory and Quantum Control Theory

This paper presents a survey of some new applications of algebraic Riccati equations. In particular, the paper surveys some recent results on the use of algebraic Riccati equations in testing whether a system is negative imaginary and in synthesizing state feedback controllers which make the closed loop system negative imaginary. The paper also surveys the use of Riccati equation methods in the control of quantum linear systems including coherent H∞ control.This work was supported by the Australian Research Council (ARC) under grants FL110100020 and DP160101121 and the Air Force Office of Scientific Research (AFOSR), under agreement number FA2386-16-1-4065

Performance improvement of bearingless multi-sector PMSM with optimal robust position control

Bearingless machines are relatively new devices that consent to suspend and spin the rotor at the same time. They commonly rely on two independent sets of three-phase windings to achieve a decoupled torque and suspension force control. Instead, the winding structure of the proposed multi-sector permanent magnet (MSPM) bearingless machine permits to combine the force and torque generation in the same three-phase winding. In this paper the theoretical principles for the torque and suspension force generation are described and a reference current calculation strategy is provided. Then, a robust optimal position controller is synthesized. A Multiple Resonant Controller (MRC) is then integrated in the control scheme in order to suppress the position oscillations due to different periodic force disturbances and enhance the levitation performance. The Linear-Quadratic Regulator (LQR) combined with the Linear Matrix Inequalities (LMI) theory have been used to obtain the optimal controller gains that guarantee a good system robustness. Simulation and experimental results will be presented to validate the proposed position controller with a prototype bearingless MSPM machine