Arkadiusz Mystkowski

The Robust Control of Magnetic Bearings for Rotating Machinery

The fast progress in the applications of active magnetic suspension systems needs to apply the modern control theory. This paper deals with H∞ and H2 control of rigid rotor movement, which is supported in magnetic bearings. The robust control of magnetic bearings is investigated analytically. The nominal model of active magnetic suspension of rotor and the uncertainty model were derived. The standard PID control and robust control are compared and performance of nominal feedback configuration with weights is presented. We propose a robust control with a multi-objective controller to achieve good robust stability when the model of a plant is uncertain. The behavior of multiplicative uncertainty of magnetic suspension system is shown. The aim of optimal robust control is to improve the magnetic suspension taking into account the energy limitation (i.e., to avoid the saturation of actuators). The H2 performance and H∞ performance depend on a proper selection of weighting functions. So a very important step in the controller design process is to choose the appropriate weight functions: We, Wu, Wd. The influence of noise is limited by weight functions. We also put limits on input and output signals. The stability of a system with disturbance interaction is discussed. The simulations of a well-posed and internally stable magnetic system are presented. The success of the robust control is demonstrated through results of numerical simulations.

Robust nonlinear position-flux zero-bias control for uncertain AMB system

This paper presents a robust nonlinear control law that combines a parametric uncertainty of the single one-degree-of-freedom active magnetic bearing (AMB) system with disturbance. The robust nonlinear feedback tool such as control Lyapunov function (CLF) and robust stability techniques are developed. The control objective is to globally stabilise the mass position of an AMB with flux feedback. The flux-based control model for an AMB system is derived due to voltage switching strategy with voltage saturation. This strategy enables the flux control under a zero-bias or low-bias flux operation. In the zero-bias control, only one electromagnet in each axis of the AMB is active at any given time, depending on the rotor displacement. The proposed robust nonlinear CLF with a zero-bias for an uncertain AMB system can achieve a dynamic performance superior to that of a linear controller with the zero-bias or with the classical bias operations.

Implementation and investigation of a robust control algorithm for an unmanned micro-aerial vehicle

This paper presents a new method for implementation and realization of an optimal robust control algorithm in the real-time hardware-in-the-loop simulation environment for a mathematical model of the dynamics of the BULLIT micro-aircraft, with consideration of non-linearity, uncertainty, and non-stationarity of its parameters. The robust optimal control method, µ -Synthesis, applied to the autonomous flight dynamics control system of the unmanned aerial vehicle (UAV) meets desired control performances. The serial connection between the Gumstix micro-computer and the Kestrel autopilot extends the ability to implement high order robust controllers. The code of the control algorithm implemented (in the C++ language) in the memory of a Gumstix Verdex Pro single-chip micro-computer enables optimization of the threads-based approach. The hardware-in-the-loop (HIL) simulation mode was implemented in the Kestrel autopilot inner loop, and simulations of all stages of flight were performed in real-time using the actual model of the aircraft and autopilot. Finally, HIL simulations and tests were conducted in order to verify the developed control algorithm. New method for implementation and realization of an robust control algorithm.Hardware-in-the-loop simulations for a micro-UAV.Consideration of non-linearity, uncertainty, and non-stationarity of UAVs parameters.The µ -Synthesis method applied to the UAVs dynamics control.The serial connection between the Gumstix micro-computer and the Kestrel autopilot.

Sensitivity and Stability Analysis of Mu-Synthesis AMB Flexible Rotor

The paper presents the sensitivity and stability margin analyses of the flexible rotor supported by active magnetic bearings (AMBs) with the robust optimal vibrations control. The modal representation of the rotor finite element model (FEM) is investigated. Then, the open-loop system of the AMBs flexible rotor is established and critical speed analysis due to variation of bearing stiffness is performed. For the open-loop setup, the non-collocation effect of displacement sensors and magnetic actuators due to control stability problem is considered. The frequency mode analysis of the collocation and non-collocation system is presented. Next, the -synthesis control of 4-DOF AMBs rotor is investigated. The design process of -controllers, which cover uncertainty design and performance shape by chosen weighting function is shortly described. Then, the sensitivity function is calculated and used to evaluate the AMBs rotor stability margin for the -control and the PID control. The performance of the -controller are verified in experimental tests.

Uncertainty Modeling in Robust Control of Active Magnetic Suspension

Stabilization of a plant in case of uncertainty parameters and unmodeled dynamics are the main problems considered in this paper. A robust control of motion of a rigid shaft that is supported by magnetic bearings was used as an example. The dynamics of the active magnetic suspension system is characterized by instability and uncertainty. The uncertainty is modeled as an additive and multiplicative. Robust controller H∞ was designed for the defined plant with the uncertainty models. The robust controller assures high quality of control despite the uncertainty models. Robust control of vibrations of a rigid rotor is confirmed by experimental studies. A digital signal processor is used to execute the control algorithm in real time.

Feedback linearization of an active magnetic bearing system operated with a zero–bias flux

Abstract Input-output linearization by state feedback is applied to a flux-controlled active magnetic bearing (AMB) system, operated in the zero-bias mode. Two models of the AMB system are employed. The first one is described by the third-order dynamics with a flux-dependent voltage switching scheme, whereas the second one is the fourth-order system, called self-sensing AMB, since it does not require the measurement of the rotor position. In the case of that system we had to find the flat outputs to guarantee its stability. The proposed control schemes are verified by means of numerical simulations performed within the Matlab environment.

Nonlinear position-flux zero-bias control for AMB system

This paper reports on a novel nonlinear controller for a single one-degree-of-freedom (1-DOF) Active Magnetic Bearing (AMB) system. The nonlinear feedback tools such as Lyapunov based techniques, control Lyapunov functions (CLFs), and feedback passivation control are developed. The control objective is to globally stabilize the mass position of an AMB with flux feedback. The flux-based control model for an AMB system is derived due to voltage switching strategy with voltage saturation. This strategy enables the flux control under a zero-bias operation. The proposed nonlinear CLF with a zero-bias can achieve a dynamic performance superior to that of a linear controller with the zero-bias or with the classical bias operations.

Robust Optimal Control of MAV Based on Linear-Time Varying Decoupled Model Dynamics

This paper discusses a nonlinear robust control design procedure to micro air vehicle that uses the singular value (μ) and μ-synthesis technique. The optimal robust control law that combines a linear parameters varying (LPV) of UAV (unmanned aerial vehicle) are realized by using serial connection of the Kestrel autopilot and the Gumstix microprocessor. Thus, the robust control feedback loops, which handle the uncertainty of aerodynamics derivatives, are used to ensure robustness stability of the UAV local dynamics in longitudinal and lateral control directions.

Application of Unfalsified Control Theory in Controlling MAV

Controlling the flight of Micro Aerial Vehicles (MAV) is a highly challenging task, mostly due to nonlinearity of their models and highly varying longitudinal and lateral derivatives coefficients [. As such, it requires a proper form of robust control. The demand for such control is very high, as it is required in many applications. The following paper presents the application of Unfalsified Control Theory developed by Michael G. Safonov [1, 2, 6, . This interesting approach is based on the adaptive switching control, and does not require any previous knowledge of the controlled plant. The controlled dynamics is decoupled due to longitudinal and lateral motion of the Bell 540 single-delta wing micro aerial vehicle. The work involves design and simulation of the proper robust controller. The simulation is based on already obtained nominal model of the Bell 540 vehicle [. The developed controllers were proved to be efficient, based on performed calculations and simulation in Matlab.

The Robust Control of Magnetic Suspension with Rapidly Changing of Rotor Speed

An optimal robust vibration control of a rotor supported magnetically over a wide angular speed range is presented in the paper. The laboratory stand with the high speed rotor (max. 24000 rpm) was designed. The wide bandwidth controller with required gain, which is necessary to stabilize the structurally unstable and active magnetic bearing system was computed. For controller design, the weighting functions putted on the input and output signals were chosen. For control design, the dynamics of the rotor and uncertain parameters were considered. The optimized control system by minimization of the H norm putted on transient process of the system was presented. The robust controller was designed with considered asymmetrically magnetic bearings, signal limits and power amplifiers dynamic. The success of the robust control is demonstrated through computer simulations and experimental results. Matlab-Simulink was used for the numerical simulation. The experimental results show the effectiveness of the control system as good vibrations reducing and robustness of the designed controller in all dynamic states.