Μ-synthesis Control Research Articles

Robust vibration control of flexible panel: modeling and simulation

PurposeThis paper aims to develop a robust controller to control vibration of a thin plate attached with two piezoelectric patches in the presence of uncertainties in the mass of the plate. The main goal of this study is to tackle dynamic perturbation that could lead to modelling error in flexible structures. The controller is designed to suppress first and second modal vibrations.Design/methodology/approachOut of various robust control strategies, μ-synthesis controller design algorithm has been used for active vibration control of a simply supported thin place excited and actuated using two piezoelectric patches. Parametric uncertainty in the system is taken into account so that the robust system will be achieved by maximizing the complex stability radius of the closed-loop system. Effectiveness of the designed controller is validated through robust stability and performance analysis.FindingsResults obtained from numerical simulation indicate that implementation of the designed controller can effectively suppress the vibration of the system at the first and second modal frequencies by 98.5 and 88.4 per cent, respectively, despite the presence of structural uncertainties. The designed controller has also shown satisfactory results in terms of robustness and performance.Originality/valueAlthough vibration control in designing any structural system has been an active topic for decades, Ordinary fixed controllers designed based on nominal parameters do not take into account the uncertainties present in and around the system and hence lose their effectiveness when subjected to uncertainties. This paper fulfills an identified need to design a robust control system that accommodates uncertainties.

µ-Synthesis Control Applied to Counter the Seismic Load Action on a Building Structure

µ-Synthesis Control Applied to Counter the Seismic Load Action on a Building Structure

Robust control for four wheel independently-actuated electric ground vehicles by external yaw-moment generation

This paper presents a robust controller for four wheel independently-actuated (FWIA) electric ground vehicles to preserve vehicle stability and improve vehicle handling performance. Thanks to the actuation flexibility of FWIA electric ground vehicles, an external yaw moment, which is usually employed to regulate the vehicle yaw and lateral motions, can be easily generated with the torque differences between the left and right side motors. A μ-synthesis control method which can deal with unmodeled dynamics and parametric uncertainties is proposed by taking the external yaw moment as the control input. Simulations with a high-fidelity, CarSim®, full-vehicle model are carried out to demonstrate the effectiveness of the proposed control system. Simulation results in various driving scenarios with vehicle payload variations show the robustness of the proposed controller.w

Modelling robustness for a flexible grid‐tied photovoltaic generation system

Robustness to modelling inaccuracy is a vital characteristic of a controller, because no matter how accurate a model is, modelling inaccuracies always exist. However, it is difficult to achieve satisfactory nominal and robust performance of a grid-tied photovoltaic (PV) generation system at the same time, using traditional controller design methods. To solve this problem, a μ-synthesis control method combined with the application of linear fraction transformation (LFT) is proposed in this study. The proposed method is designed with object transforming and implemented with DK iteration. The μ-analysis and simulation results prove that the objective can be achieved under various microgrid conditions, determined by factors such as grid connection point voltage, load conditions and component parameter perturbations. Compared with traditional controller design methods, the grid-tied PV generation system under μ-synthesis control exhibits comparatively large perturbation margin for nominal performance and robust stability, and simultaneously is capable of guaranteeing the preset perturbation range for robust performance.

Comparison of Robust Control Techniques for Use in Continuous Stirred Tank Reactor Control

This work deals with the design and the application of a robust control on a chemical reactor. The reactor is exothermic one. There are two parameters with only approximately known values in the reactor. These parameters are the reaction enthalpies. Three robust control techniques are used - robust PI controller found by plotting the stability boundary locus in the plane of controller parameters that is called (kp, k)-plane, H∞ control and μ-synthesis control. The presented simulation results confirm applicability of mentioned approaches to safe control of nonlinear processes.

Robust Control for Ride Comfort Improvement of an Active Suspension System considering Uncertain Driver's Biodynamics

This paper presents a robust output feedback control design for a half-car active suspension system by considering driver's biodynamics. Because of different kinds of passengers there is a wide range of variations in biodynamics' parameters, and an appropriate robust control design approach, μ-synthesis approach, is used to tackle these parametric uncertainties. The performance of active suspension system with designed controller is compared with the open loop one in both frequency and time domain simulations. The results show that μ-synthesis based controller achieves great performance in ride comfort. In addition, suspension deflections, road holding and actuators force remain in reasonable regions. Finally, analysis of robust performance indicating that the μ-synthesis controller remains stable in a wide range of frequency domain despite parametric uncertainties, which is also validated by a specific case in this paper.

μ-Synthesis robust controller design for the supercavitating vehicle based on the BTT strategy

In order to maintain the stability of the supercavitating vehicle in the turning process, a pair of elevator is used to achieve the functionality of the ailerons and the roll damping is provided by a pair of rudder. The turn centripetal force of the supercavitating vehicle is mainly supplied by a cavitator. In this paper, a control strategy based on BTT control for the supercavitating vehicle is proposed. The mathematical model of the BTT supercavitating vehicle is established, and the full state model is designed to include a pitch channel and a yaw–roll channel, and a μ-synthesis controller is designed respectively for the dual channels, and the simulation research of control effect is carried out.

μ-Synthesis Control of Photovoltaic System

Traditional control methods are usually difficult to achieve a good compromise between nominal performance and robust performance, in order to improve the flexibility and robustness of the PV power grid-connection system without affecting its nominal performance, aiming at the effect on flexible PV power grid-connection by component parameter perturbation, a μ-synthesis robust control method of flexible grid-connection of photovoltaic power based on model matching is proposed. Model matching problem including the actual controlled objects like inverters, is transformed into a generalized system with uncertainty block being abstracted, thus further is attributed to a structured uncertainty problem, which can be solved by DK iteration. The μ-analysis and simulation results show that the designed μ-synthesis controller, makes the robust performance of the closed-loop system satisfied, and advantages are especially more obvious in the case of system component parameter perturbation.

AMB Vibration Control for Structural Resonance of Double-Gimbal Control Moment Gyro With High-Speed Magnetically Suspended Rotor

This paper explores a robust μ-synthesis control scheme for structural resonance vibration suppression of high-speed rotor systems supported by active magnetic bearings (AMBs) in the magnetically suspended double-gimbal control moment gyro (MSDGCMG). The derivation of a nominal linearized model about an operating point was presented. Sine sweep test was conducted on each component of AMB control system to obtain parameter variations and high-frequency unmodeled dynamics, including the structural resonance modes. A fictitious uncertainty block was introduced to represent the performance requirements for the augmented system. Finally, D-K iteration procedure was employed to solve the robust μ-controller. Rotor run-up experiments on the originally developed MSDGCMG prototype show that the designed μ-controller has a good performance for vibration rejection of structural resonance mode with the excitation of coupling torques. Further investigations indicate that the proposed method can also ensure the robust stability and performance of high-speed rotor system subject to the reaction of a large gyro torque.

A Study on μ Synthesis Robust Control for Independent Drive Electric Vehicle to Enhance Stability

This paper presents the design of μ-synthesis control for Independent Drive Electric Vehicle, Applying this method, external disturbances and model uncertainties can be taken into consideration. The controller is set up based on the toolbox of MATLAB/SIMULINK and the weighting functions selection is discussed according to the actuator and the control performance index. In order to investigate the feasibility of the controller, simulations with different velocity and disturbances were employed, the simulation results show that the proposed controller can keep the car against modeling error, external disturbances and get good handling performance.

μ-Synthesis Based Adaptive Robust Control of Linear-Motor-Driven Stages with High-Frequency Flexible Modes

Linear motors have good potential to achieve high speed and high accuracy by eliminating gear related mechanical problems. By using the effective model compensation of nonlinear rigid-body dynamics, the close-loop bandwidth limitation due to the appearance of neglected high-frequency flexible modes has to be the main issue to maximize the achievable performance. In this paper, the modeling and identifications are carried out to verify the existing rigid-body and high-frequency dynamics. The μ-synthesis based adaptive robust control strategy is developed. The adaptive feedforward loop is used to keep good online parameter estimation and nonlinear model compensation, and also transfers the trajectory tracking problem into the traditional regulation problem which μ-synthesis control can more easily deal with. Since considering the fundamental flexible mode as a part of the nominal plant model, the μ-synthesis feedback loop can achieve higher close-loop bandwidth with the appearance of various model uncertainties. Comparative experiments have been done and the results show the excellent tracking performance of the propose algorithm.

$\mu$-Synthesis for Frequency Uncertainty of the ICPT System

A μ-controller is designed based on the structured singular value with regard to the frequency uncertainty of a real inductively coupled power transfer (ICPT) system. Due to system-parameter variations (such as system load) and nonlinear features of ICPT systems, the operating frequency will be perturbed accordingly. Uncertainty in the operating frequency will contribute to electromagnetic interference and power losses, and even instability of ICPT systems. To fulfill a robust stability and robust performance (RSRP) design, a generalized state-space averaging model for a nominal ICPT system is established by developing the equivalent circuit equations and expanding the related circuit variables as the Fourier series. A linear fractional transformation of this nominal model and its uncertainty is discussed to generate a standard configuration for μ-synthesis. The D-K iteration method is proposed for the “optimal” RSRP design. Computer simulation and a practical experiment are conducted to verify the RSRP of the μ-synthesis control system to ensure that the μ-synthesis algorithm is effective for ICPT systems.

Design and Development of a ?-Synthesis Controller for a Flexible Robotic Manipulator, Modelled as a Rotating Euler-Bernoulli Beam

In this paper, a robust control strategy for a robotic manipulator, modelled as a cantilever rotating Euler-Bernoulli beam, is developed. Imprecision in the payload mass, unknown properties of the manipulator link, and torque disturbance are included as the sources of uncertainty. The objective is to achieve a desired angular rotation while the vibration of the manipulator tip is suppressed and the control system remains in a stable region. The control input of the system is an external driving torque. For formulation of the continuous system, the mode summation technique is used and equations of motion are described in the Laplace domain. Then, unstructured uncertainties are included in the form of multiplicative input uncertainty. The μ-synthesis control approach is used and an H∞ optimal robust controller is developed based on the DK-iteration algorithm. Results show that the designed controller guarantees the robust stability and performance of the perturbed system against existing uncertainties. Consequently, stability of the closed-loop system, disturbance rejection, and trajectory tracking performance are achieved.

Robust controller design for an electromagnetic active suspension subjected to mixed uncertainties

This article focuses on the modelling and robust control of a DC motor-based electromagnetic active suspension. Due to the small damping of the motor, the moments of inertia of the rotor and the nut can significantly affect the high-frequency performance of the suspension system and so, they are taken into consideration in the system modelling. In addition, parameter variations of the vehicle system and the unmodelled high-order dynamics of the actuator could influence the control effectiveness. Thus, the mixed uncertainties, composed of both multiple parameter uncertainties and the unmodelled high-order dynamics of the suspension and actuator are taken into account in the system model. To ensure the robustness and performance of the uncertain suspension system, a robust controller based on mixed µ-synthesis is designed. An easy method of choosing the weighting functions is proposed. The simulation results show the mixed µ-synthesis controller can meet the requirement of robust performance in the presence of mixed uncertainties and can achieve good ride comfort.

Design, Construction, and Modeling of a Flexible Rotor Active Magnetic Bearing Test Rig

A successful industrial application of flexible rotors supported on active magnetic bearings (AMBs) requires careful attention not only to rotordynamic design aspects but also to electromagnetic and feedback control design aspects. Model-based control design provides the framework to ensure efficient, reliable, and safe operation of turbomachinery on AMBs. This paper describes in detail the design, construction, and modeling process for a high performance AMB test rig which typifies a small industrial super-critical centrifugal compressor. A unique aspect of the design are the two additional radial AMBs to allow the application of simulated destabilizing fluid or electromagnetic forces to the rotor. These forces are difficult to predict and can lead to rotordynamic instability of industrial machinery if not properly accounted for. This test rig provides a realistic platform to evaluate stabilizing control algorithms for high performance turbomachinery. A complete model of rotor, AMB actuators and accompanying electronics, is constructed from individually verified component models. Model validation is confirmed through the successful design and implementation of a μ-synthesis controller.

Oil whip instability control using μ-synthesis technique on a magnetic actuator

Rotating machines have a wide application range and since those machines have high trust levels, several rotor vibrations control methods are investigated in order to avoid sudden cracks, improve rotor performance or even to reach higher operation speeds by controlling some instabilities, critical speeds resonances or oil whip effect. Rotor instabilities are associated to the operation speed and can have structural or dynamic sources from the shaft, bearings and foundation or even from an actuator external force. This work focuses on a strategy that uses the μ-synthesis control technique to attenuate the oil whip instability effect of flexible hydrodynamically supported rotors and allows the rotor to operate in higher speeds. For the identified rotor model and the synthesized controller applied on a magnetic actuator, the control system stability and performance specifications are analyzed with regard to the model uncertainties and μ-synthesis controlled vibration levels are compared to PID controller in vertical and horizontal directions. The performance specifications within the μ-synthesis are optimized to suppress unbalance vibration and, in order to contribute to industrial acceptance, the controller design is presented as a strategy which focuses on a design at reduced effort.

μ-Synthesis controller design for a DC-motor-based active suspension with parametric uncertainties

This paper presents a µ-synthesis controller design method for a DC-motor-based active suspension. Considering multiple parametric uncertainties, a full-car suspension model with DC-motor actuator is built up and a µ-synthesis controller is proposed for the perturbed suspension system. Both frequency and time domain simulations are conducted, and results show that the µ-synthesis controller achieves better performance in ride comfort compared with H∞ controller. Analyses of robust stability and robust performance have been done, indicating that the µ-synthesis controller is able to maintain both of them, which is also validated by a case in this paper. Consequently, it can be concluded that the designed µ-synthesis controller can deal with parametric uncertainties for a DC-motor-based active suspension.

µ-synthesis for unmanned underwater vehicles current disturbance rejection

This note focuses attention on a novel approach to disturbance rejection when the µ-synthesis control procedure is applied to Unmanned Underwater Vehicles (UUVs). Environmental external disturbances simplify to ocean current for a totally submerged vehicle and greatly contributes for hydrodynamical loads and the tether cable disturbance. Our case scenario deals with the incorporation of the sea current disturbance to the plant model employed for control design. In the proposed design method, we substitute the structured unmodeled dynamics uncertainty, which is generally difficult to come up with and eventually utilized to represent external disturbances, by parametric uncertainty, relatively easier and straightforward to come by. The sea-current load parameters are, therefore, treated as parametric uncertainty and fit in the µ design framework. Assuming that both vehicle motion and current direction lie in the horizontal plane, the incoming (to vehicle) current vector sets a horizontal circumference sector in which it may vary. When in the 3D space, current uncertainty renders a cone in space. For validation purposes, the linear controller is simulated with the nonlinear vehicle model.

Robust Control of the Elastodynamic Vibrations of a Flexible Rotor System With Discontinuous Friction

The work presented here deals with the control of a flexible rotor system using the μ-synthesis control technique. This technique allows for the inclusion of modeling errors in the control design process in terms of uncertainty weights. The dynamic model of the rotor system, which includes discontinuous friction, is highly nonlinear and has to be linearized around an operating point in order to use μ-synthesis. The difference between the linear and nonlinear models is characterized in terms of uncertainty weights and included in the control design process. The designed controller is robust to uncertainty in the dynamic model, spillover, actuator uncertainty, and noise. The theoretical findings of the μ-synthesis control design are validated through simulations and the results are presented and discussed here.

A Study on μ-Synthesis Control for Four-Wheel Steering System to Enhance Vehicle Lateral Stability

This paper presents the design of μ-synthesis control for four-wheel steering (4WS) vehicle and an experimental study using a hardware-in-the-loop (Hil) setup. First, the robust controller is designed and the selection of weighting functions is discussed in the framework of μ-synthesis control scheme, considering the varying parameters induced by running vehicle condition. Second, in order to investigate the feasibility of the four-wheel steering control system, the 4WS vehicle control system is built using dSPACE DS1005 platform. The experimental tests are performed using the Hil setup which has been constructed using the devised rear steering actuating system. The dynamics performance is evaluated by experiment using the Hil setup under the condition of parameter variations. Finally, experimental results show that the μ-synthesis controller can enhance good vehicle lateral maneuverability.