Nonlinear Actuator Dynamics Research Articles

Adaptive stabilization for a class of wave equations with uncertain nonlinear boundary actuator dynamics

This paper investigates the stabilization of a wave equation with uncertain boundary actuator dynamics. The remarkable characters of the system under investigation are revealed by the essential nonlinearities involved in the boundary actuator and the serious parametric unknowns coming from anti-damping coefficient at uncontrolled boundary and those in the actuator, which result into the incapability of the traditional control methods on this topic. For this, a novel adaptive control strategy is proposed in this paper. Specifically, a Riemann variables based state transformation is first introduced to change the original system into a new one whose stabilization implies that of the original system. Then, a state-feedback controller joint with some adaptive laws which are smartly chosen for the compensation of unknown parameters is explicitly designed by a finite-dimensional backstepping procedure. Owing to the compensation of boundary actuator dynamics, the performance analysis of the closed-loop system is more complicated than that of the related literature. For this, a rigorous recursive step is given to show the stability of the resulting closed-loop system. Finally, a numerical example is provided to verify the effectiveness of the proposed theoretical results.

Adaptive control for heterodirectional 2 × 2 hyperbolic PDEs with spatially varying coefficients and uncertain nonlinear actuator dynamics

In this paper, we aim to develop adaptive asymptotic stability for heterodirectional 2 × 2 hyperbolic PDEs with parametric-strict-feedback nonlinear actuator dynamics. First, we transform the heterodirectional 2 × 2 hyperbolic PDEs with spatially varying coefficients into a stable target subsystem by utilizing the infinite-dimensional backstepping transformation. Second, an adaptive state feedback controller is constructed by combining finite-dimensional state transformation and adaptive compensation technology to assure the boundedness of all the signals in the closed-loop system. Meanwhile, we show that the PDE states converge to zero pointwise in space, the nonlinear ODE states and the control input also converge to zero. Finally, a simulation example is provided to illustrate the effectiveness of the proposed method.

Adaptive Synchronization for Networked Parabolic PDE Systems With Uncertain Nonlinear Actuator Dynamics

This article focuses on the synchronization control of networked uncertain parabolic partial differential equations (PDEs) with uncertain nonlinear actuator dynamics. Compared to existing networked PDE systems, control input occurs in ordinary differential equation (ODE) subsystems rather than in PDE ones. Compared to existing results, where the exact system parameters must be known for the entire system, this paper further considers parabolic PDE-ODE systems with unknown parameters affecting the interior of the PDE domain. Due to the unknown parameters and uncertain nonlinear actuator dynamics, the existing distributed algorithms and stability analysis tools cannot be utilized to solve the synchronization problem of cascaded parabolic systems. To address this difficulty, this study designs a novel passive identifier to estimate the states and unknown parameters. Subsequently, based on the passive identifier and Lyapunov function method, a synchronization controller is presented for cascaded parabolic PDE systems to ensure that the synchronization control and the boundedness of all the closed-loop signals are achieved. Lastly, the effectiveness of the obtained results is illustrated using simulation.

Actuation of an electrohydraulic manipulator with a novel feedforward compensation scheme and PID feedback in servo-proportional valves

Achieving good tracking control beyond 0.1Hz by electrohydraulic manipulators still remains challenging due to the coupling of nonlinear actuation dynamics and multiple actuations. A novel order-separated feedforward, or FF, model has been proposed for estimating the major part of the commands of servo-proportional valves for metering their ports to monitor oil flow in the paired cylinders. Motion studies have been executed in serial manipulation mode by using such control to two valves and in serial–parallel mode to eight valves. Oil leakage and cylinder friction have been included as lower-order effects for the narrow radial clearance and near-zero lap in the valves each paired with a low-friction cylinder. Other assumptions of negligible inertia and suspended weight under the pistons have been validated by a numerical exercise. A PID feedback has been added during real-time tracking by an FFPID controller. Reciprocating and circular motion demands in the serial mode and heave tracking in serial–parallel mode, all in a vertical plane, have been executed. More precise and smoother tracking has been achieved up to 1Hz in the serial mode mostly with lower expense of energy than a conventional PID-alone controller. Results indicate FF guidance to mitigate oscillations occasionally apparent in PID-only case due to either hunting among multiple solutions or gain sensitivity of the nonlinear system. Good heave tracking has been obtained up to 0.2Hz. Substantial disturbance rejection capability of the controller has been demonstrated against tension arising from the connecting oil hoses. A potential use of the FF model in diagnosing emerging valve or cylinder fault with their aging has also been explained.

Multi-Actuation Controller for Performance Vehicles: Optimal Torque Allocation and Active Aerodynamic

A multi-actuation model predictive controller is designed to improve the stability of the performance vehicles during high-speed maneuvers. The actuators included in this study are four electric motors for the wheels and two active aerodynamic wings at the front and rear of the vehicle. The designed controller integrates optimal corner torque allocation with an optimal active aerodynamics control system. A model predictive control scheme is used to adjust the air wings angle of attack and optimize the corner torques. A high-level constraint adjustment module is added to the controller to observe nonlinear tire behavior and optimize aerodynamic wings activation as required. Nonlinear tire behavior and actuator dynamics are considered and included in the prediction model. The controller performance is verified in simulation with MATLAB/Simulink and CarSim.

Influence of System and Actuator Nonlinearities on the Dynamics of Ring-Type MEMS Gyroscopes

This study investigates the nonlinear dynamic response behavior of a rotating ring that forms an essential element of MEMS (Micro Electro Mechanical Systems) ring-based vibratory gyroscopes that utilize oscillatory nonlinear electrostatic forces. For this purpose, the dynamic behavior due to nonlinear system characteristics and nonlinear external forces was studied in detail. The partial differential equations that represent the ring dynamics are reduced to coupled nonlinear ordinary differential equations by suitable addition of nonlinear mode functions and application of Galerkin’s procedure. Understanding the effects of nonlinear actuator dynamics is essential for characterizing the dynamic behavior of such devices. For this purpose, a suitable theoretical model to generate a nonlinear electrostatic force acting on the MEMS ring structure is formulated. Nonlinear dynamic responses in the driving and sensing directions are examined via time response, phase diagram, and Poincare’s map when the input angular motion and nonlinear electrostatic force are considered simultaneously. The analysis is envisaged to aid ongoing research associated with the fabrication of this type of device and provide design improvements in MEMS ring-based gyroscopes.

Effective Compensation of Nonlinear Actuator Dynamics Using a Proposed Linear Time-Varying Compensation

AbstractActuator tracking and compensation are important in the general field of experimental structural dynamics to effectively conduct vibration testing. Real-time hybrid substructuring (RTHS) is...

Quantized Feedback Control of Active Suspension Systems Based on Event Trigger

As the deviation error will accumulate during the data acquisition and transcoding process of an active suspension system, this paper presents a sliding-mode-based quantized feedback control method. The aim of the controller is to improve the vertical performance of vehicles in the presence of external interferences. A 7-DOF suspension model with nonlinear springs and actuator dynamics is built for the control purpose. Firstly, a static quantizer on the uplink channel and a dynamic quantizer on the downlink channel are considered in the sliding mode controller to reduce the cumulative error and suppress the sprung mass motions. Secondly, an event trigger mechanism is introduced in the controller design process to reduce energy consumption and operation frequency of the actuator. The overall stability of the designed controller is proved by the Lyapunov functions. Finally, numerical simulations are carried out to evaluate the efficacy of the proposed controller. Different quantitative and trigger conditions are discussed, and the random road excitation is considered as the external disturbance input. The results of the control method indicate that the designed controller can improve the riding comfort with little loss of handling stability compared with the passive system. In addition, the trigger mechanism can improve the working efficiency of actuators effectively.

Identification and assessment of a nonlinear dynamic actuator model for controlling an experimental flexible wing

In this paper, the effect of nonlinear actuator dynamics on the performance of an active load alleviation system for an experimental flexible wing is studied. Common nonlinearities such as backlash or rate limits are considered for the control surface actuator. An aeroelastic simulation model of a flexible wing with control surface is being used. With this, a parameter study is carried out to quantify the impact of the individual nonlinearities on the overall closed-loop performance by means of describing functions. Finally, the nonlinear actuator model with parameters identified from dedicated tests is experimentally validated allowing for an accurate prediction of the expected gust load alleviation performance.

Adaptive stabilization for a reaction–diffusion equation with uncertain nonlinear actuator dynamics

This paper is devoted to the stabilization of a reaction–diffusion equation with uncertain nonlinear actuator dynamics described by a cascaded parabolic PDE–ODE system. Essentially different from the systems in the related literature, control input appears in the ODE subsystem rather than in the PDE one, and moreover, the actuator dynamics are nonlinear and possess uncertainties rather than linear without uncertainty. Note that the existing control schemes so far are ineffective to handle such systems, and hence the stabilization problem for these systems is still unsolved. For this, backstepping approaches in both infinite and finite-dimension are smartly combined with the adaptive dynamic compensation technique in order to solve the control problem. Specifically, by using an infinite-dimensional backstepping transformation and its inverse, the original PDE subsystem is first changed to a new one from which control design is much convenient. Then, based on the new system together with the actuator dynamics, an adaptive state-feedback controller is explicitly constructed by using a couple of finite-dimensional backstepping transformations, which guarantees that all the states of the resulting closed-loop systems are bounded. Moreover, both the control input and the states of the original system converge to zero ultimately. Finally, a simulation example is provided to validate the effectiveness of the established theoretical results.

Dual adaptive robust control for uncertain nonlinear active suspension systems actuated by asymmetric electrohydraulic actuators

This study investigates the vibration control issue of active suspension systems. Unlike previous results that neglect the actuator dynamics or consider the impractical symmetrical hydraulic cylinder model, this paper incorporates more reasonable asymmetric electrohydraulic actuator into active suspension system and derives its dynamic model. However, whether active suspension or electrohydraulic actuator suffers from nonlinearities (e.g. nonlinear spring, nonlinear damper and nonlinear actuator dynamics) and parameters uncertainties (e.g. the variations of sprung mass and hydraulic fluid’s bulk modulus as well as hydraulic cylinder original control volumes) , which were rarely synthetically considered in the existing researches.To address these issues, we develop a novel dual adaptive robust controller (ARC). An ARC is firstly designed for main-loop system for stabilizing the car body and improving ride comfort in the presence of nonlinearities and parameter uncertainties as well as road disturbances. In order to meet the constraints requirements of suspension system, the tunable parameters in main-loop control law are optimized by solving linear matrix inequality with kidney-inspired algorithm. Another ARC is further synthesized for sub-loop system to deal with the nonlinear and uncertain dynamics in electrohydraulic actuator for ensuring the force tracking performance. Meanwhile, the uncertain parameters are estimated online to compensate the model deviation. The terminal control law is able to guarantee the asymptotic stability of close-loop system within Lyapunov framework. Finally, the effectiveness and robustness of the proposed controller are demonstrated via excessive simulation experiments over different road conditions.

Chaotic motion due to lateral Casimir forces during nonlinear actuation dynamics.

We investigated here the influence of the lateral Casimir force on the dynamical actuation of devices with interacting materials covering a broad range of optical properties ranging from poor to good conductors, such as, for example, nitrogen doped SiC and Au, respectively. The conservative actuating system shows a central heteroclinic orbit surrounded by a finite number of homoclinic orbits, because at higher periods, an increased lateral Casimir force will be necessary to counterbalance the restoring force. As a result, the conservative system reaches stable operation sooner for the higher conductivity materials (Au-Au), indicating the significant impact of the material optical properties on the lateral Casimir force. Furthermore, for the non-conservative driven systems, the decrement of the Melnikov parameter α leads to a faster disappearance of the satellite homoclinic orbits in the Poincaré portraits, followed by a strong shrinkage of the central heteroclinic orbit toward unstable chaotic motion. The latter is more pronounced for the lower conductivity materials since comparison shows the Au-Au system to be significantly more stable than the SiC-SiC system. Therefore, in actuating systems where the lateral Casimir force could play a significant role, the higher conductivity materials appear to be a better choice to ensure stable operation against a chaotic motion.

Identification and Modeling of the Airbrake of an Experimental Unmanned Aircraft

This paper presents the modeling, system identification, simulation and flight testing of the airbrake of an unmanned experimental aircraft in frame of the FLEXOP H2020 EU project. As the aircraft is equipped with a jet engine with slow response an airbrake is required to increase deceleration after speeding up the aircraft for flutter testing in order to remain inside the limited airspace granted by authorities for flight testing. The airbrake consists of a servo motor, an opening mechanism and the airbrake control surface itself. After briefly introducing the demonstrator aircraft, the airbrake design and the experimental test benches the article gives in depth description of the modeling and system identification referencing also previous work. System identification consists of the determination of the highly nonlinear (saturated and load dependent) servo actuator dynamics and the nonlinear aerodynamic and mechanical characteristics including stiffness and inertia effects. New contributions relative to the previous work are a unified servo angular velocity limit model considering opening against the load or closing with it, the detailed construction and evaluation of airbrake normal and drag force models considering the whole deflection and aircraft airspeed range, the presentation of a unified aerodynamic - mechanic nonlinearity model giving direct relation between airbrake angle, dynamic pressure and servo torque and the transfer function-based modeling of stiffness and inertial effects in the mechanism. The identified servo dynamical model includes system delay, inner saturation, the aforementioned load dependent angular velocity limit model and a transfer function model. The servo model was verified based-on test bench measurements considering the whole opening angle and dynamic load range of the airbrake. New, unpublished measurements with gradually increasing servo load as the servo moves are also considered to verify the model in more realistic circumstances. Then the full airbrake model is constructed and tested in simulation to check realistic behavior. In the next step the airbrake model integrated into the nonlinear simulation model of the FLEXOP aircraft is tested by flying simulated test trajectories with the baseline controller of the aircraft in software-in-the-loop (SIL) Matlab simulation. First, the standalone airbrake simulation is compared to the SIL results to verify flawless integration of airbrake model into the nonlinear aircraft simulation. Then deceleration times with and without airbrake are compared underlining the usefulness of the airbrake in the test mission. Finally, real flight data is used to verify and update the airbrake model and show the effectiveness of the airbrake.

Model Predictive Control of Half-Car Active Suspension Systems Using Particle Swarm Optimisation

This paper presents the design of a particle swarm-optimised model predictive controller (MPC) for a half-car nonlinear electrohydraulic suspension system as it traverses a deterministic road disturbance. The particle swarm optimisation (PSO) algorithm uses an objective function which is based on conflicting active vehicle suspension system (AVSS) design specifications such as: ride comfort, road holding, road handling, suspension travel and power consumption. An inner-loop PID-based force feedback control is incorporated in the design to ensure good force tracking. The half-car model is composed of nonlinear suspensions and actuator dynamics. Simulation results demonstrate the superior performance of the proposed control scheme over the passive vehicle suspension system (PVSS) and the non-optimised MPC in rejecting the deterministic road disturbance.

Neural Extended State Observer Based Intelligent Integrated Guidance and Control for Hypersonic Flight

Near-pace hypersonic flight has great potential in civil and military use due to its high speed and low cost. To optimize the design and improve the robustness, this paper focuses on the integrated guidance and control (IGC) design with nonlinear actuator dynamics in the terminal phase of hypersonic flight. Firstly, a nonlinear integrated guidance and control model is developed with saturated control surface deflection, and third-order actuator dynamics is considered. Secondly, a neural network is introduced using an extended state observer (ESO) design to estimate the complex model uncertainty, nonlinearity and disturbance. Thirdly, a command-filtered back-stepping controller is designed with flexible designed sliding surfaces to improve the terminal performance. In this process, hybrid command filters are implemented to avoid the influences of disturbances and repetitive derivation, meanwhile solving the problem of unknown control direction caused by nonlinear saturation. The stability of the closed-loop system is proved by the Lyapunov theory, and the controller parameters can be set according to the relevant remarks. Finally, a series of numerical simulations are presented to show the feasibility and validity of the proposed IGC scheme.

Electrohydraulic Active Suspension Fuzzy-Neural Based Control System

A design of a new controller via a combination of fuzzy controller and artificial neural network (ANN) force tracking solution for a full vehicle suspension system with nonlinear electrohydraulic actuator dynamics is proposed. The comparison between the new Fuzzy-ANN force tracking controller designed with passive suspension system and PID-ANN controller previously developed is presented. Simulations and results obtained show that the Fuzzy-ANN combined controller can improve the stability problems caused by disturbances and road conditions, providing a superior passenger comfort.

Stabilization of Two-Dimensional Nonlinear Systems Described by Fornasini--Marchesini and Roesser Models

The paper considers nonlinear two-dimensional systems described by the Fornasini--Marchesini or Roesser state-space models. Conditions for such systems to have a physically motivated exponential stability property are derived using vector Lyapunov functions. A form of passivity, termed exponential passivity, is introduced and used, together with a vector storage function, to develop a feedback based control law that guarantees exponential stability of the controlled system. For cases where noise is present, stochastic dissipativity in the second moment is defined and then a particular case of this property, termed passivity in the mean square, is used, together with a vector storage function, to develop a feedback based control law such that the controlled system also has this property. Two physically motivated particular cases, a system with nonlinear actuator dynamics and additive noise and a linear system with state-dependent noise, respectively, are also considered to demonstrate the effectiveness of the new results.

Stochastic Stability of Some Classes of Nonlinear 2D Systems

The paper considers nonlinear discrete and differential stochastic repetitive processes using the state-space model setting. These processes are a special case of 2D systems that originate from the modeling of physical processes. Using the vector Lyapunov function method, sufficient conditions for stability in the mean square are obtained in the stochastic setting, where the vast majority of the currently known results are for deterministic dynamics. Based on these results, the property of stochastic exponential passivity in the second moment is used, together with the vector storage function, to develop a new method for output feedback control law design. An example of a system with nonlinear actuator dynamics and state-dependent noise is given to demonstrate the effectiveness of the new results.

Control of active suspension system considering nonlinear actuator dynamics

Application of the state-dependent Riccati equation and approximating sequence of Riccati equation techniques for the control of active suspension system considering nonlinear actuator dynamics will be investigated. First, equation of motion of the vehicle model is written in terms of the nonlinear state equations. Then, a performance index is formed for the minimization of the acceleration of the sprung mass, suspension deflection, velocity of the sprung mass, tire deflection, velocity of the unsprung mass, pressure decrease through the piston, and rate of pressure decrease through the piston. A sinusoidal bump and road roughness are considered as the road disturbances. After that, control input is expressed in terms of the Riccati differential equation variables and the state variables. Finally, quarter vehicle suspension system model of a Ford Fiesta Mk2 is taken into consideration in numerical simulations to test the performances of the both techniques. The results are compared to those of equivalent passive suspension system.

Development of rotary hydro-elastic actuator with robust internal-loop-compensator-based torque control and cross-parallel connection spring

Hydraulic actuation systems have high power-to-weight ratio and durability characteristics, but its the non-backdrivability and high output stiffness of hydraulic prevented it from being actively applied to interactive control systems, especially in robotics. This paper describes a force/torque control strategy to address these interactive hydraulic system control problems, with hydro-elastic actuation, which is a combination of a hydraulic actuator with a spring installed on the output side. This configuration simplifies the hydraulic actuator force/torque control problem into a motion control problem. To achieve high performance, first we introduced a robust internal- loop compensator (RIC) for hydraulic motion control, which has equivalent properties to a disturbance observer (DOB) and applicability in non-linear hydraulic actuator dynamics by decoupling the inner-loop compensator and outer-loop controller. This also minimizes sensor requirements and computation costs versus conventional hydraulic motion controllers. Based on this first strategy, second, we propose link-side motion feedback to compensate for undesirable velocity disturbances from the link side to provide high-accuracy torque control for the HEA system. Finally, we propose cross-parallel connection strategy to HEA spring to achieve high durability and deflection linearity Experimental results with custom-designed hardware showed torque controllability, backdrivability, low output impedance, and robustness in linking motion disturbance in time domain zero-torque and stiffness control experiments, without losing much of the high-power potential.