Unknown Constant Parameters Research Articles

Power capture optimization of variable-speed wind turbines using an output feedback controller

One of the major factors that can increase the efficiency of wind turbines is through control of the rotor speed to track the optimal value. A high performance controller can significantly increase the amount of energy that can be captured from wind. The main problem associated with controller design is the presence of uncertainties in the dynamic model of the system, which can be associated with unknown constant parameters and/or unmodeled dynamics such as external disturbances. several adaptive and robust control approaches have been developed to account for these uncertainties. In this paper, a robust controller is presented that compensates for both types of uncertainties; the full mechanical and electrical dynamics of the turbine are considered. These dynamics require acceleration of the rotor to provide feedback information which is not available in sufficiently accurate form during practice. Therefore, in this approach, an observer estimates this information using the speed of the rotor as the output, with the estimation error considered during the stability analysis. This presents one of the main advantages of the approach; the simulation results illustrate the effectiveness of the controller.

Аdaptive flux observer for permanent magnet synchronous motors

The paper deals with the observer design problem for a flux in permanent magnet synchronous motors. It is assumed that some electrical parameters such as resistance and inductance are known numbers. But the flux, the angle and the speed of the rotor are unmeasurable. The new robust approach to design an adaptive flux observer is proposed that guarantees globally boundedness of all signals and, moreover, exponential convergence to zero of observer error between the true flux value and an estimate obtained from the adaptive observer. The problem of an adaptive flux observer design has been solved with using the trigonometrical properties and linear filtering which ensures cancellation of unknown terms arisen after mathematical calculations. The key idea is the new parameterization of the dynamical model containing unknown parameters and depending on measurable current and voltage in the motor. By applying the Pythagorean trigonometric identity the linear equation has found that does not contain any functions depending on angle or angular velocity of the rotor. Using dynamical first-order filters the standard regression model is obtained that consists of unknown constant parameters and measurable functions of time. Then the gradient-like estimator is designed to reconstruct unknown parameters, and it guarantees boundedness of all signals in the system. The proposition is proved that if the regressor satisfies the persistent excitation condition, meaning the “frequency-rich” signal, then all errors in observer exponentially converges to zero. It is shown that observer error for the flux explicitly depends on estimator errors. Exponential convergence of parameter estimation errors to zero yields exponential convergence of the flux observer error to zero. The numerical example is considered.

On fractional order composite model reference adaptive control

This paper presents a novel composite model reference adaptive control approach for a class of fractional order linear systems with unknown constant parameters. The method is extended from the model reference adaptive control. The parameter estimation error of our method depends on both the tracking error and the prediction error, whereas the existing method only depends on the tracking error, which makes our method has better transient performance in the sense of generating smooth system output. By the aid of the continuous frequency distributed model, stability of the proposed approach is established in the Lyapunov sense. Furthermore, the convergence property of the model parameters estimation is presented, on the premise that the closed-loop control system is stable. Finally, numerical simulation examples are given to demonstrate the effectiveness of the proposed schemes.

Modular Multilevel Converter With an Adaptive Observer of Capacitor Voltages

A modular multilevel converter (MMC) is an attractive solution for power conversion without transformers. The MMC consists of cascade connections of floating dc capacitors. In this paper, an adaptive observer design has been proposed to estimate the capacitor voltages from the measurement of arm currents. This work introduces the capacitance value of the cell capacitors as a parameter uncertainty for making the system performance robust with unknown constant parameters. It may be used for predictive control, condition monitoring for capacitors, and diagnosis check for capacitor health. In addition, a pulsewidth modulation (PWM) technique for MMC has been explored. The PWM technique is performed using a carrier-based level-shifted PWM strategy. It does not necessitate the calculation of duty cycles, and can be easily implemented in a DSP. By using the PWM technique, harmonics in the phase voltage is shifted to twice the switching frequency. Theoretical analysis is included in this paper for showing stability and convergence of the proposed observer. Analytical expressions are verified by simulation and experimental results.

Adaptive observers for speed sensorless IMs

In this paper, one proposes an approach which allows the design adaptive observers for a class of uniformly observable nonlinear MIMO systems with linear parameterisations. The structure of the proposed observer is simple and it is able to give rise to different observers: 1 adaptive high gain observer for linearly parameterised; 2 adaptive sliding mode observer for linearly parameterised with tanh commutation function; 3 adaptive sliding mode observer for linearly parameterised with arctan commutation function. These observers are applied to jointly estimate states rotor flux, rotating speed and torque load and unknown constant parameters stator resistance.

On the algebraic parameter identification of vibrating mechanical systems

This paper proposes an on-line algebraic parameter identification method in time domain for multiple degrees-of-freedom linear mass–spring–damper mechanical systems using position measurements. The constant parameters of mass, stiffness and damping are algebraically estimated from transient real-time measurements. Analytical and numerical results prove the accuracy and efficiency of the proposed identification approach for reference trajectory tracking control tasks on multiple-input–multiple-output vibrating mechanical systems with unknown constant parameters.

Adaptive observer-based control for a class of nonlinear stochastic systems

In this paper, the adaptive state estimation and state-feedback stabilization problems for a class of nonlinear stochastic systems with unknown constant parameters are studied. The sequential design methods are proposed to construct the adaptive controllers. Adaptive state and parameter estimators are designed by using a stochastic Lyapunov method and the separation theory of the design for the state-feedback gain and observer gain, which guarantees that the closed-loop system is asymptotically stable in the mean-square sense. Sufficient conditions for the existence of parameters estimator are given in terms of linear matrix inequalities. Finally, the numerical examples are provided to illustrate the feasibility of the proposed theoretical results.

Exact optimal solution for a class of dual control problems

This paper considers a discrete-time stochastic optimal control problem for which only measurement equation is partially observed with unknown constant parameters taking value in a finite set of stochastic systems. Because of the fact that the cost-to-go function at each stage contains variance and the non-separability of the variance is so complicated that the dynamic programming cannot be successfully applied, the optimal solution has not been found. In this paper, a new approach to the optimal solution is proposed by embedding the original non-separable problem into a separable auxiliary problem. The theoretical condition on which the optimal solution of the original problem can be attained from a set of solutions of the auxiliary problem is established. In addition, the optimality of the interchanging algorithm is proved and the analytical solution of the optimal control is also obtained. The performance of this controller is illustrated with a simple example.

Adaptive control of a class of non-linear systems preceded by backlash-like hysteresis

We consider a class of uncertain non-linear systems preceded by unknown backlash-like hysteresis, which is modelled by a differential equation. We propose a new state feedback robust adaptive control scheme using a backstepping technique and properties of the differential equation. In this control scheme, we construct a new continuous function to design an estimator to estimate the unknown constant parameters and the unknown bound of a ‘disturbance-like’ term. The transient performance of the output tracking error can be guaranteed by the introduction of pre-estimates of the unknown parameters in our controller together with update laws. We do not require bounds on the ‘disturbance-like’ term or unknown system parameters in this scheme. The global stability of the closed-loop system can be proved.

Adaptive State Estimation for a Class of Nonlinear Stochastic Systems under Generalized Lipschitz Condition

This paper is concerned with adaptive observer design problem for a class of nonlinear stochastic systems. Unknown constant parameters are assumed to be norm bounded. In order to better use the structural knowledge of the nonlinear part, a generalized Lipschitz condition is introduced to the adaptive observer design for a class of nonlinear stochastic systems for the first time. Based on a Lyapunov-Krasovskii functional approach and stochastic Lyapunov stability theory, we present a new adaptive observer design condition with ultimately exponentially bounded in sense of mean square for errors systems in terms of linear matrix inequality (LMI). A numerical example is exploited to show the validity and feasibility of the results.

Zero-error tracking control of uncertain nonlinear systems in the presence of actuator hysteresis

In this paper, the problem of adaptive tracking control is addressed for a class of nonlinear systems with unknown constant parameters and unknown actuator nonlinearity. The actuator nonlinearity is modelled as the backlash-like hysteresis, which is described by a differential model. The prior knowledge on the control gain sign is not required, and only the assumption on the reference signal is made. By combining the adaptive backstepping technique with the Nussbaum gain approach, an adaptive compensation controller design approach is developed. It is proved that the proposed control approach can guarantee that all the signals in the closed-loop system are bounded, and the tracking error can converge to zero asymptotically despite the presence of the actuator hysteresis. Two simulation examples are included to illustrate the effectiveness of the proposed approach.

Observer and model predictive control for on-line parameter identification in nonlinear systems

This paper develops an on-line model parameter identification approach for multivariable systems, which are nonlinear in terms of state representation and/or in terms of parameters. Combining the observation theory and the model based predictive control theory, an optimal closed loop experiment design for on-line identification of model parameters is given. During only one experiment, an optimal time-varying input is computed to optimize a criterion, while the unknown model parameters are estimated at the same time. The criterion is based on the sensitivities of the model outputs with respect to the unknown parameters that are estimated. The approach does not require to measure all the process state. Moreover output constraints allow to maintain the behaviour into a prescribed region and/or stabilize the process in closed loop. This approach is illustrated through an unstable rolling delta wing with one input, two measured states and five unknown constant model parameters.

Inverse optimal adaptive stochastic gain assignment for a class of nonlinear systems with Markovian jump

This paper deals with the inverse optimal adaptive stochastic gain assignment problem for a class of Markovian jump nonlinear systems with constant unknown parameters. The Wiener noises have bounded but unknown covariance. It is shown that a sufficient condition to solve this problem is the existence of a Lyapunov function for a corresponding auxiliary system. By employing backstepping technique and common Lyapunov function method, an adaptive control law is designed, which solves this problem for a class of Markovian jump nonlinear systems in strict-feedback form. A numerical example is given to illustrate the theoretical analysis result.

Positive invariant set estimation of adaptive controller in the presence of input saturation

SUMMARYFor a class of linear dynamical systems with constant unknown parameters, an adaptive control scheme is developed that provides stable adaptation in the presence of input magnitude constraints. Whereas for open‐loop stable systems the results are global, for open‐loop unstable systems, the problem of nonconservative estimation of the nonempty positive invariant set is cast into an LMI framework, which can be efficiently solved numerically via convex optimization. To achieve this, a standard result toward invariant set characterization is appropriately extended to accommodate bounded disturbance and model uncertainties. In addition to closed‐loop stability, performance bounds of the adaptive closed‐loop system are analyzed, and the degradation due to the possible control deficiency is quantified. Simulation examples of aerospace applications are included to illustrate the proposed method. Copyright © 2012 John Wiley & Sons, Ltd.

Enforcing Consensus on Adaptive Parameter Estimation of Structurally Perturbed Infinite Dimensional Systems

The aim of this note is to investigate the agreement between state and parameter estimates for a class of infinite dimensional systems that utilize distributed adaptive filters. It is assumed that the unknown parameters take the form of a structured perturbation with an unknown constant parameter, and the nominal system satisfies an infinite dimensional analog of positive real lemma. The proposed adaptive observers generated by m agents follow the structure of adaptive identifiers for infinite dimensional systems with the added feature of a penalty term in both the state and parameter estimates. Unlike earlier efforts, the proposed adaptive laws include a penalty term of the mismatch between the parameter estimates generated by the other agents. Conditions that provide uniform boundedness of the estimator dynamics and the parameter estimates are examined. Additionally, the effects of these modifications on the agreement amongst the state and parameter estimates are studied. The convergence of the deviation from the mean estimate is established as a metric for the performance of the consensus filters for both state and parameter estimates. The effects of the proposed consensus enforcement are illustrated with a diffusion partial differential equation example, which yield convincing numerical findings.

Continuous adaptive observer for state affine sampled‐data systems

SUMMARYIn this paper, a hybrid adaptive observer is designed for a class of nonlinear sampled‐data systems with constant unknown parameters. The proposed observer uses a predictor of the output between the sampling times. This predictor is re‐initialized at each sampling time. This observer is very simple to implement and converges exponentially under some sufficient conditions. An explicit relation between the bound of the maximum allowable sampling time (τMASP) and the parameters of the observer is also given. Copyright © 2012 John Wiley & Sons, Ltd.

Boundary second-order sliding-mode control of an uncertain heat process with unbounded matched perturbation

The primary concern of the present paper is the regulation of an uncertain heat process with collocated boundary sensing and actuation. The underlying heat process is governed by an uncertain parabolic partial differential equation (PDE) with Neumann boundary conditions. It exhibits an unknown constant diffusivity parameter and it is affected by a smooth boundary disturbance, which is not available for measurements and which is possibly unbounded in magnitude. The proposed robust synthesis is formed by the linear feedback design and by the ”Twisting” second-order sliding-mode control algorithm, suitably combined and re-worked in the infinite-dimensional setting. A non-standard Lyapunov functional is invoked to establish the global asymptotic stability in a Sobolev space, involving spatial state derivatives of the same order as that of the plant equation. The stability proof is accompanied by a set of simple tuning rules for the controller parameters. The effectiveness of the developed control scheme is supported by simulation results.

Lyapunov-based adaptive state estimation for a class of nonlinear stochastic systems

This paper is concerned with an adaptive state estimation problem for a class of nonlinear stochastic systems with unknown constant parameters. These nonlinear systems have a linear-in-parameter structure, and the nonlinearity is assumed to be bounded in a Lipschitz-like manner. Using stochastic counterparts of Lyapunov stability theory, we present adaptive state and parameter estimators with ultimately exponentially bounded estimator errors in the sense of mean square for both continuous-time and discrete-time nonlinear stochastic systems. Sufficient conditions are given in terms of the solvability of LMIs. Moreover, we also introduce a suboptimal design approach to optimizing the upper bound of the mean-square error of parameter estimation. This suboptimal design procedure is also realized by LMI computations. By a martingale method, we also show that the related Lyapunov function has a non-negative Lyapunov exponent.

Toward design and fabrication of wind-driven vehicles: Procedure to optimize the threshold of driving forces

Wind energy has been continuously considered as a green, available, and economical alternative source of energy. For centuries, the transformed wind energy to drag-force has been used for transportation in watercrafts. With improvement of aerodynamics, the airfoil was invented to create and use a higher magnitude aerodynamic force, lift-force, in order to elevate airplanes. Later, the lift-force was horizontally applied as the thrust force in land/water wind-crafts. Whereas in airplanes horizontal airfoils (wing) create a vertical lift-force, installed vertical airfoils (wing-sail) produce a horizontal lift-force in wind-crafts. Therefore, this force can be used as thrust (driving) force in lift-based ice, water, and land vehicles. If the prevailing wind is constantly available, the vehicle speed can even exceed the wind velocity. Due to the complex kinematics of such vehicles, however, it should be noted that there would be always an optimum for the thrust force in order to control and navigate the vehicle to the destination point, and to avoid the severe undesired side-forces. This optimum is calculated in wind-craft trajectory software (WTS) which requires many inputs, including variable and constant parameters. Variable parameters consist of wind direction and magnitude in addition to vehicle’s position, velocities, and accelerations. On the other hand, design characteristics of the wind-driven vehicle are known as constant parameters. The land-yacht body’s drag is an unknown constant parameter which alters according to the relative wind. This implies that several wind tunnel experiment in different wind directions and speeds are required in order to obtain the drag coefficients.Therefore in order to bypass the wind tunnel measurements, this study aims to propose a fast and economical procedure to find the aforementioned drag coefficient by integration of a measurement and by a simulation approach. The obtained data can be later used in the optimization and control module of the WTS. The performance of this procedure has been investigated using a case study. For this purpose, a 1:4 prototype three-wheel land-yacht is first designed and fabricated. The land-yacht comprises of three major parts; horizontal airfoil (axle), vertical airfoil, and body. The dimensions of these elements are obtained after development of a code based on kinematics of the land-yacht. The axle is designed to increase the stability of the land-yacht, whereas the shape of the body is intended to produce a low drag coefficient in various directions. Furthermore, a set of experiments has been conducted to measure the body drag of the land-yacht in a direction parallel to the relative wind. This experiment is later used to develop and validate a computational fluid dynamics (CFD) model in order to estimate the drag of the land-yacht body in its various directions against the relative wind. The results show the adequate efficacy of this procedure to provide the required data for the optimization and control module of the WTS.

Robust Adaptive Control for Gun Control System of Tank

In this note, a class of gun control system of tank is considered with all uncertainties, such as unknown constant parameters, unlinearly parts, unparameterized parts, unmodeled parts, unknown external disturbance and so on. An robust adaptive control law is designed with backstepping technique. Compared to exist results on tank gun control problem , our control scheme combine the robust control and the adaptive estimator of unknown constant parameters and can compensate all uncertainties Accurately. The stability of closed loop system and the tracking performance can be guaranteed by this control law. Simulation studies show that this controller is effective.