Robust Adaptive Gain Higher Order Sliding Mode Observer Based Control-constrained Nonlinear Model Predictive Control for Spacecraft Formation Flying

This work deals with the development of a decentralized optimal control algorithm, along with a robust observer,for the relative motion control of spacecraft in leader-follower based formation. An adaptive gain higher order sliding mode observer has been proposed to estimate the velocity as well as unmeasured disturbances from the noisy position measurements.A differentiator structure containing the Lipschitz constant and Lebesgue measurable control input, is utilized for obtaining the estimates. Adaptive tuning algorithms are derived based on Lyapunov stability theory, for updating the observer gains,which will give enough flexibility in the choice of initial estimates.Moreover, it may help to cope with unexpected state jerks. The trajectory tracking problem is formulated as a finite horizon optimal control problem, which is solved online. The control constraints are incorporated by using a nonquadratic performance functional. An adaptive update law has been derived for tuning the step size in the optimization algorithm, which may help to improve the convergence speed. Moreover, it is an attractive alternative to the heuristic choice of step size for diverse operating conditions. The disturbance as well as state estimates from the higher order sliding mode observer are utilized by the plant output prediction model, which will improve the overall performance of the controller. The nonlinear dynamics defined in leader fixed Euler-Hill frame has been considered for the present work and the reference trajectories are generated using Hill-Clohessy-Wiltshire equations of unperturbed motion. The simulation results based on rigorous perturbation analysis are presented to confirm the robustness of the proposed approach.

Disturbance Observer Based Speed Control of PMSM Using Fractional Order PI Controller

In this paper, fractional order PI(FOPI) control is developed for speed control of permanent magnet synchronous motor(PMSM). Designing the parameters for FOPI controller is a challenging task, especially for nonlinear systems like PMSM.All three PI controllers in the conventional vector controlled speed drive are replaced by FOPI controllers. Design of these FOPI controllers is based on the locally linearized model of PMSM around an operating point. This operating point changes with the load torque. The novelty of the work reported here is in use of Non Linear Disturbance Observer(NLDO) to estimate load torque to obtain this new operating point. All three FOPI controllers are then designed adaptively using this new operating point. The scheme is tested on simulation using MATLAB/SIMULINK and results are presented.

Fractional order integral sliding mode control for PMSM based onfractional order sliding mode observer

In view of the variation of system parameters and external load disturbance affecting the high-performance control of permanent magnet synchronous motor(PMSM),a fractional order integral sliding mode control(FOISMC)strategy is developed for PMSM drive system by means of fractional order sliding mode observer(FOSMO).Based on FOISMC technology,a fractional order integral sliding mode regulator(FOISM-based regulator)is designed,and a global integral sliding mode surface design method is presented,which can guarantee the global robustness of the system.Combining fractional order theory and sliding mode control theory,the FOSMO is constructed to achieve better identification accuracy of the speed and rotor position.Meanwhile the sliding mode load observer is used to observe the load torque in real time,and the observed value is transmitted to speed regulator to improve the capability of accommodating the challenge of load disturbance.Simulation results validate the feasibility and effectiveness of the proposed scheme.

Reduced order observer based identification of base isolated buildings

The objective of this study is to identify system parameters from the recorded response of base isolated buildings,such as USC hospital building,during the 1994 Northridge earthquake.Full state measurements are not available for identification.Additionally,the response is nonlinear due to the yielding of the lead-rubber bearings.Two new approaches are presented in this paper to solve the aforementioned problems.First,a reduced order observer is used to estimate the unmeasured states.Second,a least squares technique with time segments is developed to identify the piece-wise linear system properties.The observer is used to estimate the initial conditions needed for the time segmented identification.A series of equivalent linear system parameters are identified in different time segments.It is shown that the change in system parameters,such as frequencies and damping ratios,due to nonlinear behavior of the lead-rubber bearings,are reliably estimated using the presented technique.It is shown that the response was reduced due to yielding of the lead-rubber bearings and period lengthening.

Observer based projective reduced-order synchronization of different chaotic systems

The projective reduced-order synchronization of two different chaotic systems with different orders is investigated based on the observer design in this paper.According to the observer theory,the reduced-order observer is designed.The projective synchronization can be realized by choosing the transition matrix of the observer as a diagonal matrix.Further,the synchronization between hyperchaotic Chen system(fourth order)and Rssler system(third order)is taken as the example to demonstrate the effectiveness of the proposed observer.Numerical simulations confirm the effectiveness of the method.

Parametric Approach for the Normal Luenberger Function Observer Design in Second-order Descriptor Linear Systems

In this paper, the normal Luenberger function observer design for second-order descriptor linear systems is considered. It is shown that the main procedure of the design is to solve a so-called second-order generalized Sylvester-observer matrix equation. Based on an explicit parametric solution to this equation, a parametric solution to the normal Luenberger function observer design problem is given. The design degrees of freedom presented by explicit parameters can be further utilized to achieve some additional design requirements.

Design of Luenberger function observer with disturbance decoupling for matrix second-order linear systems-a parametric approach

A simple method for disturbance decoupling for matrix second-order linear systems is proposed directly in matrix second-order framework via Luenberger function observers based on complete parametric eigenstructure assignment. By introducing the H2 norm of the transfer function from disturbance to estimation error, sufficient and necessary conditions for disturbance decoupling in matrix second-order linear systems are established and are arranged into constraints on the design parameters via Luenberger function observers in terms of the closed-loop eigenvalues and the group of design parameters provided by the eigenstructure assignment approach. Therefore, the disturbance decoupling problem is converted into an eigenstructure assignment problem with extra parameter constraints. A simple example is investigated to show the effect and simplicity of the approach.

Robust Fractional-Order Proportional-Integral Observer for Synchronization of Chaotic Fractional-Order Systems

In this paper, we propose a robust fractional-order proportional-integral(FOPI) observer for the synchronization of nonlinear fractional-order chaotic systems. The convergence of the observer is proved, and sufficient conditions are derived in terms of linear matrix inequalities(LMIs) approach by using an indirect Lyapunov method. The proposed FOPI observer is robust against Lipschitz additive nonlinear uncertainty. It is also compared to the fractional-order proportional(FOP) observer and its performance is illustrated through simulations done on the fractional-order chaotic Lorenz system.

Nonlinear Control of an Induction Motor Using a Reduced-Order Extended Sliding Mode Observer for Rotor Flux and Speed Sensorless Estimation

This article proposes an innovative strategy to the problem of non-linear estimation of states for electrical machine systems. This method allows the estimation of variables that are difficult to access or that are simply impossible to measure. Thus, as compared with a full-order sliding mode observer, in order to reduce the execution time of the estimation, a reduced-order discrete-time Extended sliding mode observer is proposed for on-line estimation of rotor flux, speed and rotor resistance in an induction motor using a robust feedback linearization control. Simulations results on Matlab-Simulink environment for a 1.8 kW induction motor are presented to prove the effectiveness and high robustness of the proposed nonlinear control and observer against modeling uncertainty and measurement noise.

The Design of Reduced-order Observer for Systems with Monotone Nonlinearities

与单调非线性为系统关于存在和完整顺序的观察员的设计方法基于讨论，一个还原剂顺序观察员设计方法在线性矩阵不平等(LMI ) 有的假设下面被开发积极明确的矩阵答案和还原剂顺序观察员获得矩阵被 LMI 的解决方案计算。由线性转变，不包含系统产量的衍生物的信息的一个还原剂顺序观察员被提供。一个模型被模仿，一些结论基于还原剂顺序观察员的结果的比较被得出到完整顺序的观察员的。模拟证明这份报纸开发的设计方法有好性能。

Unified parametric approaches for high-order integral observer design for matrix second-order linear systems

A type of high-order integral observers for matrix second-order linear systems is proposed on the basis of generalized eigenstructure assignment via unified parametric approaches. Through establishing two general parametric solutions to this type of generalized matrix second-order Sylvester matrix equations, two unified complete parametric methods for the proposed observer design problem are presented. Both methods give simple complete parametric expressions for the observer gain matrices. The first one mainly depends on a series of singular value decompositions, and is thus numerically simple and reliable; the second one utilizes the fight factorization of the system, and allows eigenvalues of the error system to be set undetermined and sought via certain optimization procedures. A spring-mass-dashpot system is utilized to illustrate the design procedure and show the effect of the proposed approach.

Observer design for matrix second-order linear systems: a parametric approach

The issue of designing a type of generalized Luenberger observers for matrix second-order linear (MSOL) systems was addressed in the matrix second-order framework. By introducing the concept of stable matrix pair for MSOL systems, sufficient and necessary conditions for the design of the type of generalized Luenberger observers were given under the assumption of controllability and observability of the MSOL system. Based on the proposed conditions and the right coprime factorization of the system, a parametric approach to the design of such type of observers was presented. The proposed approach provides all the degrees of design freedom, which can be further utilized to achieve additional system specifications. A spring-mass system was utilized to show the effect of the proposed method.

Robust fault detection in linear systemsbased on full-order state observers

A parametric approach to robust fault detection in linear systems with unknown disturbances is presented. The residual is generated using full-order state observers （FSO）. Based on an analytical solution to a type of Sylvester matrix equations, the parameterization of the observer gain matrix is given. In terms of the design degrees of freedom provided by the parametric observer design and a group of introduced parameter vectors, a sufficient and necessary condition for fullorder state observer design with disturbance decoupling is then established. By properly constraining the design parameters according to this proposed condition, the effect of the disturbance on the residual signal is also decoupled, and a simple algorithm is developed. The presented approach offers all the degrees of design freedom. Finally, a numerical example illustrates the effect of the proposed approach.

Conventional and Added-Order Proportional Nonlinear Integral Observers

In this paper, a kind of fire new nonlinear integrator and integral action is proposed. Consequently, a conventional Proportional Nonlinear Integral (P_NI) observer and two kinds of added-order P_NI observers are developed to deal with the uncertain nonlinear system. The conditions on the observer gains to ensure the estimated error to be ultimate boundness, which shrinks to zero as the states and control inputs converge to the equilibrium point, are provided. This means that if the observed system is asymptotically stable, the estimated error dynamics is asymptotically stable, too. Moreover, the highlight point of this paper is that the design of nonlinear integral observer is achieved by linear system theory. Simulation results showed that under the normal and perturbed cases, the pure added-order P_NI observer can effectively deal with the uncertain nonlinearities on both the system dynamics and measured outputs.

Observer design and output feedback stabilization for linear singular time-delay systems with unknown inputs

The design of a functional observer and reduced-order observer with internal delay for linear singular timedelay systems with unknown inputs is discussed. The sufficient conditions of the existence of observers, which are normal linear time-delay systems, and the corresponding design steps are presented via linear matrix inequality（LMI）. Moreover, the observer-based feedback stabilizing controller is obtained. Three examples are given to show the effectiveness of the proposed methods.

Sliding-mode observers for systems with unknown inputs and measurement disturbances

The method to design sliding-mode observers for systems with unknown inputs and measurement disturbances is presented in the paper. An augmented system is constructed by viewing the measurement disturbances as unknow inputs. For such an augmented system, the so-called observer matching condition is not satisfied. Based on the construction of auxiliary outputs, the observer matching condition may be satisfied. High-order sliding-mode differentiators are developed to obtain the estimates of those unmeasurable variables contained in the auxiliary output vector. Employing the estimate of auxiliary output vector, a sliding-mode observer is designed. The simulation results to a real model show that the proposed method is effective.

Research on the stability, controllability and observability for fractional order LTI systems

The state space representations of fractional order linear time- invariant（LTI） systems are introduced, and their solution formulas are deduced hy means of Laplace transform. The stability condition of fractional order LTI systems is given, and its proof is deduced by means of using linear non - singularity transform and the derivative property of Mittag-Leffler function. The controllability condition of fractional m＇der LTI systems is given, and its proof is deduced by means of using its characteristic polynomial and the Cayley-Hamilton theorem. The observability condition of fractional order LTI systems is given, and its proof is deduced by means of their solution formulas. Finally an example is given to prove the correctness of the stability, controllability, and observability conditions mentioned above, s are deduced by means of Laplace transform. Their stability, controllability and observability conditions are given as well as their proofs.

Study on Four Disturbance Observers for FO-LTI Systems

This paper addresses the problem of designing disturbance observer for fractional order linear time invariant U+0028 FO-LTI U+0029 systems, where the disturbance includes time series expansion disturbance and sinusoidal disturbance. On one hand, the reduced order extended state observer U+0028 ROESO U+0029 and reduced order cascade extended state observer U+0028 ROCESO U+0029 are proposed for the case that the system state can be measured directly. On the other hand, the extended state observer U+0028 ESO U+0029 and the cascade extended state observer U+0028 CESO U+0029 are presented for another case when the system state cannot be measured directly. It is shown that combination of ROCESO and CESO can achieve a highly effective observation result. In addition, the way how to tune observer parameters to ensure the stability of the observers and reduce the observation error is presented in this paper. Finally, numerical simulations are given to illustrate the effectiveness of the proposed methods. © 2014 Chinese Association of Automation.

Target Tracking Algorithm Using Finite-time Convergence Smooth Second-order Sliding Mode Controller for Mobile Robots

Target tracking control for wheeled mobile robot （WMR） need resolve the problems of kinematics model and tracking algorithm.High-order sliding mode control is a valid method used in the nonlinear tracking control system,which can eliminate the chattering of sliding mode control.Currently there lacks the research of robustness and uncertain factors for high-order sliding mode control.To address the fast convergence and robustness problems of tracking target,the tracking mathematical model of WMR and the target is derived.Based on the finite-time convergence theory and second order sliding mode method,a nonlinear tracking algorithm is designed which guarantees that WMR can catch the target in finite time.At the same time an observer is applied to substitute the uncertain acceleration of the target,then a smooth nonlinear tracking algorithm is proposed.Based on Lyapunov stability theory and finite-time convergence,a finite time convergent smooth second order sliding mode controller and a target tracking algorithm are designed by using second order sliding mode method.The simulation results verified that WMR can catch up the target quickly and reduce the control discontinuity of the velocity of WMR.

Boundary Control Problems for 2 ×2 Cooperative Hyperbolic Systems with Infinite Order Operators

In this study, boundary control problems with Neumann conditions for 2 × 2 cooperative hyperbolic systems involving infinite order operators are considered. The existence and uniqueness of the states of these systems are proved, and the formulation of the control problem for different observation functions is discussed.