Luenberger State Observer Research Articles

Full-speed domain position sensorless control strategy for PMSM based on a novel phase-locked loop

This paper proposes a full-speed-domain position-sensor-less control strategy for precise control under forward and reverse rotation conditions to address the weak convex polarity of surface-mounted permanent magnet synchronous motor (SPMSM). The strategy comprises several key stages: pre-positioning of the rotor, constant current variable frequency (I/F) start-up, construct the Luenberger State Observer, and utilization of an improved phase-locked loop (PLL) for position estimation. In the pre-positioning stage, a constant amplitude current is applied to drag the rotor to a predetermined position. Subsequently, the I/F start-up stage accelerates the motor to a predetermined speed before transitioning to the Luenberger observer for closed-loop speed control, which is based on an extended back electromotive force (back-EMF) a two-phase rotating coordinate system. The improved PLL for position and speed estimation features three components: a phase discriminator (PD), a voltage-controlled oscillator (VCO), and loop filter (LF). Experimental results demonstrate the efficacy of the proposed strategy, showing quick start-up response, speed estimation error below 2 RPM, rotor position estimation error under 0.6 degrees post-loop closure, stable tracking during rapid speed changes, and consistent accuracy and stability even under reverse rotation conditions, thereby meeting the control strategy’s objectives.

Improved model predictive control based on Luenberger state observer for LC‐coupling hybrid active power filter

AbstractAn improved model predictive control (MPC) with Luenberger state observer is proposed in this article for LC‐coupling hybrid active power filter (LC‐HAPF). Traditionally, the implementation of MPC for LC‐HAPF requires additional sensors to measure coupling capacitor voltage, thereby increases the system cost and reduces reliability. The existence of one‐step sampling delay in practice will also affect the final compensation performance. To relax these problems, both continuous and discrete models are deduced first. Then, the Luenberger observer is utilized based on the discrete model to mitigate the steady‐state error without additional sensors. In addition, the sampling delay compensation is provided by improving the prediction horizon. Finally, the effectiveness of the improved MPC for LC‐HAPF is verified by experiment results, indicating that the proposed method has fast dynamic response and low steady‐state error.

Model-based Luenberger State Observer for Detecting Interturn Short-Circuits in PM Machines

Model-based Luenberger State Observer for Detecting Interturn Short-Circuits in PM Machines

Adaptive observer design for uncertain hyperbolic PDEs coupled with uncertain LTV ODEs; Application to refrigeration systems

The problem of estimating the temperatures and the heat transfer coefficient of a concentric tube heat exchanger coupled with a heater is considered in this work. Measurements collected from the extremities of the exchanger tube are used to estimate the heat distribution over the length of the exchanger, which induces a boundary estimation problem. This system, which is part of any standard cooling plant, is particularly challenging due to the distributed nature of its variables. It is modeled by a system of (2 × 2) hyperbolic PDEs, coupled with an ODE at the boundary. To solve the estimation problem, we consider a general class of systems consisting of a (2 × 2) hyperbolic system coupled with a set of nX linear time-varying (LTV) ODEs at the boundary. Both the PDE and the ODEs have uncertain parameters to be estimated. The objective is to estimate the PDE states, the ODE states, and the parameters simultaneously with no assumption on the ODEs stability. We design a Luenberger state observer, and our method is mainly based on the decoupling of the PDE estimation error states from that of the ODEs via swapping design. We then derive the observer gains from the Lyapunov analysis of the decoupled system after proving the boundedness of the swapping filters. We give sufficient conditions of the exponential convergence of the adaptive observer through differential Lyapunov inequalities (DLIs). Finally, we apply the developed theory on the coupled heat exchanger–heater model to evaluate the performance of the observer in numerical simulations.

Takagi–Sugeno Fuzzy Model-Based Control for Semi-Active Cab Suspension Equipped with an Electromagnetic Damper and an Air Spring

Variable damping shock absorbers have received extensive attention for their efficient vibration reduction performance, and air springs have also been widely used in high-end commercial vehicles due to their nonlinear stiffness characteristics. This paper presents a novel semi-active cab suspension integrated with an air spring and a variable damping electromagnetic damper (A-EMD). The electromagnetic damper (EMD) prototype was designed, manufactured and tested. Then, due to the interference of nonlinear stiffness characteristics of the air spring with the controller in the subsequent design, the Takagi–Sugeno fuzzy method was adopted to segmentally linearize its nonlinearity, based on which an H∞ state feedback semi-active controller was designed to control the EMD to generate variable damping force. Furthermore, a Luenberger state observer was designed to provide immeasurable state parameters for the controller. Numerical simulations were carried out to validate the effectiveness of the proposed approaches, and the results show that the proposed control strategy can significantly improve the ride comfort of the A-EMD system. The vibration dose value (VDV) acceleration under the bump road and the frequency-weighted acceleration root mean square (FWA-RMS) under the random road decreased by 36.05% and 19.77%, respectively, compared with the passive suspension system.

Inter-Turn Short-Circuit Faults Diagnosis in Synchronous Reluctance Machines, Using the Luenberger State Observer and Current's Second-Order Harmonic

Interturn short-circuit faults are one of the most (if not the most) harmful electrical machine failures, that if not detected and mitigated at a very incipient stage of development may involve serious consequences, both in terms of repair costs and safety. This article proposes a novel interturn fault diagnostic technique for synchronous reluctance machines based on the Luenberger state observer and current's second-order harmonic. The superiority of the proposed approach over the conventional model-based techniques is the ability to evaluate the severity of the fault as well as the efficiency in detecting faults in early stages and under various operating conditions. The effectiveness of the proposed method is demonstrated and validated through several experimental tests.

Tuning Parameters-Based Fault Estimation Observer for Time-Delay Fuzzy Systems Over a Finite Horizon

In this work, the problem of fault and state estimation is studied for Takagi–Sugeno fuzzy systems with time-varying delay and external disturbance over a finite horizon. A fuzzy rule-based fault estimator with two tuning parameters, including the current system output information, is designed. Based on which, the Luenberger state observer is then considered to estimate the immeasurable states of the system addressed. The aim of taking into account the tuning parameters in the estimator design is to improve the accuracy of the fault estimation. More precisely, by defining error variables in accordance with actual and estimated system states and faults, an augmented system is formulated to achieve the desired results. By using the existing stability theory and integral inequality, a delay-dependent criterion for ensuring that the states of the augmented system are bounded over a finite horizon is derived. Subsequently, conditions for determining the observer gain matrices are presented. Two simulation examples, including an application example of the truck-trailer model, are provided to demonstrate the advantages of the theoretical results that have been established. In particular, the importance of the use of tuning parameters is discussed.

Exponential extended dissipative performance for delayed discrete-time neural networks under memoryless resilient-based observer design

This paper is concerned with the problem of exponentially extended dissipative criteria for a class of delayed discrete-time neural networks (DNNs) subject to resilient observer-based controller design. For this objective, a memoryless full-order Luenberger state observer is designed, and further, its observer error system is calculated with resilient control. Initially, some new improved weighted summation inequalities are proposed by combining weighted summation inequality and an extended reciprocal convex matrix inequality. By constructing the suitable Lyapunov-Krasovskii functional (LKF) and utilizing the developed summation inequalities, the exponentially extended dissipative criterion is obtained for the considered delayed DNNs. The designed observer and resilient control gain matrices can be determined by solving a set of linear matrix inequalities (LMIs) subject to the prescribed exponential decay rate. Finally, two numerical examples are carried out to illustrate the feasibility and effectiveness of the established theoretical results obtained through the newly developed summation inequalities.

Anti-disturbance stabilization for a hybrid system of non-uniform elastic string

This paper is concerned with the anti-disturbance boundary feedback stabilization for a hybrid system coupling a non-uniform elastic string with a rigid body at one end by the active disturbance rejection control technology. An infinite-dimensional disturbance estimator and a Luenberger state observer are designed to estimate the disturbance and state of the system, respectively, based on which, a boundary output feedback control is further proposed to stabilize the system. The control consists of two parts: one part is for the stabilization of system without external disturbance, and the other part is for the rejection of the disturbance by virtue of the disturbance estimator. The well-posedness and exponential stability of the closed-loop system are proved by employing the semigroup theories and frequency domain method. Besides, all the signals of the closed-loop system are shown to be uniformly bounded. Finally, some numerical simulations are presented to validate the effectiveness of the proposed control strategy.

An Inductor Current Sensorless Control Strategy Based on Modified VSG Method for Single-Phase Microgrid Application With Seamless Transfer Capability

This paper proposes an inductor current sensorless control strategy based on modified virtual synchronous generator (VSG) method for single-phase inverter-interfaced microgrid application. Firstly, the outer power loop with Q-U integral term is presented for output reactive power enhancement, and an inner voltage regulation loop based on luenberger state observer is proposed to reduce the inductor current sensor. Meanwhile, in order to improve the response speed of the observer, the luenberger observer is designed based on the optimal pole assignment method. Secondly, a seamless switching strategy based on the modified VSG method is proposed, which can realize the seamless transition between the island mode and grid-connected mode. Finally, a single-phase 3kW VSG prototype is built, and the effectiveness and correctness of the proposed control strategy is verified by the simulation and experimental results.

Optymalizacja wzmocnienia obserwatora Luenbergera w układzie predykcyjnego sterowania systemem aktywnego zawieszenia

MPC Driven control systems very often are requiring the introduction of a mechanism predicting the state of the object unavailable for measurements. Depending on the case, a different number of state variables will be unobtainable. Widely used systems to obtain essential data of the condition of an object are Luenberger state observer and different types of Kalman filters. The authors propose a new method of Luenberger observer synthesis based on Luenberger gain optimization using performance index corresponding to generalized system performance. The developed method allows us to obtain better-performing observer from the point of view of the adopted criterion, compared to similar estimators derived from the Sylvester equation and classic Kalman filters, even despite the occurrence of disturbances. The developed method will be presented on an example of an active suspension system with MPC.

Analysis of equivalent‐input‐disturbance‐based control systems and a coordinated design algorithm for uncertain systems

AbstractThe control method based on the equivalent‐input‐disturbance (EID) estimator and the Luenberger state observer has received much attention in recent years. However, the property of EID‐based control systems is still not well investigated. A number of design procedures were proposed but lacked sufficient theoretic justification. In this article, the two‐degree‐of‐freedom nature of an EID‐based control system is revealed. Specifically, the reference‐tracking is determined by an outer loop, while the disturbance rejection and robustness is determined by an inner loop consisting of the EID estimator and state observer. The bandwidth constraints on the inner loop are analyzed for plants having zeros or poles in the open right‐half plane by using the Bode and the Poisson integral formulas. These analyses provide a theoretic justification for conventional design procedures. Further, a coordinated design algorithm is provided for the EID‐based uncertain control systems. In addition, a comprehensive comparison of the EID‐based and the disturbance observer (DOB) based control systems is conducted in the system design aspect. Lastly, comparative studies of the EID‐based and DOB‐based control methods are given for various types of plants to validate the developed design algorithm.

A state observation and torque compensation–based acceleration slip regulation control approach for a four-wheel independent drive electric vehicle under slope driving

Wheel slipping of four-wheel independent drive electric vehicle on slope will reduce vehicle controllability and driving stability, thereby reducing vehicle safety. In order to solve the problem of wheel slipping and optimize the speed control performance of four-wheel independent drive electric vehicle on slope, an acceleration slip regulation control strategy of slope drive is proposed in this paper. First, we design a road identification algorithm to identify the current road conditions of the four-wheel independent drive electric vehicle, and calculate the optimal slip ratio of the current road surface by curve fitting method. Then, with the optimal slip ratio as the control objective, the acceleration slip regulation control strategy is designed to maximize the utilization of wheel adhesion coefficient to prevent wheel slip. Third, a slope identification algorithm based on Luenberger state observer is designed to identify the various slopes of the uphill and downhill road, after which a torque compensation algorithm is designed according to the identification slope, to compensate for the longitudinal component of vehicle gravity at different slopes. Fourth, a slope torque distribution algorithm is proposed based on acceleration slip regulation and slope identification. Finally, through the joint simulation platform of MATLAB/Simulink and CarSim, it is shown that the proposed control strategy can better restrain wheel slipping on the uphill and downhill road, and has better dynamic characteristics and stability.

A Road Identification Method Based on Road Slope Information for Four-Wheel Independent Drive Electric Vehicles

Four-wheel independent drive electric vehicles (4WID EV) drive safely and stably, which depends on current road conditions, especially road friction coefficient and slope, and different driving control strategies are used according to road conditions. Therefore, a road identification method is proposed to estimate the road information. Firstly, we design a road identification algorithm to identify the current road conditions of 4WID EV, and calculate the optimal slip ratio of the current road surface by curve fitting method. When the wheel slip ratio is controlled near the optimal slip ratio, the wheel adhesion coefficient can be maximized to prevent the wheel from slipping. Then, a slope identification algorithm based on Luenberger state observer is designed to identify the various slopes of uphill and downhill, and it provides a reference for the calculation of the slope compensation torque. Finally, through the joint simulation platform of MATLAB/Simulink and Carsim, it shows that the proposed road identification can identify the current road conditions and slope effectively.

Adaptive Boundary Observer Design for coupled ODEs-Hyperbolic PDEs systems

We consider the state estimation of ηξ hyperbolic PDEs coupled with ηX ordinary differential equations at the boundary. The hyperbolic system is linear and propagates in the positive x-axis direction. The ODE system is linear time varying (LTV) and includes a set of ηθ unknown constant parameters, which are to be estimated simultaneously with the PDE and the ODE states using boundary sensing. We design a Luenberger state observer, and our method is mainly based on the decoupling of the PDE estimation error states from that of the ODEs via swapping design. We then derive the observer gains through the Lyapunov analysis of the decoupled system. Furthermore, we give sufficient conditions of the exponential convergence of the adaptive observer through differential Lyapunov inequalities (DLIs) and we illustrate the theoretical results by numerical simulations.

Improved UDE and LSO for a Class of Uncertain Second-Order Nonlinear Systems Without Velocity Measurements

In recent years, the uncertainty and disturbance estimator (UDE) technique has been widely used for robustness improvement in state-feedback control systems. This article extends the design of the UDE to output feedback scenarios by considering the robust control problem of a class of Euler–Lagrange systems with a nonlinear velocity term but having no velocity measurements. We propose a simple feedback-control scheme that includes a modified Luenberger state observer (LSO) to estimate the velocity and a modified UDE to estimate exogenous disturbances. The novel feature of the scheme is that a mutual coupling between LSO and UDE is introduced to improve the estimation and control precision. To analyze the performance of the fifth-order nonlinear closed-loop system, we decompose it into a second-order tracking-error subsystem and a third-order estimation-error subsystem and propose a linear nonsingular state transformation and an ingenious parameter mapping for the estimation-error subsystem. Finally, by the singular perturbation theory, we derive a simple stability condition and a single-parameter tuning approach to reduce the steady-state estimation errors and tracking errors. The performance improvement resulting from the mutual coupling effect and the effectiveness of the tuning approach are demonstrated by numerical simulations and experimental verifications on a 3-DOF helicopter platform.

Analytical Synthesis of the State Observer of a Bilinear Dynamic System with Vector Input

The problem of estimating the state vector of a bilinear dynamic system with vector input is under consideration. It is shown that, with fulfillment of multiple constraints, a Luenberger state observer can be formed, with an estimation error tending to zero. A step-by-step algorithm for determining the observer coefficient matrices is proposed, based on matrix canonization and modal control methods.

Fault detection in rotating machinery by using the modal state observer approach

The existence of cracks in rotating shafts can lead to failures, which imply economic losses and security issues. In the last decades, attention has been devoted to this subject leading to the development of vibration-based structural health monitoring techniques. In this paper, a fault detection methodology based on the so-called modal state observer is applied for detecting transversal cracks in a horizontal rotating shaft. A rotor composed by a flexible horizontal shaft, two rigid discs, and two self-aligning ball bearings is used. The Luenberger state observer is formulated in the modal domain to estimate the rotor vibration responses described in the modal domain. Consequently, the most affected vibration modes due to the crack existence can be determined. The kernel density estimator is applied to quantify the influence of a crack over the dynamic behavior of the rotor. The time domain vibration responses measured directly on the rotating machine are used for comparison purposes. Numerical and experimental investigations are presented by considering both breathing and open cracks. The breathing behavior of the crack is simulated according to the Mayes model, in which the crack transition from fully open to fully closed is described by a cosine function. The additional flexibility introduced in the shaft by the crack is determined by using the linear fracture mechanics theory. The obtained results demonstrated that the methodology conveyed represents a good alternative technique to detect faults in rotating machines.

Passive Fault-tolerant Control Based on Weighted LPV Tube-MPC for Air-breathing Hypersonic Vehicles

This paper proposes a novel passive fault-tolerant control method using weighted tube-based model predictive control (Tube-MPC) via polytopic linear parameter varying (LPV) for air-breathing hypersonic vehicles. Firstly, the longitudinal LPV model of the vehicle is established by the Jacobi linearization and tensor-product (T-P). The random drift fault or loss of efficiency fault over the elevator deflection is transformed equivalently into the additional item as bounded disturbance. Based on invariant set theory, a weighted Tube-MPC control method is proposed. In traditional Tube-MPC controller design, the worst case of the fault is generally considered. In order to balance control performance and robustness of the control system, this paper introduces a weighted strategy, where the weighted factor α is used to change the robust positive invariant (RPI) set for incomplete fault set. The robustness of the system is sacrificed, so that the invariant set can be reduced to expand the domain of the nominal control input. In this way, the control performance of the nominal system can be improved. In the actual flight, the states of the hypersonic vehicle system cannot be measured completely, and therefore a polytopic Luenberger state observer is developed to estimate the unmeasured states. The control errors and estimate errors are limited by two incomplete disturbance minimum RPI (idmRPI) sets. Finally, simulations verify the fault-tolerant ability and tradeoff regulating ability of the designed control system.

EID-based sliding mode investment policy design for fuzzy stochastic jump financial systems

This paper proposes a sliding mode investment policy design for nonlinear stochastic financial systems which can be represented by the well-known Takagi–Sugeno fuzzy model. When modeling the financial systems, it is more important to consider the unpredictable investment changes and worldwide unpredictable events which can be regarded as external disturbances. The equivalent-input-disturbance (EID) approach combined with sliding mode investment policy design is implemented to reject the unpredictable investment changes for having better investment. Moreover, the Luenberger state observer is constructed for the addressed financial system to estimate the unpredictable investment changes and worldwide unpredictable events. More precisely, a sliding mode investment policy design is developed by solving the obtained linear matrix inequality (LMI)-based constrained algorithm. Finally, the obtained results of the addressed fuzzy stochastic financial system are verified through numerical simulation to show efficiency of the proposed sliding mode investment policy design.