Full-order Observer Research Articles

Observer design of discrete-time generalized quasi-one-sided Lipschitz nonlinear systems with multiple delays

Abstract In this article, the generalized quasi-one-sided Lipschitz condition is drawn into the topic of observer design for a kind of discrete-time nonlinear systems with multiple delays. The sufficient conditions for the asymptotic stability of full-order observer and reduced-order observer for systems are proposed, respectively. Under this condition, the two types of observers for systems can be designed, although the system parameter (A 0,C) is not detectable.

Human-in-the-Loop Consensus Control for Multiagent Systems With External Disturbances.

In this article, the human-in-the-loop leader-follower consensus control problem is addressed for multiagent systems (MASs) with unknown external disturbances. A human operator is deployed to monitor the MASs' team by transmitting an execution signal to a nonautonomous leader in response to any hazard detected, with the control input of the leader unknown to all followers. For each follower, a full-order observer, in which the observer error dynamic system decouples the unknown disturbance input, is designed for asymptotic state estimation. Then, an interval observer is constructed for the consensus error dynamic system, where the unknown disturbances and control inputs of its neighbors and its disturbance are treated as unknown inputs (UIs). To process the UIs, a new asymptotic algebraic UI reconstruction (UIR) scheme is proposed based on the interval observer, and one of the significant features of the UIR is the capacity to decouple the control input of the follower. The subsequent human-in-the-loop asymptotic convergence consensus protocol is developed by applying an observer-based distributed control strategy. Finally, the proposed control scheme is validated through two simulation examples.

Stability Improvement of Adaptive Full-Order Observer for Sensorless Induction Motor Drives in Low-Speed Regenerating Mode

In the applications of high power induction motor railway traction systems, the switching frequency of power devices is relatively low. This restriction will severely reduce the accuracy and stability of conventional discrete model for adaptive full-order observer (AFO) in extremely high-speed region. What’s worse, due to the neglect of flux error during speed estimation derivation, the conventional AFO cannot maintain stability under low-speed regenerating mode. The above two reasons limit the application of AFO in rail traction systems for full speed range. To address this problem, this paper utilizes a high-accuracy discretization which is achieved in combined reference frames and feedback gains are designed in z-domain to ensure stability and dynamic performance of AFO. Moreover, a modified speed estimation mechanism with the error of d-axis current is developed to guarantee stability in extremely low-speed regenerating mode. Rigorous simulations and experiments are performed to verify that the proposed AFO model achieves excellent sensorless control performance in full speed range.

Study on QEMF Model and Adaptive Full-Order Observer Design for Universal Sensorless Control of IPMSMs

Quadratic extended electromotive force (QEMF) model enabled the use of traditional high-speed adaptive estimation methods combined to high-frequency signal injection (HFSI) for full-range sensorless position control of interior permanent magnet synchronous motors (IPMSMs). However, the first QEMF model presented in literature only works with HFSI in the q-axis, due to the QEMF being a function of the q-axis current derivative. The q-axis HFSI is known to produce undesired torque ripple. Furthermore, q-axis signal injection can be insufficient for low-speed position estimation in IPMSMs with low salience. A recent study demonstrated that the QEMF concept can be modeled as a function of the d-axis current derivative. In this paper, the influence of d-axis HFSI on QEMF is investigated and compared to the q-axis HFSI method. Furthermore, the electromotive force based observers are usually designed for medium to high-speed operation. Here, the adaptive full-order observer is adapted in order to achieve universal sensorless control through QEMF based d-axis HFSI. The state observer and adaptive law are designed by a cascade methodology, which guarantees accurate EEMF estimation and robustness throughout the entire operating speed range. Experimental results are presented in order to validate the proposed method and analysis under full-range sensorless control.

Dynamic sliding mode control based on a full-order observer: Underactuated electro-mechanical system regulation

Dynamic sliding mode control based on a full-order observer: Underactuated electro-mechanical system regulation

Adaptive Full-Order Observer for Sensorless Variable Flux Reluctance Motor Drives Considering Field Current Adjustability and Stator Resistance Mismatch

Adaptive Full-Order Observer for Sensorless Variable Flux Reluctance Motor Drives Considering Field Current Adjustability and Stator Resistance Mismatch

Functional and dual observer based prescribed-time control of linear systems by periodic delayed feedback

In this paper the prescribed-time output feedback stabilization of linear systems is addressed using both a functional observer, which includes the reduced-order observer as a special case, and a dual observer. The approach is built upon smooth periodic delayed feedback which is a special case of linear periodic time-varying feedback. In contrast to existing periodic control approaches, the proposed feedback achieves prescribed-time convergence of the state to zero rather than asymptotic convergence. At the same time its synthesis requires solving algebraic equations rather than periodic differential equations. Compared with full-order observer based output feedback, the dimensions of the dynamic equations in the reduced-order observer and dual observer based output feedback are respectively n−p and n−m, where n,m and p are respectively the number of state variables, inputs and outputs, which indicates that the established controllers are less expensive than the full-order observer based controllers in implementations. A numerical example is given to verify the effectiveness of the proposed methods.

Trajectory tracking control of nonholonomic wheeled mobile robots using only measurements for position and velocity

This paper studies the trajectory tracking control of nonholonomic wheeled mobile robots, and only measurements for Cartesian position and velocity are used. A full-order observer is proposed to estimate the unmeasurable attitude and filter the position signal. Its effectiveness relies on the persistent excitation (PE) condition of non-zero linear velocity. Using the observer states, we design a local tracking controller that guarantees: (a) the linear velocity input is positive, and (b) the position tracking error is convergent to zero locally asymptotically. Experiments performed on a robot built in-house illustrate the control algorithm.

DEVELOPMENT AND CONFIGURATION OF A FULL-ORDER OBSERVER FOR «CABLE LINE – INDUCTION MOTOR» ELECTRICAL COMPLEX

Link for citation: Rakov I.V., Glazyrin A.S., Kladiev S.N. Development and configuration of a full-order observer for «cable line – induction motor» electrical complex. Bulletin of the Tomsk Polytechnic University. Geo Аssets Engineering, 2023, vol. 334, no. 10, рр. 219-231. In Rus. The relevance. The task of oil production specialists is to minimize all types of energy consumption, ensuring an increase in oil production profitability because of the following reasons. First of all, availability of oil reserves with low energy consumption decreases, and the number of gushing wells reduces, along with increase in water content in the extracted liquid. One of the methods of reducing energy consumption in wells with low and moderate flow rate, equipped with electric submersible pumps, is a well transfer from continuous to periodic operation mode, namely cyclic well operation. This involves alternating short periods of oil production (up to 15 minutes) with liquid accumulation (up to 30 minutes) in the wellbore. Well switching to a cyclic operation mode leads to a 40 % reduction in electric power consumption by the submersible electric motor, as well as increase in oil production up to 3 %. This can be achieved by partial gravitational separation of the extracted liquid at the accumulation stage. However, a negative consequence of switching to a cyclic operation mode is a reduction in an average time between failures. This is due to increase in current surges and torque during rapid acceleration of the submersible electric motor to the rated speed. Transition from a scalar control system with an open loop to a vector control system without sensors can settle these problems. To implement a vector control system, it is necessary to obtain information about the state variables of a submersible electric motor. Construction of a full-order observer based on explicit mathematical models is considered as a promising method of obtaining information, taking into account the main advantages and disadvantages of direct measurement and indirect estimation of state variables. Based on the above, the urgent task is to develop a full-cycle observer for the electromechanical complex «cable line – induction motor» and a methodology for its configuration. The settlement of this issue will create prerequisites for implementation of a vector control system by a submersible electric motor. The main aim: to develop and experimentally validate the effectiveness of a full-order observer for the electrical complex «cable line – induction motor» using voltage and current measurements at a cable line input. Methods: literature analysis, system analysis, mathematical modeling, experimental research. Results. The authors have developed and tested a full-order observer for the «cable line – induction motor» electrical complex. The results of this study confirm the efficiency of the developed observer and its potential applicability for implementing a vector control system for electric submersible pumps. Ultimately, this will enable the transition of low- and medium-flow-rate oil wells to a cyclically operated mode without a significant reduction of the mean time between failures.

Observer Design for a Lorenz Oscillator

This article addresses the design problem of observers for the oscillator, focusing on the nonlinearities present in the model, which arise from the product between components of the state vector. These nonlinearities are particularly interesting because they allow obtaining an error dynamics that can be used to study the convergence properties of the observation scheme. In this sense, the design of a full-order observer is proposed, which is characterized by being a replica of the original system, with the addition of a correction term. Additionally, a numerical evaluation of the presented results is performed.

Distributed Generation Based WADC for Inter-Area Oscillations Considering Unknown Inputs

Inter-area oscillations (IAOs) are one of the main problems for contemporary power systems because of their low-damping characteristics. Additionally, the damping behaviors of IAOs might be further deteriorated by the addition of low inertial distributed generation (DG) to the power system. Therefore, a novel wide-area damping controller (WADC) for DG-integrated power systems is developed utilizing a modal linear quadratic regulator (LQR) technique that only targets essential IAOs without degrading other local modes. The states participated in linear combination from modal LQR are generally unavailable and need to be estimated. Full order observers are frequently used in literature, although they may not function if some inputs are unavailable. Hence, an unknown input observer (UIO) is suggested in this paper to estimate the states despite certain inputs being unknown. The proposed methodology is then tested on a DG-integrated 4-machine, 11-bus system and 10-machine, 39-bus system to validate the overall proposed design process. Results show that the proposed WADC successfully dampens the crucial IAO modes by 10% and 15% while not degrading other modes of the system.

Secure control scheme for CPSs under DoS attacks via multiple transmission channels and unknown input observer

The paper investigates the secure control problems for cyber–physical systems (CPSs) when the transmission channels suffer from Denial-of-Service (DoS) attacks based on switching observer and unknown input reconstruction (UIR). Firstly, an augmented system whose system state consists of the original system state and the measurement noises is set up, and the preconditions for the original system and augmented system are discussed in detail. Secondly, a full-order observer is constructed to generate the estimations of the augmented system state. Besides, based on the state estimation, an algebraic UIR method is developed and the UIR decouples the control input signal successfully. Thirdly, under the situation that some transmission channels suffer from DoS attacks, an observer-based secure controller is designed based on state estimation feedback and UIR feedback in view of a switching system. The stability of the switching system is analyzed as well. Finally, to verify the effectiveness of the proposed protocols, two simulation examples and the comparison with existing methods are given.

Graphical Multiple-Error Feedback Matrix Design for Stability and Robustness Enhancement of Speed-Sensorless Induction Motor Drives

For speed-sensorless induction motor (IM) drives, the feedback matrix is a significant technique to enhance the stability in low-speed regenerating region. However, further analyzes show it has difficulty for existing methods in maintaining the stability and robustness with parameter uncertainties. To cope with this problem, in this article, a graphical design method of multiple-error feedback matrix (ME-FBM) is presented for adaptive full-order observer. First, the flux error is introduced by projection of current error. Adopting flux error and current error, the ME-FBM is graphically developed to satisfy the stability necessary condition by reconstructing the stability function. As a result, the unstable region is eliminated during low-speed regenerating mode. On this basis, the gains of ME-FBM is graphically selected to reduce the error of estimated rotor flux and improve the robustness against parameter uncertainties at low-stator frequencies. Finally, the effectiveness of proposed ME-FBM is verified on a 2.2 kW IM experimental setup.

Improved Position Sensorless Control for PMLSM via an Active Disturbance Rejection Controller and an Adaptive Full-Order Observer

Position and speed information are very important to realize the efficient control for permanent magnet linear synchronous motor (PMLSM). In order to obtain more accurate position estimation signals, this article investigates an improved position sensorless control method for PMLSM by combining an active disturbance rejection control (ADRC)-based speed controller and an adaptive full-order observer (AFO)-based position estimator. The AFO is constructed based on model reference adaptive system (MRAS), which can obtain more accurate position estimation signal by introducing a current error feedback gain matrix. However, there are lots of thrust fluctuations existing in PMLSM caused by end effect, which will affect the estimation accuracy. Since it is difficult to reduce the influence of thrust fluctuation by only improving the observer itself, an ADRC-based speed controller is designed to improve the anti-interference ability of control system, thereby improving the position estimation accuracy. For the ADRC controller, an second-order linear extended state observer (LESO) is designed to observe the thrust fluctuation and an nonlinear state error feedback (NLSEF) control law is introduced to compensate the observed disturbance. The effectiveness and superiority of the proposed method have been verified by simulation and experimental results.

Exponential output feedback control for a class of strict-feedback nonlinear systems with different time-delay states

In this paper, the output feedback control scheme is developed to investigate the exponential stabilisation problem for a class of strict-feedback nonlinear systems subject to different time-delay states. First of all, the memoryless full-order observer and output feedback controller which depend on the same designed parameter are provided respectively. And then, by tactfully introducing the suitable Lyapunov–Krasovskii functional and selecting the applicable parameter to be designed, the exponential stability of the closed-loop system can be achieved. Finally, a numerical example is used to illustrate the effectiveness of the proposed control scheme.

Output-feedback control of viscous liquid–tank system and its numerical approximation

We solve the output-feedback stabilization problem for a tank with a liquid modeled by the viscous Saint-Venant PDE system. The control input is the acceleration of the tank and a Control Lyapunov Functional methodology is used. The measurements are the tank position and the liquid level at the tank walls. The control scheme is a combination of a state feedback law with functional observers for the tank velocity and the liquid momentum. Four different types of output feedback stabilizers are proposed. A full-order observer and a reduced-order observer are used in order to estimate the tank velocity while the unmeasured liquid momentum is either estimated by using an appropriate scalar filter or is ignored. The reduced order observer differs from the full order observer because it omits the estimation of the measured tank position. Exponential convergence of the closed-loop system to the desired equilibrium point is achieved in each case. An algorithm is provided that guarantees that a robotic arm can move a glass of water to a pre-specified position no matter how full the glass is, without spilling water out of the glass, without residual end point sloshing and without measuring the water momentum and the glass velocity. Finally, the efficiency of the proposed output feedback laws is validated by numerical examples, obtained by using a simple finite-difference numerical scheme. The properties of the proposed, explicit, finite-difference scheme are determined.

Realization of Indirect Magnetic Suspension with Indirect Sensing through Conductive Wall

The magnetic suspension of a ferromagnetic object (floator) across a conductive wall was achieved without directly sensing the displacement of the floator. When a floator is inside a chamber made of conductive material, the cross-wall detection of the motion of the floator is impossible or at least difficult with an eddy-current type displacement sensor. This study discussed two approaches to the problem. In the first approach, an electromagnet directly actuates the floator across the wall. In the second approach, the floator is indirectly actuated through a permanent magnet; such suspension is called as double series magnetic suspension. Because a critical problem due to induced voltage is expected in the former, the latter was focused. In the latter system, the motion of the first floator (permanent magnet) outside the chamber is detected directly. In contrast, the motion of the floator inside the chamber is not detected. Instead, its displacement and velocity are estimated by an observer, which is referred to as indirect sensing. Because the system is controllable and observable even with indirect sensing, the system can be stabilized by feeding back these estimated signals. To demonstrate the validity of such an approach, an experimental apparatus was designed and manufactured. A full-order observer was built for the estimation. The displacement estimated by the observer was compared with the actual displacement. Then, magnetic suspension with indirect sensing was achieved by replacing the sensor signal by the estimated signal.

РАЗРАБОТКА НАБЛЮДАТЕЛЯ ЛЮЕНБЕРГЕРА ПОЛНОГО ПОРЯДКА ВЕКТОРА ПЕРЕМЕННЫХ СОСТОЯНИЯ УЧАСТКА КАБЕЛЬНОЙ ЛИНИИ С ПОВЫШЕННОЙ ПАРАМЕТРИЧЕСКОЙ РОБАСТНОСТЬЮ

In addition, in the Russian Federation, 75 % of oil-producing wells in operation at old fields are low- to medium-flow rate wells. One way to increase the profitability of oil production from low- to medium-flow rate wells using ESPs is to reduce the power consumption of the Submersible Electric Motor (SEM) by switching the ESP from a scalar open-loop control system to a sensorless vector control system. To implement the vector control system for ESPs, it is necessary to develop a methodology for identifying the parameters of the electrical equipment in the power channel of the ESP, as well as to implement a full-order observer of the SEM vector state variables to create a feedback channel for angular speed. One of the electrical components in the ESP power channel that affects the accuracy of the SEM vector state variable estimation is the power cable, which can reach up to 5 km in length. Such a long cable length results in the output voltage at the cable end being significantly different in amplitude and frequency from the measured input voltage, and the cable parameters themselves change as the temperature of the well varies depending on the depth. Failure to estimate the output voltage of the cable will result in incorrect estimation of the torque and angular speed of the SEM, which, in turn, may cause the angular speed of the SEM to oscillate and the ESP to trip at the bottom of the well. Due to the above factor, the development of a full-order observer for the vector state variables of the cable line with increased parametric robustness is a relevant and timely task

Reduced-Order Observer Design for Robot Manipulators

This letter investigates the design of reduced-order observers for robot manipulators. Observer stability conditions are obtained based on a Lyapunov analysis. The proposed observer is enhanced with a hybrid scheme that may adjust the gains to cope with possible unbounded velocities of the robot joints. Thanks to such hybrid strategy, the observer works accurately both for robots driven by open-loop controllers and by output feedback controllers. Numerical simulations illustrate the efficacy of the reduced-order observer in several scenarios, including a comparison with the performance of a classical full-order observer.

A Modified Robotic Manipulator Controller Based on Bernstein-Kantorovich-Stancu Operator.

With the development of intelligent manufacturing and mechatronics, robotic manipulators are used more widely. There are complex noises and external disturbances in many application cases that affect the control accuracy of the manipulator servo system. On the basis of previous research, this paper improves the manipulator controller, introduces the Bernstein-Kantorovich-Stancu (BKS) operator, and proposes a modified robotic manipulator controller to improve the error tracking accuracy of the manipulator controller when observing complex disturbances and noises. In addition, in order to solve the problem that the coupling between the external disturbances of each axis of the manipulator leads to a large amount of computation when observing disturbances, an improved full-order observer is designed, which simplifies the parameters of the controller combined with the BKS operator and reduces the complexity of the algorithm. Through a theoretical analysis and a simulation test, it was verified that the proposed manipulator controller could effectively suppress external disturbance and noise, and the application of the BKS operator in the manipulator servo system control is feasible and effective.