State Observer Design Research Articles

A deep learning-based predictive controller for the optimal charging of a lithium-ion cell with non-measurable states

Battery charging is a complex task, which needs to be addressed by a proper control methodology to find the highest charging current while guaranteeing safety. Among the different approaches, model predictive control appears particularly suitable due to its ability in dealing with nonlinear systems and constraints. However, its use in a realistic scenario is limited due to the high computational burden required by the online solution of an optimal control problem. A neural network-based algorithm is here proposed to significantly reduce the real-time computational effort by approximating the predictive control law. In addition, for the first time to the authors’ knowledge, an adaptation of the proposed deep learning-based algorithm is presented for the case in which the battery’s internal states are not measurable. The superiority of proposed methodology is highlighted in simulation by comparing it with a predictive controller coupled with a properly designed state observer.

Design and Robustness Analysis of Multiple Extended State Observer Based Controller (MESOBC) for AVR of the Power System

Automatic voltage regulator (AVR) is installed on the synchronous generators in the power system and plays a very important role in maintaining the generator output voltage besides changes in load demand, parametric uncertainties, and operating temperature. As the load is continuously varying in the system, the AVR needs controllers to track and regulate the voltage of the synchronous generator much faster. This paper shows an initial attempt to design a robust multiple extended state observer (MESO) to estimate the variation in lump disturbances (i.e., load demand and parametric uncertainties) from all the components of the AVR. MESO-based controller (MESOBC) can track such matching and mismatching of both types of irregularities and regulate the terminal voltage of the generator accordingly. MESOBC performance is matched with strong published AVR designs for a standard condition, ±30% load voltage variation and for simultaneous changes in AVR parameters with ±30% load voltage variations. Integrated square error (ISE) is chosen as an objective function to compare the output of MESOBC with other published AVR designs in view of graphical AVR responses and by calculating various numerical values for AVR responses. At last, the robustness of MESOBC is also checked through sensitivity analysis, and it is seen that MESOBC guaranteed robust performance for the AVR of the power system under diverse operating conditions.

Wave-filtering finite-time self-learning extended state observers for robotic surface vehicles

This paper presents wave-filtering finite-time self-learning extended state observers for robotic surface vehicles subject to unknown control gains and ocean disturbances. By incorporating wave filtering technique and concurrent learning into the extended state observer design, the low-frequency motion components and wave-frequency motion components of robotic surface vehicles can be estimated, in addition to the unknown control gains, total disturbance and unmeasured velocity. A salient feature of the proposed approach is that wave-frequency motion components are filtered from the position and yaw angle sensor measurements to avoid mechanical wear and tear of the propulsion system components caused by wave-frequency motion signals. The result is extended to a wave-filtering finite-time self-learning extended state observer which improves the estimation performance considerably. The efficacy of the proposed two wave-filtering self-learning extend state observers for robotic surface vehicles with unknown control gains is substantiated via simulations.

Novel Extended State Observer Design for Uncertain Nonlinear Systems via Refined Dynamic Event-Triggered Communication Protocol.

In this article, an extended state observer (ESO) design problem is investigated for uncertain nonlinear systems subject to limited network bandwidth. First, for rational information exchange scheduling, a dynamic event-triggered (DET) communication protocol is proposed. Different from the traditional static event-triggered strategies with fixed thresholds, an internal dynamic variable is introduced to be adaptively adjusted by a dual-directional regulating mechanism. Thus, more desirable tradeoff between observation performance and communication resource efficiency is achieved. Second, inspired by our early work on Takagi-Sugeno fuzzy ESO (TSFESO), a novel paradigm of event-triggered TSFESO is initially proposed. Third, under the DET mechanism, the TSFESO design approach is derived to carry out exponential convergence for estimation error dynamics. Finally, the effectiveness of the proposed method is verified by numerical examples. The nonlinear estimating efficiency and linear numerical tractability are integrated in TSFESO. In addition, a generalized ESO formulation is developed to allow some nonadditive uncertainties incompatible with total disturbance, such as improved event-triggered strategy, and thus, the application sphere of ESO is further expanded.

Clustering-based average state observer design for large-scale network systems

This paper addresses the aggregated monitoring problem for large-scale network systems with a few dedicated sensors. Full state estimation of such systems is often infeasible due to unobservability and/or computational infeasibility; therefore, through clustering and aggregation, a tractable representation of a network system, called a projected network system, is obtained for designing a minimum-order average state observer. This observer estimates the average states of the clusters, which are identified under explicit consideration of estimation error. Moreover, given the clustering, the proposed observer design algorithm exploits the structure of the estimation error dynamics to achieve computational tractability. Simulations show that the computation of the proposed algorithm is significantly faster than the usual H2/H∞ observer design techniques. On the other hand, compromise on the estimation error characteristics is shown to be marginal.

Delayed sampled-data output feedback stabilization for a class of nonlinear system

Delayed sampled-data output feedback stabilization for a class of nonlinear system has been considered in this paper without resorting to state observer. Co-design between sampling period and scaling gain has been firstly introduced to deal with challenges in sampled-data control of nonlinear system such as unavailable state variables and unknown nonlinear perturbations. Using the co-designed sampled-data difference controller, not only exibility of choosing approximation step in delayed feedback has been greatly enhanced but also robustness to unknown perturbations has been guaranteed through the tuning of scaling gain. Globally asymptotic stabilization has been guaranteed using the delayed sampled-data output feedback controller without design of state observer.

Finite-time ESO-based cascade-free FCS-MPC for NNPC converter

This article addresses a novel finite control-set model predictive control solution for nested neutral point-clamped converter. More specifically, it is formed by incorporating a finite-time extended state observer design into a cascade-free finite control-set model predictive control architecture. In this architecture, a finite-time extended state observer is developed to estimate the total disturbances, and an integral error term and a dynamic reference design point of view are embedded into the proposed design so as to improve the performance. The main features of this proposal are: first of all, the detailed knowledge of the physical structure of the controlled plant is not required; second, a cascade-free structure is achieved in finite control-set model predictive control solution without weighting factors and steady-state error; and third, the proposed methodology can operate with different systems not just power converters, while keeping the fast transient response. In contrast to existing finite control-set model predictive control approaches, it can be found that our modification not only can track fast to their references but also can have superior robustness performance. Finally, the proposed solution is verified by comprehensive results that prove the theoretical researches for nested neutral point-clamped converter, while meeting the harmonic standards.

Barrier Lyapunov Function-based adaptive prescribed-time extended state observers design for unmanned surface vehicles subject to unknown disturbances

This paper studies the prescribed-time observer design problem for unmanned surface vessels (USVs) in the presence of unknown ocean disturbances. An adaptive prescribed-time extended state observer (APESO) is designed to estimate the lumped disturbances consisting of model uncertainties and external disturbances due to wind, waves and ocean currents and reconstruct unmeasured velocities information for USVs. Different from existing finite/fixed-time extended state observers for USVs, the APESO can accomplish observations within a prescribed time with a tiny peaking observation errors. The upper bound of the settling time of the APESO is tightly and explicitly prescribed by only one design parameter, resulting in a simple and weakly conservative parameter tuning process for temporal demands. Moreover, the barrier Lyapunov function (BLF) and prescribed performance function (PPF)-based adaptive mechanism is introduced into the observer design, which can improve the transient performance by self-adjusting the observer correction term along with the ocean disturbance amplitude. Finally, the performance and ascendancy of the proposed APESO are exhibited by simulation comparisons.

Design and implementation of passivity-based controller for active suspension system using port-Hamiltonian observer

The objective of this study is to design and implement an observer for quarter-car active suspension system in Port-Hamiltonian form. A novel state observer is designed for active suspension system modelled in port-Hamiltonian form to estimate the states in presence of road disturbances. The observer is designed considering suspension deflection alone as the output, which is an easily measurable output. Performance of the proposed observer is evaluated experimentally with road disturbance input mimicking a sudden bump and a continuously varying road input, and proven to be effective in minimising the error dynamics in presence of bounded unmodelled disturbances. To prove the effectiveness of the state-estimator, an Interconnection and Damping Assignment Passivity Based Control (IDA-PBC) designed using the desired physical properties of the closed-loop system is implemented using the observer states. Experimental results of the controller implemented using the designed state observer show good improvement in the ride comfort, ride stability and suspension stroke of the active suspension system, which proves the effectiveness of the proposed port-Hamiltonian observer in terms of minimising the error dynamics.

Reduced Order Based Active Disturbance Rejection Controller Design with Applications

Active disturbance rejection control (ADRC) has emerged as a well-addressed controller design technique in recent years. It is a suitable replacement for the error-based feedback PID controller design approaches. The ADRC constitutes two controller design techniques: linear active disturbance rejection control (LADRC) and generalized active disturbance rejection control (GADRC). The LADRC design approach requires minimal information about the plant, while in the GADRC approach, detailed information about the plant is needed. For higher-order plants, the design of ADRC controllers and extended state observers may be pretty complex and costlier. So, the performance analysis of the higher order plant becomes difficult. Therefore, to make the controller simpler, it is always advantageous to reduce the controller size. This paper proposes reduced order linear active disturbance rejection control (ROLADRC), and reduced order generalized active disturbance rejection control (ROGADRC) techniques instead of full-order LADRC and GADRC approaches. The stability equation method (SEM) and other widespread model order reduction (MOR) methods are utilized to reduce the order of the plant. Further, ROLADRC and ROGADRC are compared with existing control techniques in the literature. The effectiveness of the proposed scheme is tested on the sun tracker system (STS) for position control and power systems for load frequency control (LFC).

Asymptotically Tracking Control of Structural Balance for Discrete-Time Links System Associated with External Stimulations and State Observer

Considering that the link states of some practical networks are not measurable, it is impossible to control the links system directly to achieve structural balance. In order to handle this problem, the state observer design and the structural balance tracking control for the links system with complex dynamical networks are investigated. The dynamical model of the links system is molded as the Riccati matrix difference equation, which contains a coupling term associated with external stimulations. For the discrete-time model, the pole assignment algorithm is adopted to calculate the gain matrix for the observer of the links system. It could guarantee that the estimation error of observer for links system is globally asymptotically stable. Further, combining the effective estimation information of observer and external stimulations, an asymptotically tracking controller is proposed, which could achieve the asymptotic tracking of the reference structure balance network to the links system. Finally, the validity of the proposed method is verified by the simulation example.

An Improved Unknown Input Observer Design for Disrete-Time Fuzzy Bilinear Systems

Design methods of an observer for a discrete-time Takagi-Sugeno fuzzy bilinear system with unknown inputs is proposed. Takagi-Sugeno fuzzy bilinear system describes a large class of nonlinear systems and this system with unknown inputs even represents a realistic model for most practical systems. An unknown input observer that estimates the state of Takagi-Sugeno fuzzy bilinear system with unknown input is proposed based on multiple Lyapunov matrices. For fuzzy systems, a parallel distributed observer (PDO), which is constructed with of local linear observers and the appropriate grade of the membership functions, has been used, but its design conditions are eventually conservative. To reduce such conservativeness in observer design conditions, non-PDO with multiple Lyapunov matrices technique is proposed in this paper. Such a design method is based on a multiple Lyapunov function with double sum of the membership functions. In order to show the effectiveness of our proposed approach, a simple example is given. Finally, concluding remarks are given.

Adaptive observer for a nonlinear system with partially unknown state matrix and delayed measurements

Problem of an adaptive state observer design for nonlinear system with unknown time-varying parameters and under condition of delayed measurements is considered. State observation problem was raised by many researchers (see for example Sanx et al. (2019)). In this paper the results proposed in Bobtsov et al. (2021b), Bobtsov et al. (2021a), Bobtsov et al. (2022a), Bobtsov et al. (2022b) are developed. The problem is solved under assumption that the state matrix can be represented as sum of known and unknown parts. The output vector is measured with a known constant delay. An adaptive observer which reconstructs unmeasured state and unknown time-varying parameter is proposed.

Dissipative state observer design for nonlinear time-delay systems

This paper is concerned with the design of dissipative state observers for a family of time-delay nonlinear systems. The Dissipativity method, proposed by one of the authors for delay-free nonlinear systems, is extended here to a class of time-delay nonlinear systems. The design method consists in decomposing the time-delay estimation error dynamics into a time-delay linear subsystem and a time-varying memoryless nonlinearity, connected in a negative feedback loop. By using some storage functionals, both delay-independent and delay-dependent dissipativity criteria are derived in order to guarantee the exponential convergence property of the observer. The exponential stability of the estimation error is then ensured, assuming that the nonlinearity is dissipative with respect to a quadratic supply rate and the linear part is designed, through the observer gains, to be dissipative with respect to a complementary supply rate. The design conditions are formulated in terms of tractable bilinear (BMI’s) or linear matrix inequalities (LMI’s). An interesting advantage is that the proposed dissipative design extends and generalizes under a unified framework several methods available in the literature, since a wide diversity of nonlinearities can be considered. Numerical examples are provided to demonstrate the effectiveness of the theoretical results.

Design of a rollover index-based sliding mode controller for roll stability of three wheeled vehicles using rear differential braking

Urban vehicles (like tricycle and bicycle vehicle) are made to handle issues with traffic, air pollution, energy use, and parking restrictions in big cities. However, they are more susceptible to rollovers and stability problems because they are smaller and narrower than normal cars. Now a day, Vehicle manufacturers place a lot of emphasis on the dynamic stability of their products. As a result, develop dynamic model to predict and detect the risk of rollover and designing a controller to reduce it in a delta type configuration of tricycle vehicle is the major concern of this paper. On the basis of a two degree of freedom (2-DOF) bicycle model, develop rollover dynamics, and design state observer for sideslip angle, sliding mode and fuzzy logic controller are the major concern of this paper. The suggested rollover index (RI) accuracy has been evaluated by simulation using a high-fidelity CarSim. The performance analysis to determine the effectiveness of thus proposed controller is conducted using MATLAB/Simulink integrated with the Carsim software. Simulation results with three scenarios are shown with and without the control system. The outcome of the simulation demonstrated that fuzzy sliding mode controller (FSMC) and a fuzzy logic controller can reduces the chance of a vehicle rolling over accident.

Generalized Fuzzy Extended State Observer Design for Uncertain Nonlinear Systems: An Improved Dynamic Event-Triggered Approach

This article is concerned with extended state observer (ESO) design for uncertain nonlinear systems. First, different from standard ESO exclusively applicable for integral chain systems, a ESO formation including nonlinear and linear types is proposed for general state-space models. Inspired by our previous work, a event-triggered generalized fuzzy ESO (GFESO) is developed. Second, in order to schedule transmission rationally, an improved total disturbance-resilient dynamic event-triggered mechanism (TDRDETM) is put forward. Third, under TDRDETM, the GFESO design approach is presented in sense of exponential convergence. Finally, numerical examples illustrate the effectiveness of the given methods.

State Observer Design of Coupled Genetic Regulatory Networks With Reaction-Diffusion Terms via Time-Space Sampled-Data Communications.

In this paper, state observation of coupled reaction-diffusion genetic regulatory networks (GRNs) with time-varying delays is investigated under Dirichlet boundary conditions. First, the above GRNs are constructed to model gene regulatory properties, where the feedback regulation function of the GRNs is assumed to exhibit the Hill form and a novel method to deal with it is introduced. Then a time-space sampled-data state observer is designed for the mentioned networks and new criteria are established by utilizing the Lyapunov stability theory and the inequality techniques of Halanay et al. Finally, the validity of the theoretical results is proved by numerical examples.

Adaptive fast-finite-time extended state observer design for uncertain electro-hydraulic systems

This paper presents the design of an adaptive fast-finite-time extended state observer for electro-hydraulic actuator systems. First, state variables and subsequently the system model are divided into three independent parts, and fast-finite-time state observers with adaptive gains are designed independently for each part, guaranteeing the fast uniformly ultimate boundedness of the estimation errors. Then, based on the designed state observers and without any knowledge about the upper bounds of uncertainties or their derivatives, supplementary adaptive observers are presented to estimate the uncertainties. Besides, the adaptive gains of both observers are adjusted based on the evaluation of the absolute value of the observation errors in a straightforward manner, where rigorous analyses of the proposed strategy are provided through the Lyapunov approach. Finally, comparative simulations with respect to some leading strategies are presented to analyze the effectiveness of the proposed observers, where the convergence of the estimation errors to a small neighborhood of zero can be achieved almost regardless of the initial conditions. Indeed, in contrast to the earlier finite-time approaches which only have a relatively fast convergence rate around the equilibrium points, the proposed adaptive framework can also improve the convergence rate for zones far from the equilibrium points. It is concluded that the proposed scheme can compete with other leading strategies, making it a qualified alternative approach in the observer design with noteworthy potential.

Extended state observer design with fractional order Bode’s ideal cut-off filter in a linear motor motion control system

A desired output tracking motion control scheme of a new type of self-made linear motor is proposed in the presence of parameter uncertainties and external disturbance. An extended state observer is designed with a fractional order Bode’s ideal cut-off filter to suppress the high-frequency measurement noise. Characteristics of the linear motor are analyzed, including its working principle, mathematical model, and mechanical structure. A fractional order Bode’s ideal cut-off filter, a second-order extended state observer, a reference acceleration feedforward control scheme, and a normal proportional–derivative algorithm constitute the linear-motion control system in this article. The effectiveness of the control scheme has been verified by comparative simulations and experimental results. The proposed method is an effective way to obtain desired output tracking control performance in actual motion control engineering.

Dynamic state feedback controller and observer design for dynamic artificial neural network models

Artificial neural networks are black-box models that can be used to model nonlinear dynamical systems. This article presents a synthesis method for full dynamic state feedback controllers and state and output observers that have guaranteed properties for systems approximated by dynamic artificial neural networks. The resulting control designs are applicable to the practical situation in which the steady-state values for the control input are not known. Dynamic artificial neural networks are written in the standard nonlinear operator form, also known in the literature as the Luré formulation. A generalized form of the Luré formulation is adopted to allow for the representation of deep ℓ-layer networks, ℓ≥1. Sufficient conditions for controller synthesis and observer design are derived in the form of linear matrix inequalities, using a quadratic Lyapunov function. The synthesis method is demonstrated for the control of pH in two tanks in series and a numerical example.