Unmeasured State Variables Research Articles

Decentralized Output Feedback Adaptive NN Tracking Control for Time-Delay Stochastic Nonlinear Systems With Prescribed Performance.

This paper studies the dynamic output feedback tracking control problem for stochastic interconnected time-delay systems with the prescribed performance. The subsystems are in the form of triangular structure. First, we design a reduced-order observer independent of time delay to estimate the unmeasured state variables online instead of the traditional full-order observer. Then, a new state transformation is proposed in consideration of the prescribed performance requirement. Using neural network to approximate the composite unknown nonlinear function, the corresponding decentralized output tracking controller is designed. It is strictly proved that the resulting closed-loop system is stable in probability in the sense of uniformly ultimately boundedness and that both transient-state and steady-state performances are preserved. Finally, a simulation example is given, and the result shows the effectiveness of the proposed control design method.

Robust Regulation and Tracking Control of a Class of Uncertain 2DOF Underactuated Mechanical Systems

A strategy to design and implement a robust controller for a class of underactuated mechanical systems, with two degrees of freedom, which solves the problems of regulation and trajectory tracking, is proposed. This control strategy considers the partial measurement of the state vector and the presence of parametric uncertainties in the plant; these conditions are common in the implementation of a control system. The strategy is based on the use of robust finite time convergence observers to estimate the unmeasured state variables, unknown disturbances, and other signals needed for the control system implementation. The performance of the control strategy is illustrated numerically and experimentally.

Circle-criterion Based Nonlinear Observer Design for Sensorless Induction Motor Control

This paper deals with the design of a nonlinear observer for sensorless induction motor control. Based upon the circle criterion approach, a nonlinear observer is designed to estimate pertinent but unmeasurable state variables of the considered induction machine for sensorless control purpose. The observer gain matrices are computed as a solution of linear matrix inequalities (LMI) that ensure the stability conditions of the state observer error dynamics in the sense of Lyapunov concepts. Measured and estimated state variables can be exploited to perform a state feedback control of the machine system. The simulation results are presented to illustrate the effectiveness of the proposed approach for nonlinear observer design.

Real-time implementation of neural optimal control and state estimation for a linear induction motor

A reduced order state estimator based on recurrent high-order neural networks (RHONN) trained using an extended Kalman filter (EKF) is designed for the magnetic fluxes of a linear induction motor (LIM). The proposed state estimator does not need the mathematical model of the plant. This state estimator is employed to obtain the unmeasurable state variables of the LIM in order to use a state feedback nonlinear controller. A neural inverse optimal control is implemented to achieve trajectory tracking for a position reference. Real-time implementation results on a LIM prototype illustrate the applicability of the proposed scheme.

Non-fragile H∞ output feedback control design for continuous-time fuzzy systems

In this paper, we investigate the problem of non-fragile H∞ fuzzy control design for continuous Takagi Sugeno (T–S) fuzzy systems with uncertainties, external disturbance and unmeasurable state variables. For the case of controller and observer gain additive variations, we propose a new solution of the fragility problem by developing the non-fragile design schemes ensuring the asymptotic stability and H∞ performance for the resulting closed loop systems. By considering a fuzzy Lyapunov function and by introducing slack variables, we propose the new sufficient stabilization conditions formulated in LMI constraints which can be easily solved using the convex optimization tools. The effectiveness the proposed results are illustrated through three numerical examples.

Cascade synthesis of a state observer with nonlinear correcting influences

For the synthesis problem for an invariant tracking system for a nonlinear automated control object under incomplete measurements, we develop a decompositional procedure of observer state synthesis with sigmoidal correcting influences in order to get current estimates of the unmeasured state variables and existing uncertainties. This observer in the pre-limit situation possesses the advantages of an observer with discontinuous correcting influences operating in sliding mode; in particular, it lets us estimate external influences without introducing their dynamical model. Unlike a sliding mode observer whose order has been extended due to filters over discontinuous correcting influences, the dimension of this observer equals the dimension of the control object, and in a microprocessor implementation this observer ensures better quality (smoothness) of the signals being estimated.

Fuzzy static output feedback robust controller design for discrete-time fuzzy singularly perturbed systems

This paper investigates a static output feedback (SOF) robust control problem for discrete-time fuzzy singularly perturbed systems (FSPSs). Based on a matrix spectral norm approach, a new -dependent SOF controller is designed via linear matrix inequalities (LMIs), which guarantees that the resulting closed-loop system is asymptotically stable. In contrast to the existing results, the proposed method can deal with the systems with unmeasurable state variables and conventional non-linear systems. But the upper bound of is smaller than existing results. A simulation example illustrates the reduced conservatism of our results.

Parameter Identification in Pipeline Networks: Transient-Based Expectation-Maximization Approach for Systems Containing Unknown Boundary Conditions

The simulation of hydraulic transients within fluid line networks is important for many applications (for example, water hammer analysis within distribution networks). However, in many instances, modeling efforts are impeded by the fact that the pipeline parameters are either unknown or can vary significantly from their assumed design values. Consequently, research efforts have focused on the development of parameter identification techniques, mapping from measured transient data to pipeline parameter estimates. A limitation of previous works has been the need for systems to have all boundary conditions either measured or known (e.g., transient pressure measurements or reservoir boundary conditions). This paper aims to relax this requirement and presents a parameter identification method for fluid line networks based on transient-state measurements of the hydraulic state variables of pressure and flow, in the presence of unmeasured and unknown boundary conditions. Utilizing a Laplace-domain admittance matrix representation of the system, the contribution to the hydraulic system dynamics from the measured and unmeasured state variables (i.e., boundary conditions) is made explicit. This model is then used as the basis for the development of a parameter estimation methodology based on the expectation-maximization (EM) algorithm. The importance of the EM approach is that it provides a framework for parameter estimation in the presence of unmeasured state variables by effectively integrating out the influence of the unmeasured variables. Numerical examples demonstrate the utility of this method for a network with a range of pipeline models.

Observer‐based decentralized adaptive control for large‐scale pure‐feedback systems with unknown time‐delayed nonlinear interactions

SummaryThis paper presents an approximation design for a decentralized adaptive output‐feedback control of large‐scale pure‐feedback nonlinear systems with unknown time‐varying delayed interconnections. The interaction terms are bounded by unknown nonlinear bounding functions including unmeasurable state variables of subsystems. These bounding functions together with the algebraic loop problem of virtual and actual control inputs in the pure‐feedback form make the output‐feedback controller design difficult and challenging. To overcome the design difficulties, the observer‐based dynamic surface memoryless local controller for each subsystem is designed using appropriate Lyapunov‐Krasovskii functionals, the function approximation technique based on neural networks, and the additional first‐order low‐pass filter for the actual control input. It is shown that all signals in the total controlled closed‐loop system are semiglobally uniformly bounded and control errors converge to an adjustable neighborhood of the origin. Finally, simulation examples are provided to illustrate the effectiveness of the proposed decentralized control scheme. Copyright © 2013 John Wiley & Sons, Ltd.

Observer-based adaptive fuzzy decentralized control for stochastic large-scale nonlinear systems with unknown dead-zones

This paper studies the problem of adaptive fuzzy decentralized output feedback control for a class of uncertain stochastic large-scale nonlinear systems. The considered systems have unknown nonlinear functions, unknown dead-zones, unmodeled dynamics and unmeasurable state variables. Therefore, fuzzy logic systems are utilized to approximate the unknown nonlinear functions, and a fuzzy state observer is established to estimate the unmeasurable states. Based on the backstepping design and the supply changing function technique, a robust adaptive fuzzy decentralized output feedback control approach is developed. The proposed control approach can ensure the closed-loop system to be input-state-practically stable (ISpS) in probability, and accommodate the unmodeled dynamics and unknown dead-zones as well. The effectiveness of the proposed control approach is illustrated by a simulation example.

Position control of linear electromechanical actuator for spoiler system base on the inverse system method

A kind of robust control of linear electromechanical actuator (LEMA) spoiler system for thrust vector control (TVC) in a spacecraft was investigated. This paper presents an inverse system method (ISM) to achieve precise motion control for the LEMA spoiler system, which is based on a voice coil motor. The dynamic model of the LEMA spoiler system is established, and the inverse system of the LEMA spoiler is obtained. By linearization of the nonlinear LEMA spoiler system, the state feedback control is used to control the spoiler to follow the desired spoiler motion. A state variable observer is designed to estimate the unmeasurable state variables. Simulations and experimental setup are used to demonstrate the effectiveness of the proposed control method. The performance of proportional-integral-differential (PID) control is compared to the ISM control in simulation and ISM control is robust to large parameter variations of 50%. The experimental results show close agreement with the simulation results. The proposed method proved effective by achieving a transient time of 5.5 ms and system bandwidth of 20 Hz, so that ISM control method can more effectively handle the parameters’ perturbation, load disturbance, the variation of work temperature, and the LEMA's nonlinearity.

A robust non‐linear feedback control strategy for a class of bioprocesses

This study proposes a multiple-input/multiple-output robust approach to the control of bioprocesses based on a cascaded-loop strategy. The internal loop is a classical input-to-output feedback linearising controller which is obtained from the nominal dynamics of the bioprocess. Then, the outer loop is designed based on the internal model principle to obtain zero steady-state tracking error (and disturbance rejection) for constant signals while ensuring the robust stability of the overall closed-loop system. In addition, a robust Luenberger-like observer is proposed to estimate unmeasured state variables for the feedback linearising control law. The approach is applied to the simultaneous control of biomass and substrate concentrations in a perfusion/chemostat bioreactor, where the simulation results demonstrate the effectiveness of the proposed control strategy.

Adaptive fuzzy decentralized dynamics surface control for nonlinear large-scale systems based on high-gain observer

This paper discusses the adaptive fuzzy decentralized output-feedback control problem for a class of nonlinear large-scale systems. The systems under study have unknown nonlinearities, mismatched interconnections in control inputs, and unmeasurable state variables. Therefore, fuzzy logic systems are employed to approximate the unknown nonlinear functions in the control design; and an adaptive high-gain observer is established to estimate the unmeasured states. Based on the backstepping design technique and the dynamic surface control (DSC) approach, a novel adaptive fuzzy decentralized output-feedback control scheme is developed. It is proved that the proposed control approach can ensure that all the signals of the closed-loop system are semi-globally uniformly ultimately bounded (SUUB) and the observer error and tracking error can all converge to a small neighborhood of the origin. The effectiveness of the proposed approach is illustrated by simulation examples with comparisons with several existing methods.

Parameter identification of fluid line networks by frequency-domain maximum likelihood estimation

The accurate hydraulic simulation of fluid line networks is important for many applications, however, in many instances (such as surge analysis in water distribution networks) the system parameters are subject to much uncertainty. This paper presents a parameter identification method for fluid line networks based on transient-state measurements of the hydraulic variables of pressure and flow within the network. From a Laplace-domain admittance matrix representation of the system, a measurement model is derived that decouples the influence of unmeasured state variables from the measured state variables. This decoupled measurement model is used as the basis of the development of a frequency-domain maximum likelihood estimation method. The proposed method is applied to different case studies with successful results.

Robust adaptive fuzzy output feedback control for stochastic nonlinear systems with unknown control direction

This paper discusses the problem of adaptive fuzzy output feedback control for a class of uncertain stochastic nonlinear strict-feedback systems. The concerned systems have certain characteristics, such as unknown nonlinear functions, dynamical uncertainties, unknown control direction and unmeasured state variables. In this paper, the fuzzy logic systems are used to approximate the unknown nonlinear functions, and a filter state observer is developed for estimating the unmeasured states. To solve the problems of the dynamical uncertainties and the unknown control direction, the changing supply function and Nussbaum function techniques are incorporated into the backstepping recursive design technique, and a new robust adaptive fuzzy output feedback control approach is constructed. It is proved that the proposed control approach can guarantee that all the signals of the resulting closed-loop system are bounded in probability, and also that the observer errors and the output of the system can be regulated to a small neighborhood of the origin by choosing design parameters appropriately. A simulation example is provided to show the effectiveness of the proposed approach.

Real-time nonlinear global state observer design for solar heating systems

Nowadays it is important to investigate and develop solar water heating systems as an environmentally friendly technology. For this reason we introduce a physically-based nonlinear mathematical model that applies to a wide range of solar heating systems. In commercial solar heating systems not all state variables are monitored by direct measurements, since some of them may be technically difficult or expensive to measure. For a better monitoring and more efficient control of the system it may be useful to estimate the unmeasured state variables.As a novelty, we apply a global nonlinear state observer to a solar domestic water heating system. The state observer has been established relatively recently in the field of control theory. The state observer we worked out enables us to estimate the unmeasured state variables in real-time. This observer is global in the sense that it works starting from any initial state. A further contribution of this work is a rather general algorithm for the practical application of the real-time estimation process, and we also give bounds of the estimation error and a practical method to decrease this error.Comparing calculated and measured values for a real particular solar heating system, we justify the usability of the state observer and the estimation process.On the basis of measured data, we show that the nonlinear mathematical model corresponding to the applied nonlinear observer is more accurate than the linear model corresponding to the classical linear Luenberger-type observer, so it is reasonable to apply the nonlinear observer.

Real-time state observer design for solar thermal heating systems

Nowadays it is important to investigate and develop solar thermal heating systems as an environmental friendly technology. In the paper we demonstrate a physically-based linear mathematical model that can be applied to a wide range of solar heating systems to analyze and develop them.We construct a Luenberger type state observer for the mathematical model, which enables us to estimate in real-time the unmeasured state variables of the solar heating system. We give a general algorithm for the practical application of the estimation process.Comparing calculations and measurements, we introduce the usability of the state observer in case of a particular solar heating system that produces domestic hot water at the campus of the Szent István University, Hungary.

Precise control of linear systems subject to actuator saturation using tracking differentiator and reduced order composite nonlinear feedback control

Aiming at the actuator saturation problem and the system performance requirement, this article proposes a new control scheme, i.e. a newly developed tracking differentiator-composite nonlinear feedback (TDCNF) control law, which is the combination of a tracking differentiator (TD) and a reduced order composite nonlinear feedback (CNF) control law. The TD, used here, mainly helps to provide a smooth reference signal and largely avoid actuator saturation. The reduced order CNF control law, on the one hand, estimates those unmeasurable state variables for measurement feedback control and, on the other hand, ensures satisfactory system performance. The stability of the newly developed TDCNF is proved in detail. Finally, to verify the effectiveness of the newly developed TDCNF control law, two illustrative examples are demonstrated and therein a novel design of the proposed control law is given. Simulation results show that the proposed control law can achieve good tracking performance and effectively avoid the actuator saturation.

Observer-Based Nonlinear Feedback Controls for Heartbeat ECG Tracking Systems

The analysis and design of observed-based nonlinear control of a heartbeat tracking system is investigated in this paper. Two of Zeeman’s heartbeat models are investigated and modified by adding the control input as a pacemaker, thereby creating the control-affine nonlinear system models that capture the general heartbeat behavior of the human heart. The control objective is to force the output of the heartbeat models to track and generate a synthetic electrocardiogram (ECG) signal based on the actual patient reference data, obtained from the William Beaumont Hospitals, Michigan, and the PhysioNet database. The formulations of the proposed heartbeat tracking control systems consist of two phases: analysis and synthesis. In the analysis phase, nonlinear controls based on input-output feedback linearization are considered. This approach simplifies the difficult task of developing nonlinear controls. In the synthesis phase, observer-based controls are employed, where the unmeasured state variables are estimated for practical implementations. These observer-based nonlinear feedback control schemes may be used as a control strategy in electronic pacemakers. In addition, they could be used in a software-based approach to generate a synthetic ECG signal to assess the effectiveness of diagnostic ECG signal processing devices.

Application of a Continuous-discrete Unknown Input Observer to Estimation in Phytoplanktonic Cultures

The simultaneous estimation of unmeasured state variables and unknown inputs is particularly relevant in environmental applications, such as biological wastewater treatment or the culture of microalgae in open environments. In this study, an extension of the unknown input observer (UIO) recently proposed in (7) to nonlinear continuous-time models and discrete-time measurements is presented. This UIO takes account of the process and measurement noises, and uses a linearization around the estimated trajectory, in a way similar to the extended Kalman filter. This extended continuous-discrete UIO is applied to state and input reconstruction in continuous cultures of phytoplankton. In particular, the problem of simultaneously reconstructing the extra- and intra-cellular nitrogen concentrations together with the light intensity or the dilution rate from measurements of biomass in cultures of the marine microalgae Dunaliella tertiolecta or the cryptophyceae Rhodomonas salina are considered. Simulation results and processing of real data demonstrate the performance of the method.