Kalman State Estimator Research Articles

Milling chatter suppression based on the model predictive optimal control with Kalman state estimation

Milling chatter suppression based on the model predictive optimal control with Kalman state estimation

Wing dynamic shape-sensing from fiber-optic strain data using the Kalman state estimator

A novel method for shape sensing based on strain data and the use of the Kalman state estimator is presented and studied experimentally. Several recent studies proposed different methods in which strain data, measured in optical fibers, can be used to estimate the deformed shape of a flexible wing. Fiber optic sensors typically provide accurate, high resolution, strain data, yielding detailed prediction of a wing's deformed shape. However, in real life applications there could be moments in which the strain data is imperfect (for example, due to saturation or temperature effects), corrupted, or missing. The current study proposes to use a Kalman state estimator that weighs in strain-data and simulation output of an aeroelastic plant model to estimate the wing deformations. The method is demonstrated with a flexible wing model that is excited by prescribed control surfaces deflection in a wind-tunnel test. Strains over the front and rear wing spars are measured by Fiber Bragg Grating sensors, embedded in two optical fibers, and used to estimate the wing deformations. The latter are compared to wing deformations measured by a motion recovery camera system. Results show the advantages of the use of the Kalman state estimator when the strain data is corrupted. Additionally, with this approach, wing's modal velocities are estimated together with the wing deformations, resulting in smooth and accurate modal velocities that are readily usable by the vehicle's control system.

Linear Parameter-Varying Model Predictive Control for Hydraulic Wind Turbine

Wind speed uncertainty and measurement noise affect the control effect in hydraulic wind turbine systems. This paper proposes a model predictive control (MPC) method with a dynamic Kalman filter (KF) based on a linear parameter-varying (LPV) model to address this problem. First of all, the LPV model for a nonlinear system of a hydraulic wind turbine is established using function substitution. Then, a LPV-based KF is introduced into the MPC to provide more precise estimated results and improve the anti-interference ability of the system. According to the current condition of the hydraulic wind turbine, the method updates the Kalman state estimator at each sampling instant and computes the optimal control input by solving a quadratic programming (QP) optimization problem. The performance and the efficiency of the proposed method is validated in simulation and compared with other methods.

Model predictive control of microbial fuel cell based on Kalman state estimation

Aiming at the constraints and undetectable interference in the microbial fuel cell system, a microbial fuel cell model predictive control method based on state estimation is proposed. According to the principles and actual requirements of the microbial fuel cell system, a state space model with input constraints is established. By introducing the model predictive controller, the performance of constrained optimization control is improved. Combined with the Kalman filter estimator, the impact of unmeasured interference on the predictive controller is compensated, and the control accuracy and robustness of the system are improved. The simulation experiment finally indicate that model predictive control based on kalman state estimation makes the output voltage of system reach the desired value, the input flow meets the actual demand and the cost is optimal. In addition, it has a good ability to deal with interference.

Towards vendor-agnostic real-time optical network design with extended Kalman state estimation and recurrent neural network machine learning [Invited

The network operator’s call for open, disaggregated optical networks to accelerate innovation and reduce cost, make progress in the standardization of interfaces, and raise telemetry capabilities in optical network systems has created an opportunity to adopt a new paradigm for optical network design. This new paradigm is driven by direct measurement and continuous learning from the actual optical hardware deployed in the field. We report an approach towards practical, vendor-agnostic, real-time optical network design and network management using a combination of two learning models. We generalize our physics-based optical model parameter estimation algorithm using the extended Kalman state estimation theory and, for the first time, to the best of our knowledge, present results using real optical network field data. An observed 0.3 dB standard deviation of the difference between typical predicted and measured signal quality appears mostly attributable to transponder performance variance. We further propose using the physics-based optical model parameter values as inputs to a second learning model with a recurrent neural network such as a gated recurrent unit (GRU) to allocate the appropriate required optical margin relative to the typical signal quality predicted by the physics-based optical model. A proof of concept shows that for a dataset of 3000 optical connections with a wide variety of amplified spontaneous emission noise and nonlinear noise limited conditions, a 10-hidden-unit 2-layer GRU was sufficient to realize a margin prediction error standard deviation below 0.2 dB. This approach of measurement data-driven automated network design will simplify deployment and enable efficient operation of open optical networks.

Model reference adaptive LQT control for anti-jerk utilizing tire-road interaction characteristics

Sudden vehicle propulsion torque change under tip-in/out maneuver often leads to low-frequency longitudinal vibration due to the flexibility in the half-shaft and tire slip, which greatly affects vehicle drivability. Note that the vibration frequency is between 1 and 10 Hz and is difficult to be absorbed by the vehicle mechanical system. To optimize the vehicle drivability under tip-in maneuver, an Adaptive Linear Quadratic Tracking (ALQT) anti-jerk traction controller is proposed in this paper. Based on the experimental data, a Carsim-Simulink co-simulation model is developed for assessing control performance. A control-oriented model, considering the nonlinear characteristics of the tire-road friction coefficient and slip ratio, is then proposed. A reference model with rigid axle is used to provide the equilibrium points and reference velocity trajectory. Jacobi linearization method is then used to linearize the model along the desired trajectory and a linear deviation model based on equilibrium points is obtained. Finally, the deviation compensation receding horizon LQT controller is designed along with the Kalman state estimation. The effectiveness of the designed controller is assessed via simulation studies under different road surfaces and compared with PID and LQR controllers. The LQT controller is able to track the desired velocity profile with minimum jerk while increasing road safety. Furthermore, the effect of LQT weighting coefficients under different road surfaces are discussed. Simulation results show that the ALQT controller is able to optimize vehicle drivability under different road surfaces and the weighting matrices shall be selected based on the road condition for optimal drivability.

Control of UPQC based on steady state linear Kalman filter for compensation of power quality problems

A frequency lock loop (FLL) based steady state linear Kalman filter (SSLKF) for unified power quality conditioner (UPQC) control in three-phase systems is introduced. The SSLKF provides a highly accurate and fast estimation of grid frequency and the fundamental components (FCs) of the input signals. The Kalman filter is designed using an optimized filtering technique and intrinsic adaptive bandwidth architecture, and is easily integrated into a multiple model system. Therefore, the Kalman state estimator is fast and simple. The fundamental positive sequence components (FPSCs) of the grid voltages in a UPQC system are estimated via these SSLKF-FLL based filters. The estimation of reference signals for a UPQC controller is based on these FPSCs. Therefore, both active filters of a UPQC can perform one and more functions towards improving power quality in a distribution network. In addition to the SSLKF-FLL based algorithm, a bat optimization algorithm (based on the echolocation phenomenon of bats) is implemented to estimate the value of the proportional integral (PI) controller gains. The bat algorithm has a tendency to automatically zoom into a region where a promising alternative solution occurs, preventing the solution from becoming trapped in a local minima. The complete three-phase UPQC is simulated in the Matlab/Simulink platform and the hardware is tested under various power quality problems.

Kalman and UFIR state estimation with coloured measurement noise using backward Euler method

Under coloured noise, known modifications of the Kalman filter (KF) exist only for discrete-time state-space models produced by the forward Euler (FE) method, which fits with feedback control. In this study, the authors modify the KF and unbiased finite impulse response (UFIR) filter using the backward Euler (BE) method for models with coloured measurement noise (CMN), which better fits systems without feedback. The FE- and BE-based models differ by time indexes in the system input and noise that is essential for time-varying and Markov jump systems. Employing measurement differencing, two KF algorithms and a unique UFIR algorithm are derived for time-correlated and de-correlated noise. An equivalence of the KF algorithms is proved analytically and confirmed by simulations. Numerical examples are given for target tracking and experimental verification is provided for visual object tracking. The high efficiency of the designed algorithms in removing CMN is demonstrated experimentally.

Linear-Quadratic Tracking Control of a Commercial Vehicle Air Brake System

This article proposes to utilize linear-quadratic tracking (LQT) control to reduce the air brake system response time and vehicle stopping distance, and hence, to significantly improve the system performance of a commercial vehicle air brake system equipped with electro-pneumatic proportional valve actuators. The nonlinear dynamic model of the air brake system, consisting of a control actuator (a proportional valve) and braking actuator (the brake chamber), is developed and linearized using the q-Markov COVariance Equivalent Realization (q-Markov Cover) method in our early work. Based on the linearized dynamic model, an infinite horizon LQT controller is designed along with Kalman state estimation at each linearized operational condition. To apply the LQT control law over a wide operational range to track the target pressure, the designed controller was interpolated between the neighboring controllers to have a control law cover the entire operational range. To validate this control law, the control scheme is implemented into a dSPACE unit and validated through bench tests under different supply and reference pressures. The LQT control performance is also compared with the PID (proportional-integral-derivative) one. The bench test results confirm the effectiveness of the proposed control scheme.

Fusion Kalman and Weighted UFIR State Estimator With Improved Accuracy

In this article, estimates of the Kalman filter (KF) and weighted unbiased finite impulse response (UFIR) filter are fused in discrete time-varying state-space to improve the robustness in uncertain environments associated with industrial applications. The weighted UFIR filter is derived using the Frobenius norm and termed as Frobenius finite impulse response (FFIR) filter. It is confirmed that the FFIR filter has better performance under the uncertainties and errors in the noise statistics, while the KF filter is best when the model and noise are exactly known. Based on a numerical example of a hover system, we show that the FFIR filter is able to outperform the UFIR filter and that the fusion KF/FFIR filter is able to outperform both of them. An experimental verification provided for the drone velocity estimation under the hover operation conditions has proved a better accuracy and robustness of the proposed fusion KF/FFIR filter.

Experiments on State and Unmeasured-Parameter Estimation of Two Degree-of-Freedom System for Precise Control Based on JAUKF

We herein present system parameter estimation using the joint adaptive unscented Kalman filter and state estimation approach for a two degree-of-freedom (2-DOF) mechanical system. The unscented Kalman filter (UKF) is applied broadly in diverse engineering fields to estimate the state of the dynamic system and improve the control precision by reducing measurement noise. One aspect of parameter identification is that unmeasured parameter estimation is important in designing and maintaining the system performance with a suitable controller. This is because changes in the system parameters estimated will occur owing to external shock and deterioration in operation. State estimation has been studied thoroughly and developed widely, but not in terms of parameter estimation. Parameter estimation is important because system parameters can be altered owing to wear and tear, large disturbance, or exposure to extreme temperatures. It is difficult to disassemble and measure the parameter when it changes; hence, computational estimation is a solution. The proposed method simultaneously estimates the states as well as the parameters of custom-made 2-DOF mechanical system that is a nonlinear dynamical system. The adaptive rules in the estimation process are considered based on the moving average window method to address the effects of unexpected noise in the sensor measurements. The experimental results are analyzed to demonstrate the effectiveness of the proposed method for estimating the states and parameters. This method demonstrates better performance compared to using the joint-UKF in terms of convergence time, accuracy, and robustness to noise.

Latent Leakage Fault Identification and Diagnosis Based on Multi-Source Information Fusion Method for Key Pneumatic Units in Chinese Standard Electric Multiple Units (EMU) Braking System

To identify and diagnose the latent leakage faults of key pneumatic units in the Chinese standard Electric Multiple Units (EMU) braking system, a multi-source information fusion method based on Kalman filtering, sequential probability ratio test (SPRT), and support vector machine (SVM) is proposed. The relay valve is taken as an example for research. Firstly, Kalman’s state estimation function is used to obtain the innovation sequence, and the innovation sequence is input into the SPRT model to help recognize latent leakage faults of the relay valve. Using this method, the problem of the incomplete training set of the traditional SPRT method due to the change of the braking level and the vehicle load is solved. Secondly, the eight time-domain parameters of the relay valve input and the output pressure signal are extracted as fault characteristics, and then input to the support vector machine to realize the internal and external leakage fault diagnosis of the relay valve, which provides a reference for maintenance. Finally, this method is verified by the fault simulation data by quickly identifying latent leakage faults and diagnosing the internal and external leakage at a fault recognition rate of 100% by SVM under small sample conditions.

Robust optimal centralized controller to mitigate the small signal instability in an islanded inverter based microgrid with active and passive loads

This paper proposes a robust optimal centralized controller to mitigate the small signal instability caused by the interaction between the control loops of rectifier interfaced active loads (RIALs) and the inverter interfaced distributed generations. The proposed controller is based on a robust linear quadratic regulator with prescribed degree-of-stability (LQRPDS). In order to reduce communication system burden and improve the flexibility and reliability of the proposed controller, a kalman state estimator has been designed. The optimal values of the diagonal weighting matrices of LQRPDS and kalman estimator are obtained by formulating a bi-objective optimization problem, which is solved using a fast and elitist multi-objective non-dominated sorting genetic algorithm (NSGA-II). A full dynamical linearized state space model of an islanded MG represented in synchronous (DQ) reference frame has been considered for analyzing the stability. However, schur balanced model order reduction technique has been used to reduce the complexity in the design of the controller. Eigenvalue analysis and time-domain simulations have been presented to demonstrate the robust performance of the controller under various load configurations as well as under step load disturbances. The efficacy of the proposed centralized controller is verified by comparing its performance with that of LQR based centralized controller.

A Kalman Latency Compensation Strategy for Model Predictive Control to Damp Inter-Area Oscillations in Delayed Power Systems

Power systems control strategies that use global signals have shown better results than those based on local signals, but the remote signals are usually taken far away from the control center. Because of that, wide area power systems controlled using global signals are inherently delayed, and time delays jeopardize the stability of power systems. This paper presents a Kalman based time delay compensation strategy, which feed a Model Predictive Control (MPC) scheme to damp inter-area oscillations in power systems with latencies in their communications. A Kalman state estimator is employed to get the states. The proposal uses a dynamic reduced order model obtained using Hankel singular values. The methodology is promissory because it considers time delays in control schemes design processes, useful for either centralized or distributed wide area power system controllers based on widespread metering. This approach was validated for controlling inter-area oscillations in a test power system with two areas, 4 generators and a tie power line. Results suggest an enhancement of the power system dynamic performance upon the application of the method proposed.

Design and operation of the RFX-mod plasma shape control system

The aim of executing Single Null discharges in RFX-mod operating as a Tokamak led to the design and implementation of a plasma shape feedback control system. A fully model-based approach was followed which allowed dealing with critical issues such as the presence of a conducting shell, the strong coupling of the poloidal field coils and the voltage limits of the power supplies. A Linear Quadratic regulator and a Kalman state estimator were designed and implemented in the real time MARTe framework together with an algorithm for the real-time plasma boundary reconstruction. The problem of a number of sensors along the poloidal direction adequate only for circular discharges was also successfully tackled. The development of the system and its performances in terms of tracking and disturbance rejection capability are presented in the paper.

A General Robust MPC Design for the State‐Space Model: Application to Paper Machine Process

AbstractApplying model predictive control (MPC) in some cases such as complicated process dynamics and/or rapid sampling leads us to poorly numerically conditioned solutions and heavy computational load. Furthermore, there is always mismatch in a model that describes a real process. Therefore, in this paper in order to prevail over the mentioned difficulties, we design a robust MPC using the Laguerre orthonormal basis in order to speed up the convergence at the same time with lower computation adding an extra parameter “a” in MPC. In addition, the Kalman state estimator is included in the prediction model and accordingly the MPC design is related to the Kalman estimator parameters as well as the error of estimations which helps the controller react faster against unmeasured disturbances. Tuning the parameters of the Kalman estimator as well as MPC is another achievement of this paper which guarantees the robustness of the system against the model mismatch and measurement noise. The sensitivity function at low frequency is minimized to tune the MPC parameters since the lower the magnitude of the sensitivity function at low frequency the better command tracking and disturbance rejection results. The integral absolute error (IAE) and peak of the sensitivity are used as constraints in optimization procedure to ensure the stability and robustness of the controlled process. The performance of the controller is examined via the controlling level of a Tank and paper machine processes.

Experimental validation of Kalman filter-based strain estimation in structures subjected to non-zero mean input

Response estimation at unmeasured locations using the limited number of measurements is an attractive topic in the field of structural health monitoring (SHM). Because of increasing complexity and size of civil engineering structures, measuring all structural responses from the entire body is intractable for the SHM purpose; the response estimation can be an effective and practical alternative. This paper investigates a response estimation technique based on the Kalman state estimator to combine multi-sensor data under non-zero mean input excitations. The Kalman state estimator, constructed based on the finite element (FE) model of a structure, can efficiently fuse different types of data of acceleration, strain, and tilt responses, minimizing the intrinsic measurement noise. This study focuses on the effects of (a) FE model error and (b) combinations of multi-sensor data on the estimation accuracy in the case of non-zero mean input excitations. The FE model error is purposefully introduced for more realistic performance evaluation of the response estimation using the Kalman state estimator. In addition, four types of measurement combinations are explored in the response estimation: strain only, acceleration only, acceleration and strain, and acceleration and tilt. The performance of the response estimation approach is verified by numerical and experimental tests on a simply-supported beam, showing that it can successfully estimate strain responses at unmeasured locations with the highest performance in the combination of acceleration and tilt.

On existence, optimality and asymptotic stability of the Kalman filter with partially observed inputs

For linear stochastic time-varying systems, we investigate the properties of the Kalman filter with partially observed inputs. We first establish the existence condition of a general linear filter when the unknown inputs are partially observed. Then we examine the optimality of the Kalman filter with partially observed inputs. Finally, on the basis of the established existence condition and optimality result, we investigate asymptotic stability of the filter for the corresponding time-invariant systems. It is shown that the results on existence and asymptotic stability obtained in this paper provide a unified approach to accommodating a variety of filtering scenarios as its special cases, including the classical Kalman filter and state estimation with unknown inputs.

Soft Measurement Technology for Tractor-Semi Trailer

A three degree of freedom vehicle dynamic model of a tractor semi trailer is established and a simulation mode is set up with the Matlab/simulink software. Then, design a Kalman state estimator, using easily measured parameters to estimate the tractor side slip angle, trailer yaw rate those are difficult measured or measuring in high cost; the simulation show that: the estimated value coming from estimator agree well with the simulation measurements, and can improve the estimation accuracy by adjusting the process noise covariance matrix and measurement noise covariance matrix.

Generalized Predictive Control in a Wireless Networked Control System

The NCS (networked control system) is different from the conventional control systems which is the integration of the automation and control over communication network. When an NCS operates over the communication network, one of the major challenges is the network-induced delay in data transfer among the controllers, actuators, and sensors. This delay degrades system performance and causes system unstablility. This paper proposes a GPC (generalized predictive control) with the Kalman state estimator to compensate for the network-induced delay and packet loss. The GPC is implemented in WiNCS (Wireless NCS) based on IEEE 802.11 standard. An analytical NCS model and NS2 (network simulator version 2) are developed to simulate and evaluate the performance under the effect of various delays and packet loss rates. The result shows that the proposed GPC is adaptive and robust to the uncertainties in a time-delay system. The WiNCS is evaluated with latency and throughput measurements in various environments. The experiment setup conforming to the IEEE 802.11 standard achieves an average latency of 1.3 ms and a data throughput of 3.000 kB/s up to a distance of 70 m. The results demonstrate the feasibility of real-time closed-loop control with the proposed concept.