Adaptive friction compensation using extended Kalman–Bucy filter friction estimation

An extended Kalman–Bucy filter (EKBF)-based friction compensation method is presented and validated. The method relies on an accurate model of system rigid-body dynamics and measured motion, rather than a structured nonlinear friction model, to estimate external friction torque. The estimate is used in a traditional friction compensator to cancel friction effects. The EKBF compensator is compared with other model-based and non-model-based friction compensation strategies through position tracking experiments. Results show that when motion is dominated by static and Stribeck friction, non-model-based friction estimation and compensation using the EKBF consistently provides equal or superior performance over model-based adaptive friction compensation methods.     

Tire–road friction coefficient and tire cornering stiffness estimation based on longitudinal tire force difference generation

A sequential tire cornering stiffness coefficient and tire–road friction coefficient (TRFC) estimation method is proposed for some advanced vehicle architectures, such as the four-wheel independently-actuated (FWIA) electric vehicles, where longitudinal tire force difference between the left and right sides of the vehicle can be easily generated. Such a tire force difference can affect the vehicle yaw motion, and can be utilized to estimate the tire cornering stiffness coefficient and TRFC. The proposed tire cornering stiffness coefficient and TRFC identification method has the potential of estimating these parameters without affecting the vehicle desired motion control and trajectory tracking objectives. Simulation and experimental results with a FWIA electric vehicle show the effectiveness of the proposed estimation method.     

A sleep model and an observer using the Lotka–Volsterra equation for real-time estimation of sleep

This paper describes a novel method that estimates sleep behaviors in a real-time manner. A Luenberger-type observer was employed, which requires a dynamic model of the sleep as a priori information about the sleep stages. A reasonable sleep model is essential in this approach. The classic Lotka–Voltera equation with interpretations associated with the sleep was built and an observer was developed. The observer using heartbeat rhythm and body movement as input signals estimated and compensated the sleep depths, which shows better results than the original inputs in the standpoint of the percentage of δ-waves in total brainwaves, used as a reference. The observer compensated for phase-shift errors and non-cyclic errors of the sleep cycle. The correlation between the reference and the compensated sleep cycle behavior was 0.79, whereas that between the reference and the measurement itself was 0.65. The application of the observer improved the accuracy of the sleep cycle measurement.     

Luenberger boundary observer synthesis for Sturm–Liouville systems

A static Luenberger observer of a system with Sturm–Liouville operator is synthesised with the aid of a boundary control formulation. To this aim, approximate observability, detectability and stability of the system is studied and design results are worked out for a typical biochemical case study.     

Extending 3D Lucas–Kanade tracking with adaptive templates for head pose estimation

The Lucas–Kanade tracker (LKT) is a commonly used method to track target objects over 2D images. The key principle behind the object tracking of an LKT is to warp the object appearance so as to minimize the difference between the warped object’s appearance and a pre-stored template. Accordingly, the 2D pose of the tracked object in terms of translation, rotation, and scaling can be recovered from the warping. To extend the LKT for 3D pose estimation, a model-based 3D LKT assumes a 3D geometric model for the target object in the 3D space and tries to infer the 3D object motion by minimizing the difference between the projected 2D image of the 3D object and the pre-stored 2D image template. In this paper, we propose an extended model-based 3D LKT for estimating 3D head poses by tracking human heads on video sequences. In contrast to the original model-based 3D LKT, which uses a template with each pixel represented by a single intensity value, the proposed model-based 3D LKT exploits an adaptive template with each template pixel modeled by a continuously updated Gaussian distribution during head tracking. This probabilistic template modeling improves the tracker’s ability to handle temporal fluctuation of pixels caused by continuous environmental changes such as varying illumination and dynamic backgrounds. Due to the new probabilistic template modeling, we reformulate the head pose estimation as a maximum likelihood estimation problem, rather than the original difference minimization procedure. Based on the new formulation, an algorithm to estimate the best head pose is derived. The experimental results show that the proposed extended model-based 3D LKT achieves higher accuracy and reliability than the conventional one does. Particularly, the proposed LKT is very effective in handling varying illumination, which cannot be well handled in the original LKT.     

Robust H ∞ sliding mode observer design for fault estimation in a class of uncertain nonlinear systems with LMI optimization approach

This paper presents a new approach for the design of robust H _∞ sliding mode observer (SMO) for a class of Lipschitz nonlinear systems where both faults and uncertainties are considered. A sufficient condition using linear matrix inequality (LMI) optimization is derived to guarantee the asymptotically stability of the estimation error dynamics and compute the observer gains. A fault estimation scheme is presented where the estimation signal can approximate the fault to some degree of accuracy. Our design approach has some advantages. The Lipschitz constant of the nonlinear term in the system and the disturbance attenuation level are maximized simultaneously through convex multiobjective optimization. For this reason, the Lipschitz constant is suitable to a large class of uncertain nonlinear systems. Moreover, the fault estimation is much more robust against disturbances and nonlinear uncertainty and can preserve the fault signal shape effectively. Finally, a simulation study on a robotic arm system is presented to show the effectiveness of this approach.     

Zonotopic fault detection observer design for Takagi–Sugeno fuzzy systems

This paper considers zonotopic fault detection observer design in the finite-frequency domain for discrete-time Takagi–Sugeno fuzzy systems with unknown but bounded disturbances and measurement noise. We present a novel fault detection observer structure, which is more general than the commonly used Luenberger form. To make the generated residual sensitive to faults and robust against disturbances, we develop a finite-frequency fault detection observer based on generalised Kalman–Yakubovich–Popov lemma and P-radius criterion. The design conditions are expressed in terms of linear matrix inequalities. The major merit of the proposed method is that residual evaluation can be easily implemented via zonotopic approach. Numerical examples are conducted to demonstrate the proposed method.     

First vorticity–velocity–pressure numerical scheme for the Stokes problem

We consider the bidimensional Stokes problem for incompressible fluids and recall the vorticity, velocity and pressure variational formulation, which was previously proposed by one of the authors, and allows very general boundary conditions. We develop a natural implementation of this numerical method and we describe in this paper the numerical results we obtain. Moreover, we prove that the low degree numerical scheme we use is stable for Dirichlet boundary conditions on the vorticity. Numerical results are in accordance with the theoretical ones. In the general case of unstructured meshes, a stability problem is present for Dirichlet boundary conditions on the velocity, exactly as in the stream function-vorticity formulation. Finally, we show on some examples that we observe numerical convergence for regular meshes or embedded ones for Dirichlet boundary conditions on the velocity.     

An ESO-based integrated trajectory tracking control for tractor–trailer vehicles with various constraints and physical limitations

This paper develops an effective integrated control strategy for the trajectory tracking control of a tractor–trailer vehicle which suffers from inaccessible system states and uncertain disturbance for practical implementation. In addition, diverse problems, such as nonholonomic constraints, underactuated dynamics, physical limitations, etc, can be resolved favourably all together. Aiming to the vehicle trajectory tracking, a constrained model predictive control (MPC) is introduced as a trajectory tracking module, by which the underactuated dynamics, various constraints and physical limitations, can be tackled at the same time. For the desired velocity tracking, a robust global terminal sliding mode control (GTSMC) is employed to guarantee the finite-time convergence of the velocity tracking process, which will improve the transient performance to a great extent. Particularly, in the absence of velocity information, an extended state observer (ESO) is developed to estimate the vehicle velocity in addition to simultaneously obtaining the uncertain disturbance information, which offers prerequisite for the previous control approaches. The simulation results confirm that the presented control strategy can synthesise varied control techniques effectively and deal with diverse problems for the trajectory tracking of tractor–trailer vehicles successfully.     

On non-linear unknown input observers–applied to lateral vehicle velocity estimation on banked roads

Unknown input observers (UIOs) are observers that have stable error dynamics that are independent of unknown inputs. This paper studies such observers for non-linear systems, and shows that the error dynamics for a non-linear UIO has the same structure as the error dynamics of a non-linear observer without unknown inputs. This result is first used to provide synthesis inequalities for UIOs for a class of non-linear systems, and secondly, to inspire the design of an observer for estimation of vehicle lateral velocity on banked roads.     

New algorithms for estimation with sequentially correlated measurement noise †

This paper derives new estimation algorithms for use with systems with sequentially correlated observation noise. Both single and two-stage correlation are considered. The algorithms appear much like the well known white noise algorithms and are not much more complex.

Error analysis algorithms for the analysis of modelling errors made in using those and white noise estimation algorithms are also presented. Those algorithms permit analysis of the effect of making the white noise assumption when the observation noise is really coloured. Examples and associated illustrations are presented to show this effect

The newly derived algorithms are compared with existing, more restrictive algorithms, and Bhown to provide equivalent results for problems where both apply.     

A unified observer for robust sensorless control of DC–DC converters

Due to the large variety of converters' configurations, many different sensorless controllers are available in the literature, each one suited for a particular converter. The need for different configurations, especially on the same power supply, make it clear the advantage of having a shared control algorithm. This paper presents a unified nonlinear robust current observer for buck, boost and buck–boost converters in synchronous and asynchronous configurations. The unified observer speeds up the design, tuning and the implementation, and requires a memory cheaper code, easier to certify. Simulation and experimental results are presented to validate the approach in different scenarios.     

Design of polynomial fuzzy observer–controller for nonlinear systems with state delay: sum of squares approach

This paper investigates the problem of observer-based control for two classes of polynomial fuzzy systems with time-varying delay. The first class concerns a special case where the polynomial matrices do not depend on the estimated state variables. The second one is the general case where the polynomial matrices could depend on unmeasurable system states that will be estimated. For the last case, two design procedures are proposed. The first one gives the polynomial fuzzy controller and observer gains in two steps. In the second procedure, the designed gains are obtained using a single-step approach to overcome the drawback of a two-step procedure. The obtained conditions are presented in terms of sum of squares (SOS) which can be solved via the SOSTOOLS and a semi-definite program solver. Illustrative examples show the validity and applicability of the proposed results.     

Precompensation decoupling control with H∞ performance for 4WS velocity-varying vehicles

In this paper, a new decoupling control strategy with H_∞ performance for the three-degree-of-freedom model, including the longitudinal velocity, the lateral velocity, and the yaw rate is presented and discussed. A sliding mode controller only depending on the longitudinal velocity for the longitudinal system and a precompensation decoupling controller with H_∞ performance for the steering system are designed. These controllers are established by feeding back longitudinal velocity and yaw rate, thus observation or measurement for the lateral velocity is not required. Simulation results show that our strategy can improve the handling characteristics, safety, and comfort significantly.     

Fouling detection in a heat exchanger by observer of Takagi–Sugeno type for systems with unknown polynomial inputs

This paper proposes a new method for fouling detection in a heat exchanger. It is based on the modeling of the system in a fuzzy Takagi–Sugeno representation derived from a physical model. With this representation, the design of a fuzzy observer with unknown inputs of polynomial types is obtained via a LMI formulation. Main advantages of the proposed method are that neither specific sensor, excepted standard ones, nor special operating conditions such as steady state regime are required. Some realistic simulations show the efficiency of the proposed technique.     

Optimal digital controller and observer design for multiple time-delay transfer function matrices with multiple input–output time delays

In this article, we address the optimal digital design methodology for multiple time-delay transfer function matrices with multiple input–output time delays. In our approach, the multiple time-delay analogue transfer function matrix with multiple input–output time delays is minimally realised using a continuous-time state-space model. For deriving an explicit form of the optimal digital controller, the realised continuous-time multiple input–output time-delay system is discretised, and an extended high-order discrete-time state-space model is constructed for discrete-time LQR design. To derive a low-order optimal digital observer for the multiple input–output time-delay system, the multiple time-delay state obtained from the multiple time-delay outputs is discretised. Then, the well-known duality concept is employed to design an optimal digital observer using the low-order discretised multiple input time-delay system together with the newly discretised multiple time-delay state. The proposed approach is restricted to multiple time-delay systems where multiple time delays arise only in the input and output, and not in the state.     

Integration of MODIS LAI and vegetation index products with the CSM–CERES–Maize model for corn yield estimation

Advanced information on crop yield is important for crop management and food policy making. A data assimilation approach was developed to integrate remotely sensed data with a crop growth model for crop yield estimation. The objective was to model the crop yield when the input data for the crop growth model are inadequate, and to make the yield forecast in the middle of the growing season. The Cropping System Model (CSM)–Crop Environment Resource Synthesis (CERES)–Maize and the Markov Chain canopy Reflectance Model (MCRM) were coupled in the data assimilation process. The Moderate Resolution Imaging Spectroradiometer (MODIS) Leaf Area Index (LAI) and vegetation index products were assimilated into the coupled model to estimate corn yield in Indiana, USA. Five different assimilation schemes were tested to study the effect of using different control variables: independent usage of LAI, normalized difference vegetation index (NDVI) and enhanced vegetation index (EVI), and synergic usage of LAI and EVI or NDVI. Parameters of the CSM–CERES–Maize model were initiated with the remotely sensed data to estimate corn yield for each county of Indiana. Our results showed that the estimated corn yield agreed very well with the US Department of Agriculture (USDA) National Agricultural Statistics Service (NASS) data. Among different scenarios, the best results were obtained when both MODIS vegetation index and LAI products were assimilated and the relative deviations from the NASS data were less than 3.5%. Including only LAI in the model performed moderately well with a relative difference of 8.6%. The results from using only EVI or NDVI were unacceptable, as the deviations were as high as 21% and ?13% for the EVI and NDVI schemes, respectively. Our study showed that corn yield at harvest could be successfully predicted using only a partial year of remotely sensed data.     

Road profile estimation using an adaptive Youla–Kučera parametric observer: Comparison to real profilers

Road profile acts as a disturbance input to the vehicle dynamics and results in undesirable vibrations affecting the vehicle stability. An accurate knowledge of this data is a key for a better understanding of the vehicle dynamics behavior and active vehicle control systems design. However, direct measurements of the road profile are not trivial for technical and economical reasons, and thus alternative solutions are needed. This paper develops a novel observer, known as a virtual sensor, suitable for real-time estimation of the road profile. The developed approach is built on a quarter-car model and uses measurements of the vehicle body. The road roughness is modeled as a sinusoidal disturbance signal acting on the vehicle system. Since this signal has unknown and time-varying characteristics, the proposed estimation method implements an adaptive control scheme based on the internal model principle and on the use of Youla–Kučera (YK) parameterization technique (also known as Q-parameterization). For performances assessment, estimations are comparatively evaluated with respect to measurements issued from Longitudinal Profile Analyzer (LPA) and Inertial Profiler (IP) instruments during experimental trials. The proposed method is also compared to the approach provided in Doumiati, Victorino, Charara, and Lechner (2011), where a stochastic Kalman filter is applied assuming a linear road model. Results show the effectiveness and pertinence of the present observation scheme.