The Kalman filter (KF) is optimal with respect to minimum mean square error (MMSE) if the process noise and measurement noise are Gaussian. However, the KF is suboptimal in the presence of non-Gaussian noise. The maximum correntropy criterion Kalman filter (MCC-KF) is a Kalman-type filter that uses the correntropy measure as its optimality criterion instead of MMSE. In this paper, we modify the correntropy gain in the MCC-KF to obtain a new filter that we call the measurement-specific correntropy filter (MSCF). The MSCF uses a matrix gain rather than a scalar gain to provide better selectivity in the way that it handles the innovation vector. We analytically compare the performance of the KF with that of the MSCF when either the measurement or process noise covariance is unknown. For each of these situations, we analyze two mean square errors (MSEs): the filter-calculated MSE (FMSE) and the true MSE (TMSE). We show that the FMSE of the KF is less than that of the MSCF. However, the TMSE of the KF is greater than that of the MSCF under certain conditions. Illustrative examples are provided to verify the analytical results.

Output-only identification methods have been developed on a stochastic framework, but for the first time, a subspace-based approach is proposed without using geometric and statistical tools. This aids the computational efforts to be significantly reduced and the range of input sources to be extended in a much realistic manner for future output-only analyses. The approach encompasses any input type and can properly work for systems excited by inputs with finite periods. It is demonstrated that the row space of the output sequences spanned by column vectors of the decomposed orthonormal matrix is sufficient to reconstruct the observations. The transient and steady-state portions of the output row space, afterward, can be captured to reconstruct an integrated innovation model. The advantages of the algorithm are highlighted through several numerical and experimental examples comparing with the traditional subspace identification algorithms.

This paper presents a nonlinear disturbance observer (NDOB) for active disturbance rejection in the attitude control loop for quadrotors. An optimization framework is developed for tuning the parameter in the NDOB structure, which includes the infinity-norm minimization of the weighted sum of noise-to-output transfer function and load disturbance sensitivity function. Subsequently, the minimization generates an optimal value of the parameter based on the tradeoff between disturbance rejection and noise propagation in the system. The proposed structure is implemented on PIXHAWK, a real-time embedded flight control unit. Simulation tests are carried out on a custom built, high-fidelity simulator providing physically accurate simulations. Furthermore, experimental flight tests are conducted to demonstrate the performance of the proposed approach. The system is injected with step, sinusoidal, and square wave disturbances, and the corresponding system tracking performance is recorded. Experimental results show that the proposed algorithm attenuates the disturbances better compared to just a baseline controller implementation. The proposed algorithm is computationally cheap, an active disturbance rejection technique and robust to exogenous disturbances.

This paper introduces a robust visual tracking of objects in complex environments with blocking obstacles and light reflection noises. This visual tracking method utilizes a transfer matrix to project image pixels back to real-world coordinates. During the image process, a color and shape test is used to recognize the object and a vector is used to represent the object, which contains the information of orientation and body length of the object. If the object is partially blocked by the obstacles or the reflection from the water surface, the vector predicts the position of the object. During the real-time tracking, a Kalman filter is used to optimize the result. To validate the method, the visual tracking algorithm was tested by tracking a submarine and a fish on the water surface of a water tank, above which three pieces of blur glass were blocking obstacles between the camera and the object. By using this method, the interference from the reflection of the side glass and the fluctuation of the water surface can be also avoided.

In previous work, a new model of driver steering control incorporating sensory dynamics was derived and used to explain the performance of drivers in a simulator with full-scale motion feedback. This paper describes further experiments investigating how drivers steer with conflicts between their visual and vestibular measurements, caused by scaling or filtering the physical motion of the simulator relative to the virtual environment. The predictions of several variations of the new driver model are compared with the measurements to understand how drivers perceive sensory conflicts. Drivers are found to adapt well in general, unless the conflict is large, in which case they ignore the physical motion and rely on visual measurements. Drivers make greater use of physical motion which they rate as being more helpful, achieving a better tracking performance. Sensory measurement noise is shown to be signal-dependent, allowing a single set of parameters to be found to fit the results of all the trials. The model fits measured linear steering behavior with an average “variance accounted for (VAF)” of 86%.

This paper presents a method for real-time identification of sensor statistics especially aimed for low-cost automotive-grade sensors. Based on recent developments in adaptive particle filtering (PF) and under the assumption of Gaussian distributed noise, our method identifies the slowly time-varying sensor offsets and variances jointly with the vehicle state, and it extends to banked roads. While the method is primarily focused on learning the noise characteristics of the sensors, it also produces an estimate of the vehicle state. This can then be used in driver-assistance systems, either as a direct input to the control system or indirectly to aid other sensor-fusion methods. The paper contains verification against several simulation and experimental data sets. The results indicate that our method is capable of bias-free estimation of both the bias and the variance of each sensor, that the estimation results are consistent over different data sets, and that the computational load is feasible for implementation on computationally limited embedded hardware typical of automotive applications.

Estimating residual unbalances of a flexible rotor that is fully levitated on active magnetic bearings (AMBs) are challenging tasks due to the modeling error of AMB rotordynamic parameters. In this work, an identification algorithm has been developed for the estimation of dynamic parameters of speed-dependent AMBs and residual unbalances in a high-speed flexible rotor-bearing system. Parameters are identified during an estimation process with the help of displacement and current information at AMB locations only. For reducing the finite element model to suit the measurement availability, an improved dynamic reduction scheme has been proposed, which considers the gyroscopic matrix also in the transformation matrix. For a numerical testing of the developed identification algorithm, a multidisk flexible-shaft rotor is considered, which is fully levitated on AMBs. Speed-dependent AMB parameters have been modeled by a cubic function. Proportional–integral–derivative (PID) controllers are used to control the supply current to AMBs. Displacements and currents are generated using the finite element method of the rotor-AMB numerical model. These responses have been used in the identification algorithm for the estimation of the AMB displacement and current stiffness as well as of residual unbalances, concurrently. The algorithm with the proposed reduction scheme has shown an excellent estimation agreement in the presence of noisy responses and bias errors in rotor model parameters.

This paper proposes a detection method of driver fatigue by use of electrocardial signals. First, lifting wavelet transform (LWT) was used to reduce signal noise and its effect was confirmed by applying it to the denoising of a white-noise-mixed Lorenz signal. Second, phase space reconstruction was conducted for extracting chaotic features of the measured electrocardial signals. The phase diagrams show fractal geometry features even under a strong noise background. Finally, Kolmogorov entropy, which is a factor reflecting the uncertainty in and the chaotic level of a nonlinear dynamic system, was used as an indicator of driver fatigue. The effectiveness of Kolmogorov entropy in the judgment of driver fatigue was confirmed by comparison with a semantic differential (SD) subjective evaluation experiment. It was demonstrated that Kolmogorov entropy has a strong relationship with driver fatigue. It decreases when fatigue occurs. Furthermore, the influences of delay time and sampling points on Kolmogorov entropy were investigated, since the two factors are important to the actual use of the proposed detection method. Delay time may have significant influence on fatigue determination, but sampling points are relatively inconsequential. This result indicates that real-time detection can be realized by selecting a reasonably small number of sampling points.

Inspired by fast model predictive control (MPC), a new nonlinear optimal command tracking technique is presented in this paper, which is named as “Tracking-oriented Model Predictive Static Programming (T-MPSP).” Like MPC, a model-based prediction-correction approach is adopted. However, the entire problem is converted to a very low-dimensional “static programming” problem from which the control history update is computed in closed-form. Moreover, the necessary sensitivity matrices (which are the backbone of the algorithm) are computed recursively. These two salient features make the computational process highly efficient, thereby making it suitable for implementation in real time. A trajectory tracking problem of a two-wheel differential drive mobile robot is presented to validate and demonstrate the proposed philosophy. The simulation studies are very close to realistic scenario by incorporating disturbance input, parameter uncertainty, feedback sensor noise, time delays, state constraints, and control constraints. The algorithm has been implemented on a real hardware and the experimental validation corroborates the simulation results.

It is shown that brushless direct current (DC) motors (BLDCMs), which have found many useful applications in motion control areas, display chaotic behaviors. To avoid undesirable inherent oscillations of such DC motors, a control strategy should be adopted in the applications. So, the control problem of applied chaotic power systems is taken into account in this paper. Some important aspects of the design and implementation are considered to reach a suitable controller for the applications. In this regard, it is assumed that the system is fluctuated by unknown uncertainties and environmental noises. Additionally, a part of the system dynamics is supposed to be unknown in advance and the effects of nonlinear input saturation are fully taken into account. Then, a one input nonsmooth adaptive sliding mode controller is realized to handle the aforementioned issues. The proposed controller does not require any knowledge about the bounds of the system uncertainties and external fluctuations as well as about the parameters of the input saturation. The finite time convergence and robustness of the driven control scheme are mathematically proved and numerically illustrated using matlab simulations for DC motors.

This paper focuses on the design of an observer-based backstepping controller (BC) for a nonlinear hydraulic differential cylinder system. The system is affected by some uncertainties including modeling errors, external disturbances, and measurement noise. An observer-based control approach is proposed to assure suitable tracking performance and to increase robustness against unknown inputs. The task to estimate system states as well as unknown inputs is performed by a linear proportional-integral-observer (PIO). Input–output linearization is used to linearize the nonlinear system model to be used for the PIO structure. On the other hand, BC is utilized based on nonlinear system model to construct the Lyapunov function and to design the control input simultaneously. Stability or negativeness of the derivative of every-step Lyapunov function is fulfilled. Structural improvement regarding the combination of BC and PIO is the main aim of this contribution. This is supported by a novel stability proof and new conditions for the whole control loop with integrated PIO. Furthermore, parameter selection of BC is elaborately considered by defining a performance/energy criterion. A complete robustness evaluation considering different levels of additional measurement noise, modeling errors, and external disturbances is presented for the first time in this contribution. Experimental results validate the advantages of proposed observer-based approach compared to PIO-based sliding mode control (PIO-SMC) and industrial standard P-controller.

This paper explains the control scheme that is to be used in the magnetic suspension mass comparator (MSMC), an instrument designed to directly compare mass artifacts in air to those in vacuum, at the United States National Institute of Standards and Technology. More specifically, the control system is used to apply a magnetic force between two chambers to magnetically suspend the mass artifacts, which allows for a direct comparison (i.e., a calibration) between the mass held in air and a mass held in vacuum. Previous control efforts that have been demonstrated on a proof-of-concept (POC) of this system utilized proportional-integral-derivative (PID)-based control with measurements of the magnetic field as the control signal. Here, we implement state-feedback control using a laser interferometric displacement measurement with a noise floor of approximately 5 nm (root-mean-square). One of the unique features and main challenges in this system is that, in order to achieve the necessary accuracy (relative uncertainty of 20 × 10 −9 in the MSMC), the magnetic suspension must not impose appreciable lateral forces or moments. Therefore, in this design, a single magnetic actuator is used to generate a suspension force in the vertical direction, while gravity and the symmetry of the magnetic field provide the lateral restoring forces. The combined optical measurement and state-feedback control strategy presented here demonstrate an improvement over the previously reported results with magnetic field measurements and a PID-based control scheme.

When a parallel-plate electrostatic actuator (ESA) is driven by a voltage source, pull-in instability limits the range of displacement to one-third of the gap between plates. In this paper, a nonlinear active disturbance rejection controller (NADRC) is originally developed on the ESA. Our control objectives are stabilizing and increasing the displacement of an ESA to 99.99% of its full gap. Most of the reported controllers in literature are based on linearized models of the ESAs and depend on detailed model information of them. However, the ESA is inherently nonlinear and has model uncertainties due to the imperfections of microfabrication and packaging. The NADRC consists of a nonlinear extended state observer (NESO) and a feedback controller. The NESO is used to estimate system states and unknown nonlinear dynamics for the ESA. Therefore, it does not require accurate model. We simulate the NADRC on a nonlinear ESA in the presences of external disturbance, system uncertainties, and noise. The simulation results verify the effectiveness of the controller by successfully extending the travel range of ESA beyond pull-in point. They also demonstrate that the controller is robust against both disturbance and parameter variations, and has low sensitivity to measurement noise. Furthermore, the stability for the control system with NADRC is theoretically proved.

This paper deals with the distributed fault detection and isolation problem of uncertain, nonlinear large-scale systems. The proposed method targets applications where the computation requirements of a full-order failure-sensitive filter would be prohibitively demanding. The original process is subdivided into low-order interconnected subsystems with, possibly, overlapping states. A network of diagnostic units is deployed to monitor, in a distributed manner, the low-order subsystems. Each diagnostic unit has access to a local and noisy measurement of its assigned subsystem's state, and to processed statistical information from its neighboring nodes. The diagnostic algorithm outputs a filtered estimate of the system's state and a measure of statistical confidence for every fault mode. The layout of the distributed failure-sensitive filter achieves significant overall complexity reduction and design flexibility in both the computational and communication requirements of the monitoring network. Simulation results demonstrate the efficiency of the proposed approach.

Many industrial and laboratory applications which make use of electric machines require noninterruption operation, even in the presence of faults, such as power generation and electric vehicles. Under fault scenarios, the performance of the system is expected to degrade and control techniques may be helpful to overcome this issue. Within this context, phase faults are obviously undesired, as may lead the machine to stop operating. Switched reluctance machines (SRM), due to its inherit characteristics, are naturally tolerant to phase faults, despite the loss of performance. Most of the techniques used to improve the performance of SRMs in fault situations are related to the switching feed converter. Regarding this issue, instead of presenting an alternative converter topology, this work alternatively proposes a control approach which significantly reduces the phase faults effects on the speed of the motor. Furthermore, the high-frequency noise is attenuated when compared to the classical proportional–integral (PI) controller, commonly applied to control such sort of motors. The proposed SRM-adaptive feedforward control (AFC) controller is able to recover the speed of operation faster than a classical approach, when a feedforward action is not taken into account.

The problem of designing robust and noise-insensitive proportional–integral (PI) controllers for pressure-sensor-based combustion-timing control was studied through simulation. Different primary reference fuels (PRF) and operating conditions were studied. The simulations were done using a physics-based, control-oriented model with an empirical ignition-delay correlation. It was found that the controllable region in between the zero-gain region for early injection timings and the misfire region for late injection timings is strongly PRF dependent. As a result, it was necessary to adjust intake temperature to compensate for the difference in fuel reactivity prior to the controller design. With adjusted intake temperature, PRF-dependent negative-temperature coefficient (NTC) behavior gave different system characteristics for the different fuels. The PI controller design was accomplished by solving the optimization problem of maximizing disturbance rejection and tracking performance subject to constraints on robustness and measurement-noise sensitivity. Optimal controller gains were found to be limited by the high system gain at late combustion timings and high-load conditions; furthermore, the measurement-noise sensitivity was found to be higher at the low-load operating points where the ignition delay is more sensitive to variations in load and intake conditions. The controller-gain restrictions were found to vary for the different PRFs; the optimal gains for higher PRFs were lower due to a higher system gain, whereas the measurement-noise sensitivity was found to be higher for lower PRFs.

This paper presents a novel filter with low computational demand to address the problem of orientation estimation of a robotic platform. This is conventionally addressed by extended Kalman filtering (EKF) of measurements from a sensor suit which mainly includes accelerometers, gyroscopes, and a digital compass. Low cost robotic platforms demand simpler and computationally more efficient methods to address this filtering problem. Hence, nonlinear observers with constant gains have emerged to assume this role. The nonlinear complementary filter (NCF) is a popular choice in this domain which does not require covariance matrix propagation and associated computational overhead in its filtering algorithm. However, the gain tuning procedure of the complementary filter is not optimal, where it is often hand picked by trial and error. This process is counter intuitive to system noise based tuning capability offered by a stochastic filter like the Kalman filter. This paper proposes the right invariant formulation of the complementary filter, which preserves Kalman like system noise based gain tuning capability for the filter. The resulting filter exhibits efficient operation in elementary embedded hardware, intuitive system noise based gain tuning capability and accurate attitude estimation. The performance of the filter is validated using numerical simulations and by experimentally implementing the filter on an ARDrone 2.0 micro aerial vehicle (MAV) platform.

This paper demonstrates that the Coulomb friction, the most difficult part of friction to be compensated because of its discontinuity with respect to the velocity, can be precisely compensated without either its mathematical model or a velocity measurement, as commonly required in the literature. Instead, the necessary information needed in the friction compensation is obtained in real time from an implicit extended observer in the context of a common proportional-derivative motion control system, using the proposed linear reference compensation scheme. The robustness of this particular observer design to the time-delay uncertainty resulting from the model reduction is thoroughly investigated, which illustrates the extent to which a high bandwidth can be employed to achieve the favorable dynamic performance such that the limitation on the bandwidth of the original extended state observer (ESO) can be effectively eliminated. Finally, numerical examples are provided to validate the proposed method.

In this paper, the problem of output control for linear uncertain systems with external perturbations is studied. First, it is assumed that the output available for measurement is only the higher-order derivative of the state variable, instead of the state variable itself (for example, the acceleration for a second-order plant), and the measurement is also corrupted by noise. Then, via series of integration, an identification algorithm is proposed to identify all unknown parameters of the model and all unknown initial conditions of the state vector. Finally, two control algorithms are developed, adaptive and robust; both provide boundedness of trajectories of the system. The efficiency of the obtained solutions is demonstrated by numerical simulation.

A method to estimate ground reaction forces (GRFs) in a robot/prosthesis system is presented. The system includes a robot that emulates human hip and thigh motion, along with a powered (active) transfemoral prosthetic leg. We design a continuous-time extended Kalman filter (EKF) and a continuous-time unscented Kalman filter (UKF) to estimate not only the states of the robot/prosthesis system but also the GRFs that act on the foot. It is proven using stochastic Lyapunov functions that the estimation error of the EKF is exponentially bounded if the initial estimation errors and the disturbances are sufficiently small. The performance of the estimators in normal walk, fast walk, and slow walk is studied, when we use four sensors (hip displacement, thigh, knee, and ankle angles), three sensors (thigh, knee, and ankle angles), and two sensors (knee and ankle angles). Simulation results show that when using four sensors, the average root-mean-square (RMS) estimation error of the EKF is 0.0020 rad for the joint angles and 11.85 N for the GRFs. The respective numbers for the UKF are 0.0016 rad and 7.98 N, which are 20% and 33% lower than those of the EKF.