Enhancing performance of generalized minimum variance control via dynamic data reconciliation

The design, tuning, and implementation of controllers are crucial for the solutions to control problems. Generalized minimum variance control (GMVC) has attractive properties and it is widely used for controller performance enhancement. The measured signals of process output variables, which are used as feedback signals, are generally subject to measurement noise. However, the GMVC theory assumes the feedback signals are the process outputs, which rarely consider the unavoidable measurement noise. By additionally considering the measurement noise, the control performance of GMVC with the measurement noise is analyzed in this paper. The dynamic data reconciliation (DDR) method, which uses the information of both the process model and the measurement data to reconcile the measured signals, is introduced. It is combined with GMVC to reduce the effect of the measurement noise on the results of GMVC. The effectiveness of GMVC combined with DDR is illustrated in two case studies, where the proposed method is compared with the original GMVC and the GMVC with the conventional digital filter. The results in both SISO and MIMO control systems show that the proposed GMVC combined with DDR can reduce the effect of the measurement noise and achieve better control performance.     

Statistical information based two-layer model predictive control with dynamic economy and control performance for non-Gaussian stochastic process

In this paper, a two-layer model predictive control (MPC) hierarchical architecture of dynamic economic optimization (DEO) and reference tracking (RT) is proposed for non-Gaussian stochastic process in the framework of statistical information. In the upper layer, with state feedback and dynamic economic information, the economically optimal trajectories are estimated by entropy and mean based dynamic economic MPC, which uses the nonlinear dynamic model instead of the steady-state model. These estimated optimal trajectories from the upper layer are then employed as the reference trajectories of the lower layer control system. A survival information potential based MPC algorithm is used to maintain the controlled variables at their reference trajectories in the nonlinear system with non-Gaussian disturbances. The stability condition of closed-loop system dynamics is proved using the statistical linearization method. Finally, a numerical example and a continuous stirred-tank reactor are used to illustrate the merits of the proposed economic optimization and control method.     

Mixture quantized error entropy for recursive least squares adaptive filtering

Error entropy is a well-known learning criterion in information theoretic learning (ITL), and it has been successfully applied in robust signal processing and machine learning. To date, many robust learning algorithms have been devised based on the minimum error entropy (MEE) criterion, and the Gaussian kernel function is always utilized as the default kernel function in these algorithms, which is not always the best option. To further improve learning performance, two concepts using a mixture of two Gaussian functions as kernel functions, called mixture error entropy and mixture quantized error entropy, are proposed in this paper. We further propose two new recursive least-squares algorithms based on mixture minimum error entropy (MMEE) and mixture quantized minimum error entropy (MQMEE) optimization criteria. The convergence analysis, steady-state mean-square performance, and computational complexity of the two proposed algorithms are investigated. In addition, the reason why the mixture mechanism (mixture correntropy and mixture error entropy) can improve the performance of adaptive filtering algorithms is explained. Simulation results show that the proposed new recursive least-squares algorithms outperform other RLS-type algorithms, and the practicality of the proposed algorithms is verified by the electro-encephalography application.     

Correntropy based model predictive controller with multi-constraints for robust path trajectory tracking of self-driving vehicle

Self-driving vehicles must be equipped with path tracking capability to enable automatic and accurate identification of the reference path. Model Predictive Controller (MPC) is an optimal control method that has received considerable attention for path tracking, attributed to its ability to handle control problems with multiple constraints. However, if the data acquired for determining the reference path is contaminated by non-Gaussian noise and outliers, the tracking performance of MPC would degrades significantly. To this end, Correntropy-based MPC (CMPC) is proposed in this paper to address the issue. Different from the conventional MPC model, the objective of CMPC is constructed using the robust metric Maximum Correntropy Criterion (MCC) to transform the optimization problem of MPC to a non-concave problem with multiple constraints, which is then solved by the Block Coordinate Update (BCU) framework. To find the solution efficiently, the linear inequality constraints of CMPC are relaxed as a penalty term. Furthermore, an iterative algorithm based on Fenchel Conjugate (FC) and the BCU framework is proposed to solve the relaxed optimization problem. It is shown that both objective sequential convergence and iterate sequence convergence are satisfied by the proposed algorithm. Simulation results generated by CarSim show that the proposed CMPC has better performance than conventional MPC in path tracking when noise and outliers exist.     

Robust augmented complex-valued normalized M-estimate subband adaptive filtering algorithm against colored non-circular inputs and impulsive noise

Recently, the augmented complex-valued normalized subband adaptive filtering (ACNSAF) algorithm has been proposed to process colored non-circular signals. However, its performance will deteriorate severely under impulsive noise interference. To overcome this issue, a robust augmented complex-valued normalized M-estimate subband adaptive filtering (ACNMSAF) algorithm is proposed, which is obtained by modifying the subband constraints of the ACNSAF algorithm using the complex-valued modified Huber (MH) function and is derived based on CR calculus and Lagrange multipliers. In order to improve both the convergence speed and steady-state accuracy of the fixed step size ACNMSAF algorithm, a variable step size (VSS) strategy based on the minimum mean squared deviation (MSD) criterion is devised, which allocates individual adaptive step size to each subband, fully exploiting the structural advantages of SAF and significantly improving the convergence performance of the ACNMSAF algorithm as well as its tracking capability in non-stationary environment. Then, the stability, transient and steady-state MSD performance of the ACNMSAF algorithm in the presence of colored non-circular inputs and impulsive noise are analyzed, and the stability conditions, transient and steady-state MSD formulas are also derived. Computer simulations in impulsive noise environments verify the accuracy of theoretical analysis results and the effectiveness of the proposed algorithms compared to other existing complex-valued adaptive algorithms.     

High frequency measurement noise rejection based on disturbance observer

A new feedback controller architecture based on disturbance observer (DOB) is proposed to deal with high-frequency measurement noise for high accuracy performance. Compared with the classical DOB-based control system the proposed control structure adds another controller to compensate the feedback of system output. Thus, these influences of both high-frequency measurement noise and low-frequency external disturbance on the system output could be eliminated simultaneously. Meanwhile, the new control system architecture can potentially overcome the conflict between performance and robustness in the traditional feedback framework. A numerical example is included at the end of this paper to illustrate the effectiveness.     

Pulse nonstationary processes generated by dynamic systems with random structure

Dynamic system with a random structure described by a set of the first-order stochastic differential equations (SDE) is used as a generating model of nonstationary pulse stochastic processes. Physically the system presents the combination of the so-called partial filters related to the isolated states of the considered process, switched by a Poissonian point process and excited by a vector delta-correlated stream of impulses with the randomly distributed energy. The filters’ outputs are components of the vector Markov continuous-jump process with statistics depending on the partial SDEs operators, intensity of switching process and distributions of the exciting impulses’ energies. The approach proposed was used as a simulation model of the Middleton “Class-A “generally non-Gaussian noise. The results demonstrate that the main features of statistical characteristics of the noise envelope are reproduced rather well with the help of a bistate system with random structure.     

Tracking control of a piezo-hydraulic actuator using input–output linearization and a Cascaded Extended Kalman Filter structure

In this paper, an innovative piezo-hydraulic actuator (PHA) is considered that is intended to realize a fully variable valve control in camless combustion engines. A nonlinear model of the hydraulic system part is presented along with linear models of the remaining system parts. Accurate tracking of desired valve trajectories as well as soft landing despite disturbance forces and measurement noise is achieved using a combined control strategy. It consists of an input–output linearization of the nonlinear part as well as feedforward and linear quadratic integral (LQI) feedback control of the linear system part. Given measurements of the valve spool and engine valve positions, a Cascaded Extended Kalman Filter (CEKF) structure provides estimates for the immeasurable states. Simulation results confirm the effectiveness of the proposed approach.     

State estimation for jump markov nonlinear systems of unknown measurement data covariance

For state estimation of high accuracy, prior knowledge of measurement noise is necessary. In this paper, a method for solving the joint state estimation problem of jump Markov nonlinear systems (JMNSs) without knowing the measurement noise covariance is developed. By using the Inverse-Gamma distribution to describe the dynamics of measurement noise covariance, the joint conditional posterior distribution of the state variable and measurement noise covariance is approximated by a product of separable variational Bayesian (VB) marginals. In the newly constructed approach, the interacting multiple model (IMM) algorithm, as well as the particle-based approximation strategy, is employed to handle the computationally intractable problem and the nonlinear characteristics of systems, respectively. An interesting feature of the proposed method is that the distribution of states is spanned by a set of particles with weights, while the counterpart of measurement noise covariance is obtained analytically. Moreover, the number of particles is fixed under each mode, indicating a reasonable computational cost. Simulation results based on a numerical example and a tunnel diode circuit (TDC) system are presented to demonstrate that the proposed method can estimate the measurement noise covariance well and provide satisfied state estimation when the statistics of the measurement are unavailable.     

Design of PID controller based on a self-adaptive state-space predictive functional control using extremal optimization method

In proportional-integral-derivative (PID) controller design, obtaining high stability and desired closed-loop response are of great importance for system engineers. Most existing methodologies, which have validated their excellent control performance on the accurate mathematical model, face significant difficulties in the unavoidable model mismatches and disturbance. To overcome these drawbacks, this paper proposes a self-adaptive state-space predictive functional control (APFC) based on extremal optimization method to design PID controller called EO-APFC-PID, wherein, the self-adaptive means, i.e., a forgetting factor recursive least squares (FFRLS) mechanism is embedded into state-space predictive functional control (PFC), and the proposed EO is exploited to alleviate the challenging problem that the elements in weighting factors of APFC technique are lacking analytical knowledge. The performance of the proposed EO-APFC-PID control scheme is demonstrated and compared with one classic PID tuning method and two state-of-the-art control strategies on the chamber pressure control for a coke furnace. The experimental results fully illustrate that the proposed method is more effective and efficient than other existing control strategies for achieving a desired behavior on the most test cases considered in this paper in terms of set point tracking, input disturbance rejection and output disturbance rejection.     

Identification of Gaussian process with switching noise mode and missing data

In traditional system identification methods, it is often assumed that the output data are corrupted by Gaussian white noise which is independent and identically distributed (i.i.d.). However, this assumption may lead to poor robustness since the noise characteristic often varies throughout the sampling process. In this work, output measurements affected by switching Gaussian noise are considered. In addition, a Markov chain model is utilized to describe the multi-mode behavior of the noises. Meanwhile, the collected data are usually incomplete in practice. Taking these circumstances into account, a new algorithm for Gaussian process regression (GPR) with switching noise mode and missing data is introduced. The parameters of the model are estimated by expectation maximization (EM) algorithm via conjugate gradient (CG) method. Two numerical examples along with a continuous stirred tank reactor simulation are employed to verify the effectiveness of the proposed algorithm. The superior performance is demonstrated by comparing the proposed algorithm with other existing relevant methods.     

Maximum correntropy criterion variational Bayesian adaptive Kalman filter based on strong tracking with unknown noise covariances

The performance of the current state estimation will degrade in the existence of slow-varying noise statistics. To solve the aforementioned issues, an improved strong tracking maximum correntropy criterion variational-Bayesian adaptive Kalman filter is presented in this paper. First of all, the inverse-Wishart distribution, as the conjugate-prior, is adopted to model the unknown and time-varying measurement and process noise covariances, then the noise covariances and system state are estimated via the variational Bayesian method. Secondly, the multiple fading-factors are obtained and evaluated to modify the prediction error covariance matrix to address the problems associated with inaccurate error estimation. Finally, the maximum correntropy criterion is employed to correct the filtering gain, which improves the filtering performance of the proposed algorithm. Simulation results show that the proposed filter exhibits better accuracy and convergence performance compared to other existing algorithms.     

Kernel recursive generalized mixed norm algorithm

This work studies the problem of kernel adaptive filtering (KAF) for nonlinear signal processing under non-Gaussian noise environments. A new KAF algorithm, called kernel recursive generalized mixed norm (KRGMN), is derived by minimizing the generalized mixed norm (GMN) cost instead of the well-known mean square error (MSE). A single error norm such as l_p error norm can be used as a cost function in KAF to deal with non-Gaussian noises but it may exhibit slow convergence speed and poor misadjustments in some situations. To improve the convergence performance, the GMN cost is formed as a convex mixture of l_p and l_q norms to increase the convergence rate and substantially reduce the steady-state errors. The proposed KRGMN algorithm can solve efficiently the problems such as nonlinear channel equalization and system identification in non-Gaussian noises. Simulation results confirm the desirable performance of the new algorithm.     

Markov chain Monte Carlo based adaptive Rauch–Tung–Striebel smoother

For linear state space model, the covariance matrix setting errors of process and measurement noise deteriorate the estimation performance of Rauch–Tung–Striebel (RTS) smoother. To address this problem, the Markov Chain Monte Carlo is utilized to sample the state vector and noise covariance matrices simultaneously in this study. The Gibbs sampler is adopted and the corresponding adaptive RTS smoother is designed. Simulation results confirm the performance of proposed smoother.     

Bivariate grid-connection speed control of hydraulic wind turbines

The requirement for An electrical grid-connected wind turbine is that the synchronous generator speed is stable within a required speed range for the electrical grid. In this paper, a hydraulic wind turbine (HWT) system is considered, and the working principle and working conditions of the HWT are introduced. A novel speed control method is proposed in this paper, using both a proportional flow control valve and a variable displacement motor, which are adjusted in combination to control the speed of the HWT. By establishing a state space model of the HWT and solving the nonlinear system with a feedback linearization method, a bivariate tracking controller is constructed to realize accurate speed control under fluctuating wind speed and the load disturbance conditions. The effectiveness of the control method is verified by simulation, but experimental results highlight problems with the method. The theoretical controller is simplified to reduce sensitivity to measurement noise and modeling error. The control effect has been improved to some extent, but it is limited. Based on these results, combined with the sliding mode variable structure control method and the feedback linearization method to solve the problem of measurement noise and modeling error, and the effectiveness of the control law is finally verified experimentally. It lays a theoretical foundation for the practical application of HWT.     

General proportional integral observer (GPIO) - based disturbance compensation for minimum variance time synchronization

Precise time synchronization is an enabling technology for mission-critical time-sensitive Industrial Internet of Things (IIoT). However, the crystal oscillator clock which is widely used in IIoT may suffer from periodic disturbances caused by repetitive motion or periodic vibration. To improve the time synchronization of distributed nodes subject to periodic disturbances, this paper proposes a novel disturbance rejection framework, General-Proportional-Integral-Observer-based Disturbance Compensation (GPIO-DC), with the proof of stability, and combined with a 2-freedom control design strategy to optimize both the disturbance rejection and clock tracking performance. And the GPIO’s unique feature of blocking zeros are fully exploited to reject the periodic disturbance at its frequencies and a zero-pole optimal design algorithm is given. With the disturbance being compensated, a disturbance-free minimum variance time synchronization protocol for a complex network is developed and optimized by using Linear Matrix Inequality (LMI) to minimize the variance of networked synchronization errors. The performance of the proposed method is devalued by intensive simulation. Comparing with recent relevant research, the proposed method achieves a better performance in disturbance rejection and minimum variance.     

Precise motion control of an electromagnetic valve actuator with adaptive robust compensation of combustion force

Electromagnetic valve actuators (EMVA) can achieve independent fully flexible control of valve and thus reduce the fuel consumption significantly. In order to improve the performance of the engine, precise motion control of EMVA is requird. Most of the researches published so far focus on the compensations of nonlinearities such as frictions and parameters variations. However, the influence of the varying combustion force on the exhaust valve needs to be considered. An adaptive robust control (ARC) method was developed in this paper to compensate the major nonlinearities, including parameters variations and combustion force variations. The parameters of EMVA system were tuned online via certain adaptation law. Combustion force variations were compensated by robust control law. In addition, current saturation was caused by large combustion force, which was then solved by proposing an anti-windup compensation strategy. The effectiveness of the proposed ARC method was verified by simulations and experiments, and the results show that ARC method can adapt to parameters variations and large changes in combustion force.     

Noise variance measurement with presence of strong sine burst interference

A novel method of noise variance measurement in the presence of strong sine burst interference with unknown parameters is presented. The measurement system is based on the Adaptive Sine Pulse Shortener (ASPS) which shorts each sine pulse from which the interfering burst is composed. After this a conventional noise variance measurement method is applied. A measurement accuracy is satisfactory when the interfering signal is strong and the number of periods of interfering sine-wave in each sine pulse is great. While a practical implementation of the proposed procedure is not simple in hardware, the microprocessor implementation is quite realizable.