Real-Time Optimal State Estimation of Multi-DOF Industrial Systems Using FIR Filtering

Zhao, Shunyi,Shmaliy, Yuriy S.,Ahn, Choon Ki,Shi, Peng IEEE 2017 IEEE TRANSACTIONS ON INDUSTRIAL INFORMATICS - Vol.13 No.3

<P>Industrial processes are often organized using mechanical systems with multiple degrees-of-freedom (DOF). For real-time operation of such systems in noise environments, fast, optimal, and robust estimators are required. In this paper, information gathering about multi-DOF system states is provided using the optimal finite impulse response (OFIR) filter. To use this filter in real time, a fast iterative algorithm is developed with a pseudocode available for immediate use. Although the iterative algorithm utilizes Kalman recursions, it is more robust against uncertainties and model errors owing to the transversal structure. We use this algorithm to estimate state in the 1-DOF torsion system and the 3-DOF helicopter system.</P>

Fusion Kalman/UFIR Filter for State Estimation With Uncertain Parameters and Noise Statistics

Zhao, Shunyi,Shmaliy, Yuriy S.,Shi, Peng,Ahn, Choon Ki Institute of Electrical and Electronics Engineers 2017 IEEE transactions on industrial electronics Vol.64 No.4

<P>In this paper, we fuse the Kalman filter (KF) that is optimal but not robust with the unbiased finite-impulse response (UFIR) filter which is more robust than KF but not optimal. The fusion filter employs the KF and UFIR filter as subfilters and produces smaller errors under the industrial conditions. In order to provide the best fusion effect, the operation point where UFIR meets Kalman is determined by applying probabilistic weights to each subfilter. Extensive simulations of the three degree of freedom (3-DOF) hover system have shown that the fusion filter output tends to range close to that by the best subfilter. Experimental verification provided for a 1-DOF torsion system has confirmed validity of simulation.</P>

Adaptive-Horizon Iterative UFIR Filtering Algorithm With Applications

Zhao, Shunyi,Shmaliy, Yuriy S.,Ahn, Choon Ki,Liu, Fei Institute of Electrical and Electronics Engineers 2018 IEEE transactions on industrial electronics Vol.65 No.8

<P>The unbiased finite impulse response (UFIR) filter has strong engineering features for industrial applications, because it does not require the noise statistics and initial values. This filter minimizes the mean square error (MSE) on the optimal horizon of <TEX>$N_\mathrm{opt}$</TEX> points, and the determination of <TEX>$N_\mathrm{opt}$</TEX> is an important issue. In this paper, a new strategy is proposed to adaptively estimate <TEX>$N_\mathrm{opt}$</TEX> in real time. A concept of the maximum allowed horizon is introduced, referring to the fact that the current iteration with large horizon contains data from the previous iterations with small horizons. That allows selection of the target horizon in a single cycle of iterations and a design of the adaptive-horizon UFIR (AUFIR) filter. The proposed AUFIR filter is tested by a rotary pendulum system and a 3-degree-of-freedom (DOF) helicopter system. Higher accuracy and robustness of the AUFIR filter are demonstrated in a comparison with the Kalman filter (KF), adaptive KF, and UFIR filter.</P>

Unbiased Finite Impluse Response Filtering: An Iterative Alternative to Kalman Filtering Ignoring Noise and Initial Conditions

Shmaliy, Yuriy S.,Zhao, Shunyi,Ahn, Choon Ki IEEE 2017 IEEE control systems magazine Vol.37 No.5

<P>If a system and its observation are both represented in state space with linear equations, the system noise and the measurement noise are white, Gaussian, and mutually uncorrelated, and the system and measurement noise statistics are known exactly; then, a Kalman filter (KF) [1] with the same order as the system provides optimal state estimates in a way that is simple and fast and uses little memory. Because such estimators are of interest for designers, numerous linear and nonlinear problems have been solved using the KF, and many articles about KF applications appear every year. However, the KF is an infinite impulse response (IIR) filter [2]. Therefore, the KF performance may be poor if operational conditions are far from ideal [3]. Researchers working in the field of statistical signal processing and control are aware of the numerous issues facing the use of the KF in practice: insufficient robustness against mismodeling [4] and temporary uncertainties [2], the strong effect of the initial values [1], and high vulnerability to errors in the noise statistics [5]-[7].</P>

A Revisit to Strictly Passive FIR Filtering

Ahn, Choon Ki,Zhao, Shunyi,Shmaliy, Yuriy S.,Sakthivel, R. IEEE 2018 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS PART 2 E Vol.65 No.4

<P>This brief revisits the strictly passive finite impulse response (FIR) filtering problem in discrete-time state space. An initial result on the strictly passive FIR filter was presented by Ahn in 2012, but was restricted to state-space models with a nonsingular system matrix, which limits the scope of application. In this brief, we propose a new design condition for the strictly passive FIR filter that does not impose any restriction on the system matrix in the linear matrix inequality form. Based on this condition, new results on its connection with finite-time <TEX>${H_\infty }$</TEX> FIR filtering are presented. An application example for an afterburning engine model with a singular system matrix verifies the proposed filter’s higher robustness than the existing strictly passive infinite impulse response filter against quantization and uncertainty.</P>

Bayesian Hybrid State Estimation for Unequal-length Batch Processes with Incomplete Observations

Guoli Ji,Yaozong Wang,Shunyi Zhao,Yunlong Liu,Kangkang Zhang,Bin Yao,Sun Zhou 제어·로봇·시스템학회 2017 International Journal of Control, Automation, and Vol.15 No.6

This paper investigates state estimation problem for batch processes with unequal-length batches as wellas incomplete observations. A Bayesian hybrid state estimation method is proposed based on two dimensional (2D)correlations of states. The states of equal-length segment of time are estimated according to both within-a-batchand batch-to-batch correlations, and the states of unequal-length segment are obtained according to the correlationswithin the batch. In this way, the batch process states can be achieved in both equal-length and unequal-lengthsituations, of which the latter one is a more general case. In order to approximate state distribution of nonlinearsystem and to deal with the problem of incomplete observations, particle filter (PF) is employed. The proposedmethod shows its superiority with a nonlinear system and a gas-phase reaction process. Compared to a typicalexisting method, the proposed method provides better estimation accuracy in the situation of equal-length batches,also it shows less sensitivity to incomplete observations.

Hankel-Norm Approach to Robust FIR Estimation of Dynamic Systems Under External Disturbances

Ahn, Choon Ki,Shmaliy, Yuriy S.,Zhao, Shunyi IEEE 2018 IEEE/ASME transactions on mechatronics Vol.23 No.4

<P>We propose and develop a new Hankel-norm approach to the robust receding horizon (RH) finite impulse response (FIR) filter design in discrete-time state space under intensive external disturbances. A new condition is developed for the RH Hankel-norm FIR filter (HNFF) design based on the linear matrix inequality and an equality constraint. The proposed RH HNFF ensures unwanted memory reduction and reduces the effect of memory on errors caused by past disturbances. Another condition is also examined to avoid using the equality constraint. The approach is tested and compared with existing filters based on a numerical example to verify its high robustness against unpredictable model changes for an F-404 turbofan engine system model. An experimental study on the one-degree-of-freedom torsion system is also provided to demonstrate its validity.</P>

A New Unbiased FIR Filter With Improved Robustness Based on Frobenius Norm With Exponential Weight

Ahn, Choon Ki,Shmaliy, Yuriy S.,Zhao, Shunyi IEEE 2018 IEEE transactions on circuits and systems. a publi Vol.65 No.4

<P>This brief proposes a new unbiased finite impulse response (FIR) filter with improved robustness for state-space models in continuous time. The FIR filter proposed in this brief is called the unbiased FIR filter based on the Frobenius norm and exponential weight (UFFFNE). A new integral cost function based on the Frobenius norm for the filter gain function with exponential weight is introduced to improve its robustness. It is shown that the UFFFNE design problem can be cast into the constrained minimum-energy optimal control problem. A new analytic expression for the gain function of the UFFFNE is also proposed. The higher robustness of the proposed UFFFNE is demonstrated through a comparison with the existing minimum variance unbiased FIR filter and the conventional Kalman-Bucy filter based on a numerical example.</P>

Continuous-Time Deadbeat <tex> $H_{2}$</tex> FIR Filter

Ahn, Choon Ki,Shmaliy, Yuriy S.,Zhao, Shunyi,Li, Hongyi IEEE 2017 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS PART 2 E Vol.64 No.8

<P>This brief proposes a new continuous-time state-space H-2 finite impulse response (FIR) filter with the embedded deadbeat property for linear systems undergoing external disturbances. The new filter is called the continuous-time deadbeat H-2 FIR filter (CTDH2FF). The proposed filter demonstrates H-2 performance under disturbances and the dead-beat property otherwise. The CTDH2FF can be implemented by solving two matrix differential equations for given boundary conditions. A new formula for the minimum H-2 norm of the CTDH2FF is also discussed. Numerical simulations show that the proposed filter has much better robustness against unexpected short-term model changes than the existing filters.</P>

Minimum Weighted Frobenius Norm Discrete-Time FIR Filter With Embedded Unbiasedness

You, Sung Hyun,Ahn, Choon Ki,Shmaliy, Yuriy S.,Zhao, Shunyi IEEE 2018 IEEE transactions on circuits and systems. a publi Vol.65 No.9

<P>In this brief, we propose a new receding horizon finite impulse response (FIR) filter that minimizes the weighted Frobenius norm with embedded unbiasedness in discrete-time state-space. The filter, called the discrete-time weighted Frobenius norm unbiased FIR (DTWFNUF) filter, belongs to a class of maximum likelihood estimators. The Frobenius norm is introduced and minimized as a performance criterion to the filter gain matrix. It is shown that the DTWFNUF filter design problem can be cast into the optimization problem with the equality constraint and the filter gain matrix obtained by the Lagrange multiplier method. Higher robustness of the proposed filter is demonstrated in a comparison with the Kalman filter and minimum variance unbiased FIR filter based on a numerical example of the F-404 gas turbine engine.</P>