Vaclav Smidl

Advantages of Square-Root Extended Kalman Filter for Sensorless Control of AC Drives

This paper is concerned with a fixed-point implementation of the extended Kalman filter (EKF) for applications in sensorless control of ac motor drives. The sensitivity of the EKF to round-off errors is well known, and numerically advantageous implementations based on the square-root decomposition of covariance matrices have been developed to address this issue. However, these techniques have not been applied in the EKF-based sensorless control of ac drives yet. Specific properties of the fixed-point implementation of the EKF for a permanent-magnet synchronous motor (PMSM) drive are presented in this paper, and suitability of various square-root algorithms for this case is discussed. Three square-root algorithms-Bierman-Thorton, Carlson-Schmidt-Givens, and Carlson-Schmidt-Householder-were implemented, and their performances are compared to that of the standard implementation based on full covariance matrices. Results of both simulation studies and experimental tests performed on a developed sensorless PMSM drive prototype of rated power of 10.7 kW are presented. It was confirmed that the square-root algorithms improve the behavior of the sensorless control in critical operating conditions such as low speeds and speed reversal. In particular, the Carlson-Schmidt-Givens algorithm was found to be well suited for the considered drive.

Marginalized adaptive particle filtering for nonlinear models with unknown time-varying noise parameters

Knowledge of the noise distribution is typically crucial for the state estimation of general state-space models. However, properties of the noise process are often unknown in the majority of practical applications. The distribution of the noise may also be non-stationary or state dependent and that prevents the use of off-line tuning methods. For linear Gaussian models, Adaptive Kalman filters (AKF) estimate unknown parameters in the noise distributions jointly with the state. For nonlinear models, we provide a Bayesian solution for the estimation of the noise distributions in the exponential family, leading to a marginalized adaptive particle filter (MAPF) where the noise parameters are updated using finite dimensional sufficient statistics for each particle. The time evolution model for the noise parameters is defined implicitly as a Kullback-Leibler norm constraint on the time variability, leading to an exponential forgetting mechanism operating on the sufficient statistics. Many existing methods are based on the standard approach of augmenting the state with the unknown variables and attempting to solve the resulting filtering problem. The MAPF is significantly more computationally efficient than a comparable particle filter that runs on the full augmented state. Further, the MAPF can handle sensor and actuator offsets as unknown means in the noise distributions, avoiding the standard approach of augmenting the state with such offsets. We illustrate the MAPF on first a standard example, and then on a tire radius estimation problem on real data.

Marginalized particle filters for Bayesian estimation of Gaussian noise parameters

The particle filter provides a general solution to the nonlinear filtering problem with arbitrarily accuracy. However, the curse of dimensionality prevents its application in cases where the state dimensionality is high. Further, estimation of stationary parameters is a known challenge in a particle filter framework. We suggest a marginalization approach for the case of unknown noise distribution parameters that avoid both aforementioned problem. First, the standard approach of augmenting the state vector with sensor offsets and scale factors is avoided, so the state dimension is not increased. Second, the mean and covariance of both process and measurement noises are represented with parametric distributions, whose statistics are updated adaptively and analytically using the concept of conjugate prior distributions. The resulting marginalized particle filter is applied to and illustrated with a standard example from literature.

Reduced-order square-root EKF for sensorless control of PMSM drives

Performance of square-root extended Kalman filter (EKF) based on reduced order models for sensorless control of permanent magnet synchronous motor (PMSM) drives is studied. The reduced order model of PMSM has two-dimensional state vector comprising of: (i) electrical rotor speed, and (ii) electrical rotor position. These state quantities are estimated by the EKF without either speed or position sensor on the motor shaft. The reduction of the model order results in dramatic speed-up of calculation of the estimator which takes only a few tens of microseconds on a conventional fixed-point digital signal processor. Accuracy of the estimator is improved using square-root representation of the covariance matrix. Due to its low computational requirements, the proposed square-root EKF estimator is eligible for sophisticated diagnostics as well for sensorless control of PMSM drive in a wide range of industrial applications. Presented theoretical conclusions are verified by both simulations and experiments carried out on developed PMSM drive prototype of rated power of 10.7kW.

Improved Stability of DC Catenary Fed Traction Drives Using Two-Stage Predictive Control

Control of the main propulsion drive of a traction vehicle must secure excellent drive dynamics, but it also has to consider properties of the dc catenary. Specifically, the catenary voltage is subject to short circuits, fast changes, harmonics, and other disturbances that can vary in a wide range. Therefore, the drive is equipped by the catenary input LC filter. The filter is almost undamped by design in order to achieve maximum efficiency, and the control strategy needs to secure active damping of the filter to guarantee stability of the drive. Existing solutions for active damping usually introduce some drawback in dynamic properties of the drive. In this paper, we study the use of two-stage predictive control. Damping of the filter will be solved on a long horizon using a linear controller. Dynamic properties of the drive will be guaranteed by optimization on a short horizon using the finite control set model predictive control (FCS-MPC). These two approaches can be elegantly combined via approximate dynamic programming. The resulting algorithm can be interpreted as a standard FCS-MPC with a model-based designed cost function. Performance of the resulting controller was verified in simulations on a prototype of a main permanent-magnet synchronous motor drive of a tram and experimentally on a developed laboratory prototype of 10.7 kW.

Kalman filters unifying model-based and HF injection-based sensorless control of PMSM drives

Methods of sensorless control of PMSM drives are commonly divided into model-based and high-frequency injection based approaches. Each of these approaches uses a different algorithm for estimation of the rotor position and speed. Typically a Kalman filter is used for the model-based approach and phase-locked loop (PLL) for the hf injection based approach. In this paper, we show that the PLL is a steady state solution of the Kalman filter for a special state space model. Since this model has a commonly used state equations, we can easily combine the observation equations from the model-based approach with those from the hf injections. Several possibilities of combination are described and tested in the paper.We illustrate properties of these algorithms on experimental data in sensored mode. Sensorless control strategy based on the presented models is demonstrated on a laboratory prototype of surface mounted permanent magnet synchronous motor (PMSM) drive of rated power of 10.7kW.

Model-based extraction of input and organ functions in dynamic scintigraphic imaging

Image-based definition of input function (IF) and organ function is a prerequisite for kinetic analysis of dynamic scintigraphy or positron emission tomography. This task is typically done manually by a human operator and suffers from low accuracy and reproducibility. We propose a probabilistic model based on physiological assumption that time–activity curves (TACs) arise as a convolution of an IF and tissue-specific kernels. The model is solved via the Variational Bayes estimation procedure and provides estimates of the IF, tissue-specific TACs and their related spatial distributions (images) as its results. The algorithm was tested with data of dynamic renal scintigraphy. The method was applied to the problem of differential renal function estimation and the IF estimation and the results are compared with competing techniques on data-sets with 99 and 19 patients. The MATLAB implementation of the algorithm is available for download.

Resolver motivated sensorless rotor position estimation of wound rotor synchronous motors with Kalman filter

This paper presents a novel estimation approach to sensorless control of wound rotor synchronous motor drives. The proposed rotor position estimation strategy is motivated by principle function of a resolver and utilizes design similarity between the controlled motor and the resolver based rotor position sensor. The rotor circuit is fed by controlled three-phase bridge rectifier which produces an ac component of frequency of 300Hz in the rotor excitation (flux) current. This ac component of rotor excitation current can be understood like an injection signal. Its response on the stator is evaluated by simplified Kalman filter which estimates the rotor position. This paper describes physical principle and functionality of the proposed sensorless rotor position estimation technique and verifies the theoretical foundations by simulation and experimental results made on developed drive prototype of rated power of 10kW.

FPGA implementation of marginalized particle filter for sensorless control of PMSM drives

Marginalized particle filter is a stochastic filter combining Kalman filters with particle filters. It decomposes the model into linear and nonlinear part and applies the Kalman filter for the former and the particle filter for the latter. In effect, this allows to represent accurately the inherent non-Gaussianity and nonlinearity of the model. This allows estimation of the rotor position of the PMSM drive in the full speed range, including the standstill. The main disadvantage is its high computational cost. In this paper, we present an implementation of the marginalized particle filter in the field programmable logic array (FPGA). The parallel nature of the MPF algorithm allows to use pipelining which yields speedup in the order of magnitude in comparison to the DSP implementation. The sensorless control of the drive is implemented on a board with both DSP and FPGA, where the drive control runs on the DSP and the MPF estimator in the FPGA. Execution time of the estimator is thus negligible in the execution time of the sensorless control. Performance of the resulting sensorless control algorithm is evaluated on a developed drive prototype of rated power of 10.7kW.

Distributed Bayesian Decision-Making for Urban Traffic Control

Bayesian approach to decision-making is successfully applied in control theory for design of control strategy. The approach is based on the assumption that only one decision-maker is an active part of the system. This assumption was recently relaxed yielding distributed Bayesian decision-making theory. This extension is useful for large distributed systems which intrinsically contains a lot of uncertainty. In this paper, we apply the theory to distributed control of one example of such a system, the surface traffic network in dense urban areas