kalman filter for motor control

International Journal of Adaptive Control and Signal Processing. The Kalman Filter is a special kind of observer that provides optimal filtering of process and measurement noises if the covariances of these noises are known. In the robotic world important is rapidity and precision as well. Control signal of the Unscented Kalman Filter-based control loop for the field-oriented induction motor model (a) when tracking a see-saw setpoint (b) when tracking of a sinusoidal setpoint, Figure 16. We predicted the location of a ball as it was kicked towards the robot in an effort to stop the ball. INTRODUCTION The indirect field oriented control method is widely used for in- duction motor drives. In this paper a Kalman filter is used for recursively estimating the states and model parameters. Rank regression in combination with a rank histogram filter in observation space produces better analyses than standard regression for cases with nonlinear forward operators and relatively large analysis error. (38) and Eq. The posterior statistics are calculated (approximated) using tractable functions of the propagated sigma-points and weights. 15 show that the control signal, which is applied to the decoupled field-oriented induction motor model, remains smooth. In (Karami et al. the subset algorithm of Rousseeuw and Leroy. Simply select your manager software from the list below and click on download. Electric Power Systems Research, Particle and Kalman filtering for state estimation and control of DC motors. 22. (27) consists of two linear subsystems, where the first one has as output the magnetic flux ψrd and the second has as output the rotation speed ω, i.e. Such a controller doesn’t need a sensor or encoder to measure the speed or position of the motor; it estimates the speed and position using the measured states in form of either current or voltage. The resultant estimator is given in the form of linkage with KF. The camera capture the image of line laser reflected in front of the wheelchair to detect any existing obstacle on the wheelchair’s pathway based on the line shape of reflected line laser. The Kalman filter (Kalman, 1960; Gelb, 1974; Grewal & Andrews, 2001) is often applied during dissolving state estimation of dynamical system. ISA Transactions, Particle Filtering for State Estimation in Nonlinear Industrial Systems, Particle and Kalman filtering for fault diagnosis in DC motors, Sigma-point Kalman Filters and Particle Filters for integrated navigation of unmanned aerial vehicles, On Unscented Kalman Filtering for state estimation of continuous-time nonlinear systems, Flatness-based vehicle steering control strategy with SDRE feedback gains tuned via a sensitivity approach, Intelligent control of induction servo motor drive via wavelet neural network. Manuscript content on this site is licensed under Creative Commons Licenses. With the field-oriented method, the dynamic behavior of the induction motor is rather similar to that of a separately excited DC motor (Rigatos 2009a). 2011) the Unscented Kalman Filter (UKF) has been compared to the Extended Kalman Filter for the state estimation of a three-phase induction motor. The filter starts from the initial mean m0 and covariance Pxx0. (, Delaleau et al. An equivalent definition of differentially flat systems is as follows: Definition: The system ẋ=f(x,u), x∈Rn, u∈Rm is differentially flat if there exist relations h:Rn×Rm→Rm, φ:(Rm)r→Rn and ψ:(Rm)r+1→Rm, such that y=h(x,u,u̇,⋯,u(r)), x=φ(y,ẏ,⋯,y(r−1),y(r)) and u=ψ(y,ẏ,⋯,y(r−1),y(r)). (1) is said to be differentially flat if there exists a collection of m functions y=(y1,⋯,ym) of the system variables and of their time-derivatives, i.e. The Kalman Filtering approaches examined in this paper have shown that it is possible to reduce the number of sensors involved in the control loops of electric motors and to implement efficient state estimation-based control. If ψrd(t) is not precisely measured using Hall sensors then it can be reconstructed using some kind of observer. Schematic diagram of the EKF loop, Figure 4. The Kalman filter keeps track of the estimated state of the system and the variance or uncertainty of the estimate. First, it is that the pseudo regression vector φ(t-1) instead of the true regression vector φ(t-1) is related to the filtered estimate of the state vector in a state space representation of ARMA model. The state distribution in UKF is approximated by a Gaussian random variable, which is represented using a minimal set of suitably chosen weighted sample points. For the improvement of the convergence rate, Fisher Information Matrix (FIM) is used as a measure of the estimation accuracy. The state distribution is represented again by a Gaussian Random Variable but is now specified using a minimal set of deterministically chosen weighted sample points. (35) and Eq. You want to estimate the position and velocity of a ground vehicle in the north and east directions. One important use of generating non-observable states is for estimating velocity. Since all state variables of the circuits describing the induction motor dynamics can be expressed as functions of y=(θ,ρ) and its derivatives it can be concluded that the induction motor is a differentially flat system. Thus the linearized version of the plant is obtained: Now, the Extended Kalman Filter (EKF) recursion is as follows: First the time update is considered: by x^(k) the estimation of the state vector at instant k is denoted. when fault occurs in the feedback system. Find out about Lean Library here, If you have access to journal via a society or associations, read the instructions below. The least quartile difference (LQD) regression estimator is highly robust, since it can resist up to almost 50% largely deviant data values without becoming extremely biased. The first key problem associated with EKF is that the estimator requires all the plant dynamics and noise processes are exactly known. (3) and Eq. In the outer loop position/speed control and flux control are implemented, providing the current setpoints isq and isd which become inputs to the inner voltage control loop. 1991), (Leonard 1985). The. The equations of the induction motor in the d−q reference frame, given by Eq. Register Jurnal Ilmiah Teknologi Sistem Informasi. Finally, flatness-based control for induction motors considers also a nested control loops scheme as depicted in Fig. 2010) the Unscented Kalman Filter is applied to state estimation for fault diagnosis of induction motors. (31), are now rewritten in the form of Eq. (17), according to the relation, where ψ=ψrd and ‖ψ‖=ψsα2+ψsb2. Introduction There is increasing demand for dynamical systems to become more realizable and more cost-effective. 1994), (Marino et al. Parameter x2 of the state vector of the field-oriented induction motor model in state estimation with use of the Extended Kalman Filter (a) when tracking a see-saw set-point (b) when tracking a sinusoidal setpoint, Figure 12. Further, this is used for modeling the control of movements of central nervous systems. The sample points progressively converge to the true mean and covariance of the Gaussian random variable (Rigatos 2009d), (Rigatos 2009e). Finally, state estimation-based control was developed for the complete (sixth-order) dynamical model of the induction motor using a nonlinear flatness-based controller and the state estimation provided by the Extended Kalman Filter. 1 is described by the set of equations. The extended Kalman filter is employed to identify the speed of an induction motor and rotor flux based on the measured quantities such as stator currents and DC link voltage. M.Tech, Signal Processing, Reva Institute of Technology, Scientist (Retd. The Unscented Kalman Filter has been proposed as a suitable approach for overcoming certain drawbacks of the Extended Kalman Filter, such as (i) the need to compute Jacobians and (ii) the cumulative linearization errors which are due to truncation of higher order terms in the associated Taylor series expansion of the motor's dynamical model. Kalman Filter T on y Lacey. Watch 0 Star 0 Fork 0 0 stars 0 forks Star Watch Code; Issues 0; Pull requests 0; Actions; Projects 0; Security; Insights; Dismiss Join GitHub today. 32 2.2 Kalman controller The Kalman filter is used for estimating or pr edicting the next stage of a system based on a moving average of measurements driven by white noise, which is completely unpredictable. The above mentioned subsystem is a model equivalent to that of a DC motor and thus after succeeding ψrd→ψrdref, one can also control the motor's speed ω, using control algorithms already applied to the control of DC motors. aiyou94 / Kalman-filter-for-motor-control. Conference: 2nd National conference on “Emerging Trends in Science and Technology” held in Sapthagiri College of Engineering, Bangalore. (, Dannehl & Fuchs 2006] Dannehl, J., Fuchs, F.W. (35) and Eq. To derive the dynamic model of an induction motor the three-phase variables are first transformed to two-phase ones. It can be shown that all state variables of the induction motor can be written as functions of the flat outputs and their derivatives. (39) to Eq. The performance of standard versus rank regression is compared for both linear and nonlinear forward operators (also known as observation operators) using a low-order model. (62), while the time update of the EKF is given by Eq. Next, the following nonlinear feedback control law is defined, The control signal in the coordinates system α−b is, Substituting Eq. Extended Kalman Filter Based Speed Sensorless PMSM Control with Load Reconstruction Dariusz Janiszewski Poznan University of Technology Poland 1. The estimation is done upon undisturbed input signals from overriding controller and disturbed The extended Kalman filter (EKF) is widely used for nonlinear filter problems. The rotor position and speed are estimated from the input voltage and current using the Extended Kalman Filter. 4 (van der Merwe et al. You can use the function KALMAN to design a steady-state Kalman filter. The results of this paper differ from the previous ones in that the regression vector (in a, Abstrak For the motor model of Eq. The system state was estimated by the Kalman filter so that the measurement and observation noise signal was inhibited thus resulting in the system performance improved. Usually the DC-motor model is considered to be linear by neglecting the effect of armature reaction or by assuming that the compensating windings remove this effect. (22) into Eq. This controller makes the system's output (angle θ of the motor) follow a given reference signal xd. with the following notations L: armature inductance, I: armature current, ke: motor electrical constant, R: armature resistance, V: input voltage, taken as control input, J: motor inertia, ω: rotor rotation speed, kd: mechanical dumping constant, Γd: disturbance torque. Lean Library can solve it. Abstract High performance robot control systems also call for velocity and acceleration information from the joints. 16. Steven J Schiff 1 and Tim Sauer 2 Author information ... in brain slices would be an interesting prelude to considering such wave control in in vivo applications such as in the motor (Hatsopoulos et al 2006) or visual (Xu et al 2007) systems. The time-varying Kalman filter is a generalization of the steady-state filter for time-varying systems or LTI systems with nonstationary noise covariance. The 1×2 Jacobian Jγ(x) is. (35) and Eq. As such, the equations for the Kalman filter fall into two groups: time update equations and measurement update equations. This site uses cookies. Moreover, the Extended Kalman Filter is proposed to estimate the state vector of the nonlinear electric motor using a limited number of sensors, and control of the induction motor is again implemented through feedback of the estimated state vector. Using this plan gives the following two features. It was primarily developed by the Hungarian engineer Rudolf Kalman, for whom the filter is named. The Kalman filter is widely used in present robotics such as guidance, navigation, and control of vehicles, particularly aircraft and spacecraft. It was primarily developed by the Hungarian engineer Rudolf Kalman, for whom the filter is named. 2). 2003] Akin, B., Orguner, U., Ersak, A. The control inputs vsd, vsq are connected to vsα, vsb of Eq. These sigma points are propagated through the true nonlinear system, thus generating the posterior sigma-point set, and the posterior statistics are calculated. This is essential for motion planning and controlling of field robotics, and also for trajectory optimization. Electric Power Systems Research, Implementation of Robust Wavelet-Neural-Network Sliding-Mode Control for Induction Servo Motor Drive, Backstepping Wavelet Neural Network Control for Indirect Field-Oriented Induction Motor Drive, An adaptive high-gain observer for nonlinear systems, High-gain observer based state and parameter estimation in nonlinear systems. Control for induction motors is also studied. applications because of its low cost and high reliability. (8) can be written in the Brunovsky (canonical) form: where v=f̄(x,t)+ḡ(x,t)u. 2010), (Besanet al. Linier Regression method used in this research is stepwise model using k-Means clustering. All system variables, i.e. SAGE Publications Ltd, unless otherwise noted. In other cases the information from tachometer and accelerometer measurements is replaced by the fusion of measurements from encoders and external sensors, such as cameras, laser trackers, etc. Next, the rotating reference frame d−q on rotor, is defined (Fig. The subsystem that is described by Eq. If you have access to a journal via a society or association membership, please browse to your society journal, select an article to view, and follow the instructions in this box. Kalman Filter-based control for DC and induction motors can have several applications for the design of industrial and robotic systems of improved performance. There is a growing interest in using Kalman filter models in brain modeling. (36) one obtains the dynamics of the current tracking errors. In (Martin Rouchon 1996) the voltage-fed induction machine was shown to be a differentially flat system. The operators φ(x) and γ(x) are φ(x)=[φ1(x),φ2(x),⋯, φm(x)]T, and γ(x)=[γ1(x),γ2(x),⋯,γp(x)]T, respectively. The Unscented Kalman Filter can be also used in place of the Extended Kalman Filter and in the latter case there will be no need to compute Jacobian matrices. The measurement update of the EKF is given by Eq. Review of Kalman filters This decoupling makes possible to develop controllers of the rotor's speed/position with methods already applied to DC motors. (5) becomes, Then, setting the output to be y=x1 one can see that all state variables xi,i=1,2,3 and the control input u can be expressed as functions of this output and its derivatives. Again the tracking performance of the proposed control scheme was tested in the case of a sinusoidal and a see-saw setpoint. In Section 4, flatness-based control for the complete (sixth-order) induction motor model is analyzed. First the theory of field oriented methodology, with and without speed sensor, is described. State estimation of induction motor using unscented Kalman filter. CCA 2003, A comparative study on Kalman filtering techniques designed for state estimation of industrial AC drive systems, Simple derivative-free nonlinear state observer for sensorless AC drives, High-Performance Induction Motor Control via Input-Output Linearization, A comparative study of Kalman filtering for sensorless control of a permanent-magnet synchronous motor drive, Flatness-based control of an induction machine fed via voltage source inverter - Concept, control design and performance analysis. (23) to Eq. Introduction . For non-Gaussian inputs, approximations are accurate to at least the second-order, with the accuracy of third and higher-order moments determined by the specific choice of weights and scaling factors. Field oriented induction motor control assumes transformation of the induction motor model from the ab -reference frame to the dq reference frame and that the magnetic flux ψrd converges to a steady-state value ψrdref. Typically, these take on the form of a simple weighted sample mean and covariance calculations of the posterior sigma points. In order, this book describes induction machine, SMPM-SM, IPM-SM, and, application to LC filter limitations. If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. From the second row of Eq. The observability … For the outer speed and flux control design the stator currents are treated as new control inputs and the system behavior is described by Eq. Elimination of the speed sensors has the advantages of lower cost, ruggedness as well as increased reliability. Nounou & Rehman 2007] Nounou, H.N., Rehman, H., Rigatos & Zhang 2001] Rigatos, G., Zhang, Q. In such a situation, the. Now, considering k4T1 as disturbance, the state-space equation of the DC motor can be rewritten as. The Kalman filter is a special kind of observer which provides optimal estimation of the system states based on least-square techniques. Advanced Control Systems Lecture Series Week 14 Kalman Filters, System Identification, HIL, DOF in dynamic positioning of ships where the Kalman Filter estimates the position and the speed of the vessel and also environmental forces. Kalman filtering is used for many applications including filtering noisy signals, generating non-observable states, and predicting future states. Flatness-based control of the induction motor with the use of Extended Kalman Filtering in case of tracking a constant setpoint (a) stator's current isd (b) stator's current isq, The approach on flatness-based control of the induction motor that was presented in Section 4 needs knowledge of the electric motor's state vector x=[θ,ω,ψsd,isd,isq,ρ]. Contact us if you experience any difficulty logging in. halangan dihitung dari hasil Regresi Linier. Sign up. During the last years, there has been significant effort in improving the performance of electric motors. Finally, in Section 8 concluding remarks are given. The Unscented Kalman Filter can be used for state estimation of nonlinear electric motors, such as the induction motor analyzed in Sections 3 and 4. That means, rotor flux and stator currents estimated by KF are used as inputs Parameters of the DC motor model, The design of the nonlinear DC motor controller is according to the flatness-based control theory. exoscelet, is a more general medical, become so popular. The aim of this paper is to decrease the execution time of EKF modeling of a six-phase induction motor. You use the Kalman Filter block from the Control System Toolbox library to estimate the position and velocity of a ground vehicle based on noisy position measurements such as GPS sensor measurements. This function determines the optimal steady-state filter gain M based on the process noise covariance Q and the sensor noise covariance R. 2010] Boizot, N., Busvelle, E., Gauthier, J.-P. (. sesorless control method for permanent magnet synchronous motor (PMSM) based on Extended Kalman Filter (EKF) to accurately estimate speed and rotor position. Further, this is used for modeling the control … Thus one has. The, parameters by knowing the input and output values, to halt instead of uncontrolled movement which may be, Seo, XXI ICTAM, 15-21 August 2004, Warsaw. This is useful when you have large time delays in your sensor feedback as this can cause instability in a motor control system. You can be signed in via any or all of the methods shown below at the same time. The UKF enables to estimate rotor speed and dq-axis flux of an induction motor through the processing of only the stator currents and voltages. Transformation to the dq reference frame is again performed, however this time there is no assumption about decoupling between the rotor speed dynamics and the magnetic flux dynamics. Kalman Filter-based control for DC and induction motors can have several applications for the design of industrial and robotic systems of improved performance. (, Akin et al. Figure 1. uncontrolled movement which may be dangerous to the user. the components of w (elements of the system's state vectors) can be expressed using only the flat output y and its time derivatives. control utilize this enhanced processing capacity. The simulation results are presented. (36) a controller that satisfies the flatness properties (and thus it can be also expressed as a function of the flat outputs and their derivatives) is defined as follows: where isq* and isd* denote current setpoints. This technique consists to achieve a one-dimensional Kalman Filter acting as an alternative controller, i.e., it can provides the control actions to the dc-motor in … Once the disturbance affecting the nonlinear system becomes known it can be compensated through the introduction of an additional control term in the loop. Control Applications, 2003. The Kalman filter is the optimal linear estimator for linear system models with additive independent white noise in both the transition and the measurement systems. The usual method of optimal control of Kalman filter makes use of off-line backward recursion, which is not satisfactory for this purpose. 8, while the associated control input is shown in Fig. Access to society journal content varies across our titles. Flatness-based control can be applied to finite dimensional system of the form. The filter is named after Kalman because he published his results in a more prestigious journal and his work was more general and complete. The estimated speed is used for vector control and overall speed control. A complex-valued model is adopted that simultaneously allows a simpler observability analysis of the system and a more effective state estimation. Sign in here to access free tools such as favourites and alerts, or to access personal subscriptions, If you have access to journal content via a university, library or employer, sign in here, Research off-campus without worrying about access issues. Some society journals require you to create a personal profile, then activate your society account, You are adding the following journals to your email alerts, Did you struggle to get access to this article? In Section 3, the field-oriented induction motor model is analyzed. CAUTION: set the sample time to … Flatness-based control of the induction motor with the use of Extended Kalman Filtering in case of tracking a seesaw setpoint (a) rotor's angle θ (b) rotor's speed ω, Figure 18. 2004] Akin, B., Orguner, U., Ersak, A. 2003) and (Akin et al. Extended Kalman filters (EKF) have been widely used for sensorless field oriented control (FOC) in permanent magnet synchronous motor (PMSM). The Extended Kalman Filter is based on a linearization of the systems' dynamics using a first order Taylor expansion (Rigatos Zhang 2001). (28) to Eq. It can be expected that the practical relevance of the LQD estimator will strongly increase thereby. 17 to Fig. Sensorless control of the induction motor is again implemented through feedback of the estimated state vector. Acquire z(k) and compute: The schematic diagram of the EKF loop is given in Fig. 7 and Fig. This becomes useful when fault occurs in the feedback system. Flatness-based control of the induction motor with the use of Extended Kalman Filtering in case of tracking a sinusoidal setpoint (a) stator's current isd (b) stator's current isq. (30)-(31) are decoupled. This means that all system dynamics can be expressed as a function of the flat output and its derivatives, therefore the state vector and the control input can be written as x(t)=φ(y(t),ẏ(t),⋯,y(r)(t)) and u(t)=ψ(y(t),ẏ(t),⋯,y(r)(t)). 2004] van der Merwe, R., Wan, E.A., Julier, S.I. (51) and Eq. 2001), (Dannehl Fuchs 2006). (36) and assuming the speed and flux as constants. NEURAL KALMAN FILTER NKF Principal of this adaptive observer considers putting linear Kalman filter and neural adaptive scheme of speed estimation in cascade. (40) and Eq. The system input and the rotational speed of DC motor, the output are used for the above purposes. The estimation error covariance matrix P∈R3×3 and the KF gain K∈R3×1 were used in Eq. Linear regression method is used to obtain the model parameters by know giving the best estimate of the states and model parameters even in the presence of noise. Kalman filter algorithm is implemented in mat lab environment to estimate the states in presence of additive white Gaussian noise. The question arises whether Kalman filter models can be used on-line not only for estimation but for control. Thus the convergence rate of the estimator must be acclerated to obtain the more accurate estimates. This function determines the optimal steady-state filter gain M based on the process noise covariance Q and the sensor noise covariance R. First specify the plant + noise model. Figure 2. This two-phase system can be described in the stator-coordinates frame α−b, and the associated voltages are denoted as vsα and vsb, while the currents of the stator are isα and isb, and the components of the rotor's magnetic flux are ψrα and ψrb. GitHub is home to over 50 million developers working together to host and review code, manage projects, and build software together. Example of approximation of a 2D distribution by the Sigma-Point Kalman Filtering approach. In such a situation, the motorized wheel chair will be forced to halt instead of uncontrolled movement which may be dangerous to the user. Furthermore, the diagrams presented in Fig. DC motor control using state feedback The objective is to make the system’s output (angle θof the motor) follow a given reference signal xd. In this paper, a simple extended Kalman Filter (EKF) controller for direct torque control (DTC) of a six-phase induction machine in all speed ranges is proposed. View or download all the content the society has access to. Metode Regresi Linier yang digunakan dalam penelitian ini adalah model bertingkat dengan k-Means clustering. The paper has shown that in the design of state estimation-based control for electric motors the following should be taken into account: (i) for linear electric motor models subject to Gaussian measurement or process noise the Kalman Filter is the optimal state estimator, since it results in minimization of the trace of the estimation error's covariance matrix, (ii) for nonlinear electric motor models, subject to Gaussian noise one can use the generalization of the Kalman Filter as formulated in terms of the Extended Kalman Filter. Here, a new method that replaces the standard regression with a regression using the bivariate rank statistics is described. 2010] Karami, F., Poshtan, J., Poshtan, M. (, Kumar et al. Please read and accept the terms and conditions and check the box to generate a sharing link. There are several results on disturbance observers (e.g. The control inputs are chosen as, Denoting Δψrd=ψrd−ψrd* and Δω=ω−ω* the tracking error dynamics are given by. Parameter x3 of the state vector of the DC motor in estimation was performed with use of the Kalman Filter (a) when tracking a see-saw setpoint (b) when tracking of a sinusoidal setpoint, Figure 9. The Kalman filter was developed by Rudolph Kalman, although Peter Swerling developed a very similar algorithm in 1958. Metode Regresi Linier model bertingkat digunakan untuk merepresentasikan korelasi antara jarak line laser pada citra dan jarak halangan secara aktual. The system of Eq. (28)-(29) and Eq. The feature of this data is that the data number is scant. More sophisticated control loops, like Kalman filters, are built with specialized knowledge of the exact application. Assuming Γ̇d=0 and denoting the state vector as [x1,x2,x3]T=[θ,θ̇,θ̈]T, a linear model of the DC motor is obtained: Next, control for a nonlinear DC motor model will be presented. 2001] Delaleau, E., Louis, J.P., Ortega, R. (, Flies & Mounier 1999] Fliess, M., Mounier, H. (, Hilairet et al. Kalman is an electrical engineer by training, and is famous for his co-invention of the Kalman filter, a mathematical technique widely used in control systems and avionics to extract a signal from a series of incomplete and noisy measurements. The UKF is a discrete time filter which uses the unscented transform for approximating solutions to the filtering problem of the form. Functions f(x) and g(x) are vector field functions defined as: where k1=−F/J, k2=A/J, k3=B/J, k4=−1/J, k5=−A/L, k6=−B/L, k7=−R/L, k8=−1/L, R and L are the armature resistance and induction respectively, and J is the rotor's inertia, while F is the friction.

Gardner Max 10, Syracuse University Library, 2005 Dodge Dakota Headlights, jayaram Comedy Movies, Autonomous Desk Scratches, Snhu Campus Admissions, Canadian Physiotherapy Association Membership, 2005 Dodge Dakota Headlights,

By in Uncategorized on December 6, 2020