kalman filter for motor control

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The time-varying Kalman filter is a generalization of the steady-state filter for time-varying systems or LTI systems with nonstationary noise covariance. Penelitian ini bertujuan untuk mengusulkan sebuah pendekatan dalam mendeteksi halangan dan memperkirakan jarak halangan untuk diterapkan pada kursi roda pintar (smart wheelchair) yang dilengkapi kamera dan line laser. Time-Varying Kalman Filter. It can be observed that comparing to EKF, the UKF (sigma-point) approach succeeds improved estimation of the state vector's mean value and covariance (only 5 points are needed to approximate sufficiently the 2D distribution). Additionally, a state estimation-based control loop is implemented using the Unscented Kalman Filter. It is derived from This becomes useful when fault occurs in the feedback system. Figure 1. This paper deals with the design of an extended complex Kalman filter (ECKF) for estimating the state of an induction motor (IM) model, and for sensorless control of systems employing this type of motor as an actuator. First the case of a DC motor is considered and Kalman Filter-based control is implemented. This work presents a study over a torque-generated speed control of free wheel attached to a DC motor, for use on traction of mobile vehicles. It is assumed that the process noise w(k) and the measurement noise v(k) are uncorrelated. Using an Extended Kalman Filter for Estimating Vehicle Dynamics and Mass . Join ResearchGate to find the people and research you need to help your work. 2). It will be shown that it is possible to implement state estimation for the electric motor using measurements only the rotation angle θ and of the stator currents isa and isb. Now the subsystem that consists of Eq. Remark 1: DC motor control is performed using as control input the armature current or the field voltage. A flatness-based control approach for induction motors, 5. 2004] Akin, B., Orguner, U., Ersak, A. 2009), (Borsje et al. The paper has studied sensorless control, for DC and induction motors, using Kalman Filtering techniques. Schematic diagram of the EKF loop, Figure 4. 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. Kalman filter algorithm is implemented in mat lab environment to estimate the states in presence of additive white Gaussian noise. The proposed method is fast and can operate online. The tracking performance of the Kalman Filter-based control loop, in the case of a see-saw and a sinusoidal setpoint are depicted in Fig. Using a control input as in Eq. The new control inputs of the system are considered to be vsd, vsq, and are associated to the d−q frame voltages vd and vq, respectively. Iterative Receiver design for Underwater Communication using MIMO-OFDM, Channel estimation and Efficient Modulation schemes, Computing the Least Quartile Difference Estimator in the Plane. Metode Regresi Linier model bertingkat digunakan untuk merepresentasikan korelasi antara jarak line laser pada citra dan jarak halangan secara aktual. Kalman Filter T on y Lacey. 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. Simply select your manager software from the list below and click on download. 3. Application of an extended Kalman filter for high-performance current regulation of a vector-co... Tutorial Review of Bio-Inspired Approaches to Robotic Manipulation for... Study on the fuzzy proportional–integral–derivative direct torque cont... Stochastic Bifurcation of a Strongly Non-Linear Vibro-Impact System wi... Alonge & Ippolito 2010] Alonge, F., D'Ippolito, A. The mean and covariance of the initial state x0 are m0 and P0, respectively. It can be observed that the recursion of the Kalman Filter given 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. We predicted the location of a ball as it was kicked towards the robot in an effort to stop the ball. In order, this book describes induction machine, SMPM-SM, IPM-SM, and, application to LC filter limitations. The standard Kalman lter deriv ation is giv 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. Comparison between the estimated and the real output measurements enables the detection of failures in the motor's components. The measurement update of the EKF is given by Eq. the subset algorithm of Rousseeuw and Leroy. This decoupling makes possible to develop controllers of the rotor's speed/position with methods already applied to DC motors. 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)). The UKF algorithm consisted of two-stages, the time update and the measurement update, which are summarized as follows: The simulation experiments of Fig. Following a linearization procedure, φ is expanded into Taylor series about x^: where Jφ(x) is the m×m Jacobian of φ calculated at x^(k): where x^−(k) is the estimation of the state vector x(k) before measurement at the k -th instant to be received and x^(k) is the updated estimation of the state vector after measurement at the k -th instant has been received. This product could help you, Accessing resources off campus can be a challenge. The simulation results are presented. Sign up. which implies that the derivatives of the flat output are not coupled in the sense of an ODE, or equivalently it can be said that the flat output is differentially independent. Measuring currents isa and isb and using the estimate of angle ρ, the input measurements isd and isq can be provided to the Extended Kalman Filter. The Kalman filter is an algorithm that estimates the state of a system from measured data. 10 and Fig. The p×m Jacobian Jγ(x) is. This paper presents a detailed analysis for the Lp-stability of tracking errors when the Kalman filter is used for tracking unknown time-varying parameters. Manuscript content on this site is licensed under Creative Commons Licenses. If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. sesorless control method for permanent magnet synchronous motor (PMSM) based on Extended Kalman Filter (EKF) to accurately estimate speed and rotor position. In such a situation, the. Regarding (iii) the high-gain Extended Kalman Filter can provide additional robustness to state estimation under external disturbances and parametric variations (Boizot et al. The Extended Kalman Filter can give estimates of the non-measured state vector elements, i.e. NEURAL KALMAN FILTER NKF Principal of this adaptive observer considers putting linear Kalman filter and neural adaptive scheme of speed estimation in cascade. A flux vector control drive is a three phase induction motor controller which through advanced control algorithms and a fast and powerful microcontroller can control the speed and torque of a motor all the way down to zero speed. Such results can be exploited so as to make Kalman Filtering for electric motors as well as the associated state estimation-based control loop be more robust (Rigatos 2011). DC motor, gearbox transmission, torque sensor and human trunk (biomechanical model). 1994), (Marino et al. 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. 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. when fault occurs in the feedback system. In Section 7 the efficiency of the above mentioned Kalman Filter-based control schemes, for both the DC and induction motor models, is tested through simulation experiments. Kalman Filter. 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. 2004), (Sarrka 2007), (Kandepu et al 2008). The filter starts from the initial mean m0 and covariance Pxx0. In Section 6, the Unscented Kalman Filter is used to estimate the induction motor's state vector and subsequently a state estimation-based control loop is implemented. Example of approximation of a 2D distribution by the Sigma-Point Kalman Filtering approach. The first key problem associated with EKF is that the estimator requires all the plant dynamics and noise processes are exactly known. Besançon et al. One important use of generating non-observable states is for estimating velocity. 2010] Karami, F., Poshtan, J., Poshtan, M. (, Kumar et al. Control signal of the Extended Kalman Filter-based control loop for the field-oriented induction motor model (a) when tracking of a see-saw setpoint (b) when tracking of a sinusoidal setpoint, Figure 13. Introducing the armature reaction leads to a nonlinear system. A common problem in linear regression is that largely aberrant values can strongly influence the results. The e-mail addresses that you supply to use this service will not be used for any other purpose without your consent. In this paper a Kalman filter is used for recursively estimating the states and model parameters. Then, the rotation angle of the rotor with respect to the stator is denoted by δ. Transactions of the Society of Instrument and Control Engineers. 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. I have to tell you about the Kalman filter, because what it does is pretty damn amazing. be controlled.The covariance matrices of, and of the measurement noise R are set to. The nonlinear model of the system is used for the simulation and later implemented on the dSPACE HW to obtain experimental results. These requirements extend new method of control and operation. Moreover, a state estimation-based control loop was implemented, using the Unscented Kalman Filter to estimate the induction motor's state vector. 2). It can be noticed that the Extended Kalman Filter is an efficient approach for the implementation of state estimation-based control of the sixth-order induction motor model. Parameter x1 of the state vector of the field-oriented induction motor model in estimation was performed with use of the Unscented Kalman Filter (a) when tracking a see-saw setpoint (b) when tracking of a sinusoidal setpoint, Figure 14. 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. The motor's angular velocity was estimated by an Extended Kalman Filter which used rotor angle measurements, and sensorless control of the induction motor was again implemented through feedback of the estimated state vector. For instance the following PI controller has been proposed for the control of the magnetic flux (Marino et al. of the rotation speed ω, of the magnetic flux ψrd and of the angle ρ between the flux vectors ψra and ψrb. The usual method of optimal control of Kalman filter makes use of off-line backward recursion, which is not satisfactory for this purpose. As it can be seen in Fig. The last two implementations include calculation of the kalman gain. The extended Kalman filter (EKF) is widely used for nonlinear filter problems. Figure 1. (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. the components of w (elements of the system's state vectors) can be expressed using only the flat output y and its time derivatives. (8) can be written in the Brunovsky (canonical) form: where v=f̄(x,t)+ḡ(x,t)u. International Journal of Adaptive Control and Signal Processing. (, Bodson et al. In fact, a Kalman filter is not so much a filter as it is a mathematical model of the application, incorporating the laws of physics, and expectations of how the system should behave and respond. (28)-(29) and Eq. Extended Kalman Filter Based Speed Sensorless PMSM Control with Load Reconstruction Dariusz Janiszewski Poznan University of Technology Poland 1. Kalman and Extended Kalman Filtering for linear electric motor models, 6. 2004] Besançon, G., Zhang, Q., Hammouri, H.. View or download all content the institution has subscribed to. 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. where xk∈Rn is the state, yk∈Rm is the measurement, qk−1∈Rn is a Gaussian process noise qk−1∼N(0,Qk−1), and rk∈Rm is a Gaussian measurement noise rk∼N(0,Rk). (, Wai & Chang 2003] Wai, R.J., Chang, J.M. Sensorless control of the induction motor is again implemented through feedback of the estimated state vector. Optimized Kalman filter (STOK) is a novel adaptive filter that embeds a self-tuning memory decay and a recursive regularization to guarantee high network tracking accuracy, temporal precision and robustness to noise. Typically, these take on the form of a simple weighted sample mean and covariance calculations of the posterior sigma points. 2004) the Unscented Kalman Filter (UKF) and Extended Kalman Filter (EKF) are analyzed and compared both experimentally and theoretically in the problem of non-linear state estimation for field-oriented sensorless control of AC drives. Flatness-based control can be applied to finite dimensional system of the form. The measured state variable was supposed to be the rotor's angle θ. CAUTION: set the sample time to … 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. (5) one obtains, Thus the input-output relation can be written as, where, f̄(x)=k1ẋ2+k2ẋ3+2k3k5x2x3+2k3k6x2x32+2k3k7x32, and ḡ(x)=2k3k8x3. The UKF is a special case of Sigma-Point Kalman Filters. The UKF is a discrete time filter which uses the unscented transform for approximating solutions to the filtering problem of the form. Kalman Filter Simulation ... c is the control vector, which would contain estimated changes from direct action commands (for example, if a robot's motor was instructed to move forward). The posterior statistics are calculated (approximated) using tractable functions of the propagated sigma-points and weights. The noise signal caused by measurement and observation seriously affected the control quality in PID control of DC motor. More sophisticated control loops, like Kalman filters, are built with specialized knowledge of the exact application. Schematic diagram of the UKF loop. 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. 2005). The sampling period was taken to be Ts=0.01sec. Hybrid stepper motor (HSM), Extended Kalman Filter (EKF), position control, sensorless. (, Wai & Chang 2004] Wai, R.J., Chang, H.H. These estimates are used in the positional control system of the ship. (38) and Eq. The convergence of the tracking error to zero can be assured through the application of the following feedback control laws: For the DC motor models described in Section 2 the Kalman Filter is an efficient state estimator. To implement the Extended Kalman Filter in the induction motor's model that is expressed in the dq reference frame the following Jacobian matrices are calculated. 16. © 2008-2020 ResearchGate GmbH. state variable increments are normally computed from the observation increments by linear regression using the prior bivariate ensemble of the state and observation variable. halangan dihitung dari hasil Regresi Linier. INTRODUCTION The indirect field oriented control method is widely used for in- duction motor drives. INTRODUCTION. AC motor circuit, with the a−b stator reference frame and the d−q rotor reference frame, The classical method for induction motors control is based on a transformation of the stator's currents (isα and isb) and of the magnetic fluxes of the rotor (ψrα and ψrb) to the reference frame d−q which rotates together with the rotor (Fig. the LQD is not widely used yet due to the high computational effort needed when using common algorithms, e.g. IECON 2006, Modelling and Control of Induction Motors, Tracking control and π-freeness of infinite dimensional linear systems, Speed and rotor flux estimation of induction machines using a two-stage extended Kalman filter. Moreover, the output measurement z(k) is a p -vector, C is an p×m -matrix of real numbers, and v(k) is the measurement noise. (39) to Eq. The models included shows three different ways to implement a kalman filter in Simulink(R). Figure 5. (, Akin et al. 2006) the Unscented Kalman filter (UKF) has been applied to state observation in field oriented control of an induction motor. Figure 2. chair making very user friendly in everyday life situations. Now, considering k4T1 as disturbance, the state-space equation of the DC motor can be rewritten as. 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). Nounou & Rehman 2007] Nounou, H.N., Rehman, H., Rigatos & Zhang 2001] Rigatos, G., Zhang, Q. The covariance matrix of the measurement noise was defined E{v(i)vT(j)}=Rδ(i−j), with diagonal elements rii=10−2. 2005] Borsje, P, Chan, T.F., Wong, Y.K., Ho, S.L. Today the Kalman filter is used in Tracking Targets (Radar), location and navigation systems, control systems, computer graphics and much more. The state vector x used in the control law is estimated through Kalman Filtering, as described in 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. (28) to Eq. 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. The equations of the induction motor in the d−q reference frame, given by Eq. In such the case, the proposed method is useful. 11 the sensorless controller succeeded asympotic elimination of the tracking error despite abrupt changes in the reference trajectory, or the existence of process and measurement noises. It has great maneuverability through. (29), then one can succeed ψrd(t)→ψrdref(t). The model matrices A, B, H, Q, and R may contain unknown parameters and are often allowed to vary through time. Finally, in (Akin et al. The control inputs are chosen as, Denoting Δψrd=ψrd−ψrd* and Δω=ω−ω* the tracking error dynamics are given by. 2003) and (Akin et al. To overcome the EKF flaws, the Unscented Kalman Filter can be also considered. A complex-valued model is adopted that simultaneously allows a simpler observability analysis of the system and a more effective state estimation. 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. 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. An extended Kalman filter is implemented to perform the estimation based on a noisy measurement of wheel angular velocity. exoscelet, is a more general medical, become so popular. Contribute to aiyou94/Kalman-filter-for-motor-control development by creating an account on GitHub. Additionally, controllers for nonlinear DC motor models have been developed. The possibility to reduce the number of sensors involved in the control of electric motors has been a subject of systematic research during the last years (Holtz 2002), (Hilairet et al. It was primarily developed by the Hungarian engineer Rudolf Kalman, for whom the filter is named. 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. In such a situation, the motorized wheel chair will be forced to halt instead of uncontrolled movement which may be dangerous to the user. (35) and Eq. 15 show that the control signal, which is applied to the decoupled field-oriented induction motor model, remains smooth. Linier Regression method used in this research is stepwise model using k-Means clustering. The current paper studies sensorless control for DC and induction motors using Kalman Filtering techniques. The use of the Unscented Kalman Filter for state estimation and control of nonlinear electric motor models is a relatively new and promising topic. 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. It has been shown that the angle of the rotor position (rotation angle θ) and the angle ρ of the magnetic field (angle between flux ψa and ψb) constitute a flat output for the induction motor model (Martin Rouchon 1996), (Delaleau et al. For example a suitable state feedback controller would be, Tracking of the reference setpoint can be also succeeded for the rotor's speed and flux through the application of the control law of Eq. The control strategies explored include expert-system-based acceleration control, hybrid-fuzzy/PI two-stage control, neural-network-based direct self control, and genetic algorithm based extended Kalman filter for rotor speed estimation. In fact, the very first use of Kalman filters involved nonlinear Kalman filters in NASA's space program in the 1960s. Thus, it can be assured again that the estimation error x−x^ will be minimal and the performance of the control loop will be satisfactory. 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. Kalman filter algorithm is implemented in mat lab environment to estimate the states in presence of additive white Gaussian noise. The efficiency of the aforementioned Kalman Filter-based control schemes, for both the DC and the induction motor models, was tested through simulation experiments. For more information view the SAGE Journals Article Sharing page. This article will tell you the basic concepts that you need to know to design and implement a Kalman filter. master. 2003] Akin, B., Orguner, U., Ersak, A. Professor (E&C), Reva Institute of Technology, Bangalore. Control of the field-oriented induction motor model, 4. (33), Eq. The Jacobian Jφ(x) is the 2×2 Jacobian of φ calculated through the expansion: where x^−(k) is the estimation of the state vector x(k) before measurement at the k -th instant to be received and x^(k) is the updated estimation of the state vector after measurement at the k -th instant has been received. 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 rotor position and speed are estimated from the input voltage and current using the Extended Kalman Filter. Parameter x2 of the state vector of the DC motor in state estimation with use of the Kalman Filter (a) when tracking a see-saw set-point (b) when tracking a sinusoidal setpoint, Figure 8. Induction motors have been the most widely used machines in fixed-speed applications for reasons of cost, size, weight, reliability, ruggedness, simplicity, efficiency, and ease of manufacture. part in the FIM. Further, this is used for modeling the control … The EKF appears to be an efficient estimator for the implementation of state estimation-based control schemes. This site uses cookies. DC motors are usually modelled as linear systems and then linear control approaches are implemented. Induction Motor Vector Control Structure 3. 13 and 14 show the good tracking performance of the UKF-based control loop, in the case of time varying setpoints (such as see-saw and sinusoidal reference trajectories). no analytical derivatives are used, in order to generate a posterior sigma-point set. GitHub is home to over 50 million developers working together to host and review code, manage projects, and build software together. In Section 3, the field-oriented induction motor model is analyzed. Kalman Filtering can be applied to discrete-time state models of the form, where the state x(k) is a m -vector, w(k) is a m -element process noise vector and Φ is a m×m real matrix. 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. To implement sensorless control for the decoupled field-oriented induction motor model only measurements of the rotor's angle θ where used. In Section 4, flatness-based control for the complete (sixth-order) induction motor model is analyzed. The Kalman filter estimates a process by using a form of feedback control: the filter estimates the process state at some time and then obtains feedback in the form of (noisy) measurements. During the last few decades the field of The model's state variables were taken to be x1=θ and x2=θ̇. (4) if the latter system is written in the form of Eq. In this tutorial a slip control loop for a quarter car model is developed. Here, a new method that replaces the standard regression with a regression using the bivariate rank statistics is described. 17. Control for induction motors is also studied. The control signal of the Extended Kalman Filter-based control loop is depicted in Fig. Simulation results on flatness-based control of the induction motor when using the Extended Kalman Filter for reconstructing its state vector from output measurements are presented in Fig. (iii) to overcome certain limitations of the EKF (such as the need to compute Jacobian matrices and the cumulative linearization errors due to approximative linearization of the motor dynamics), Sigma Point Kalman Filters (SPKF), and particularly the Unscented Kalman Filter (UKF) can be used. The sigma-points are propagated through the true nonlinear function using functional evaluations alone, i.e. It can be shown that all state variables of the induction motor can be written as functions of the flat outputs and their derivatives. You want to estimate the position and velocity of a ground vehicle in the north and east directions. Some basic operations performed in the UKF algorithm (Unscented Transform) are summarized as follows: 1) Denoting the state vector mean as x^, a set of 2n+1 sigma points is taken from the columns of the n×n matrix (n+λ)Pxx as follows: Matrix Pxx is the covariance matrix of the state x and index i denotes its i -th column. The estimated speed is used for vector control and overall speed control. Access to society journal content varies across our titles. First the case of a DC motor was considered. In the control of robotic manipulators, which is actually control of the DC motors that rotate the robot's joints, the angle of each joint is usually measured with the use of an optical encoder. Review of Kalman filters 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. Abstract: This work deals with the tuning of an Extended Kalman Filter for sensorless control of induction motors for electrical traction in automotive. 1991] Marino, R., Peresada, S., Valigi, P. (, Martin & Rouchon 1996] Martin, P., Rouchon, P. (, van der Merwe et al. Also, it presents the discrete state space model of a DC model and the Kalman filter’s equations and applications. Its use in the analysis of visual motion has b een do cumen ted frequen tly. Login failed. Finally, flatness-based control for induction motors considers also a nested control loops scheme as depicted in Fig.

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