Sensorless Control for Linear Electromagnetic Actuators with Permanent Magnet Mover
Final Report Abstract
In this project, control and position estimation for linear electromagnetic actuators with permanent magnets was investigated. First, a hybrid modelling methodology was adopted to model such kind of actuators where a combination of analytical and FEM modelling of the actuator was performed. After that, the electrical, magnetic, and mechanical parameters of the real actuators were identified assuming a linear model. A new method, based on measurement of the current switching instant was developed to measure the electrical parameters online, during the stop phase of actuation. The magnetic and mechanical parameters were calculated offline based on position, current, and reference voltage measurements. After the parameters were identified, two controllers were investigated, the Linear Quadratic Regulator (LGR) controller and the Proximate Time Optimal controller for Servomechanisms (PTOS). The PTOS controller is a nonlinear type of controller based on the principle of time optimal control. It solves the drawbacks of time optimal control such chattering and steady state error with small increase in the transition time. Compared to the LQR controller it is more dynamic and utilizes the constraints on the input voltage and current better, on the expense of having a more noisy voltage reference (this could be an issue in EMC sensitive applications). The Luenberger observer, which is a state observer of the predictor corrector type was implemented to estimate the speed of the mover based on the calculated voltage reference, measured current, and a simplified linear model of the actuator. The results have shown that the estimator can well estimate the speed of the mover during the transient state. This is due to the strong back e.m.f. signal. The speed signal is then mainly integrated to get the position signal. The estimator suffers from two limitations: assumptions of linear model and load disturbance estimation. The work done in this project has a potential effect in the industry by addressing two points: position sensors and low cost microcontrollers. Position sensors are expensive, add complexity to the system, and suffer from mechanical wear. An actuator control system can in theory operate in open loop control without a position sensor (On/Off operation) with the drawback of having a high impact speed which leads to fast mechanical wear of the actuator. In this project, a solution is proposed which combines position estimation with feedback control to minimize impact speeds. The controllers developed in this work are simple enough to run on low cost microcontrollers. In addition to that, current measurement at the switching instant is very common in the industry in the field of field oriented control (FOC) for brushless DC motors (BLDC). Thus the method developed for electrical parameter estimation can be implemented on a low cost microcontroller. Since the exponential function is expensive (from a computation point of view), the exponential model can be approximated with the second order Taylor series approximation. The future work for this topic will focus on improving the controller and estimator through the following points: Implement Proximate Time Optimal control for the triple integrator plant which can better utilize the constraints on the voltage and current - Identify the nonlinear parameters of the actuator and use in the state estimator - Add a disturbance estimation scheme.
