Improving the Angular Velocity Measured with a Low-Cost Magnetic Rotary Encoder Attached to a Brushed DC Motor by Compensating Magnet and Hall-Effect Sensor Misalignments

Abstract

This paper proposes a method to improve the angular velocity measured by a low-cost magnetic rotary encoder attached to a brushed direct current (DC) motor. The low-cost magnetic rotary encoder used in brushed DC motors use to have a small magnetic ring attached to the rotational axis and one or more fixed Hall-effect sensors next to the magnet. Then, the Hall-effect sensors provide digital pulses with a duration and frequency proportional to the angular rotational velocity of the shaft of the encoder. The drawback of this mass produced rotary encoder is that any structural misalignment between the rotating magnetic field and the Hall-effect sensors produces asymmetric pulses that reduces the precision of the estimation of the angular velocity. The hypothesis of this paper is that the information provided by this low-cost magnetic rotary encoder can be processed and improved in order to obtain an accurate and precise estimation of the angular rotational velocity. The methodology proposed has been validated in four compact motorizations obtaining a reduction in the ripple of the estimation of the angular rotational velocity of: 4.93%, 59.43%, 76.49%, and 86.75%. This improvement has the advantage that it does not add time delays and does not increases the overall cost of the rotary encoder. These results showed the real dimension of this structural misalignment problem and the great improvement in precision that can be achieved.

Optimal PID Control of a Brushed DC Motor with an Embedded Low-Cost Magnetic Quadrature Encoder for Improved Step Overshoot and Undershoot Responses in a Mobile Robot Application

“…Figure 7 shows that the measured angular rotational velocity oscillates in a repeating pattern with a period of exactly 12 samples. This characteristic effect produced in low-cost magnetic encoders was firstly described and corrected by Palacin et al [ 44 ], and is mainly caused by misalignments in the exact location of the magnetic fields in the magnet and in the exact location of the hall-effect sensors. This deterministic error can be corrected empirically by computing the average speed and the error coefficients that must be applied to each encoder reading in order to obtain the average value.…”

“…As can be seen comparing Figure 7 and Figure 8 , the corrected angular rotational velocity readings gathered from the low-cost magnetic encoder are remarkably stable in open-loop measurements; therefore, this corrected velocity information will provide much more reliable feedback for the controller discussed later in this paper. Finally, as described in [ 44 ], the calibration of the correction coefficients of the low-cost magnetic encoder must be done only once during the manufacturing stage and stored in the microcontroller that must read the encoder and control the BDCM. The correct application of these calibration correction coefficients in each BDCM used in a mobile robot only requires an initial synchronization after a power-up.…”

“…The main contribution of this paper is the complete and accurate practical description of the PID controllers implemented in a medium-sized (1.76 cm tall) omnidirectional mobile robot, which uses three BDCM to directly drive its three omnidirectional wheels ( Figure 1 ). As is well known, estimating of the position and trajectory of a mobile robot [ 38 , 39 ] heavily relies on the performance of the design of the wheels [ 40 , 41 , 42 ] and on the accurate control of the rotation of the wheels [ 43 , 44 ], because small differences can lead to noticeable errors in the final position reached by the mobile robot. The use of an omnidirectional motion system in a mobile robot allows superior maneuverability and the imitation of human mobility [ 45 , 46 ], but the control of the angular rotational velocity of the wheels must be very accurate in order to reduce odometry errors [ 47 , 48 ].…”

Evaluation of the Path-Tracking Accuracy of a Three-Wheeled Omnidirectional Mobile Robot Designed as a Personal Assistant

“…The omnidirectional wheels are driven by geared brushed DC motors with a low-cost magnetic rotary encoder attached. The estimation of the angular rotational speed of the DC motors is performed by measuring and processing the pulse length of the digital signal provided by the encoder [8]. The omnidirectional motion system can move the robot up to 1.0 m/s in any direction, although 0.3 m/s is the nominal translational velocity used in most of its applications [19].…”

“…The main drawback of using a mobile robot with omnidirectional wheels is the evaluation of the odometry because the odometry is highly influenced by the practical implementation details such as the mechanical performances of the omnidirectional wheels, the accuracy of the direct and inverse kinematic models, the electrical performances of the motors used to drive the wheels, the rotary encoders used to estimate the angular rotational velocity of the wheels [8] and the tuning of the motor controllers. For example, Tsai et al [9] and Tri et al [10] proposed the implementation of omnidirectional mobile robots using Sensors 2021, 21, 7216 2 of 19 three double-line omnidirectional wheels (also known as double parallel wheels), easy to manufacture but with the drawback of having two radial distances relative to the center of the mobile robot depending on the inner or outer parallel wheel in effective contact with the ground.…”