RTC (reaction torque compensated) induction motor and its open-loop control
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Rapid change of the rotating speed of an induction motor causes large reaction torque or excessive vibration of the system base. This paper proposes a passive reaction torque compensated (RTC) induction motor considering the dynamic characteristic of open-loop speed control with a variable frequency drive. RTC mechanism converts the reaction torque into the dissipative inertial energy of the rotary stator and the potential energy of the torsion spring torque so that a part of the reaction torque or the spring torque is transmitted to the system base. First, dynamic equation and simulation model for the RTC induction motor are introduced and verified with experiments. The acceleration response of an induction motor with variable speed drive is approximated as first-order ordinary differential equation. Then, the RTC mechanism such as spring and additional inertia are designed considering derived acceleration response or torque profile. Then, an experimental set-up and its control system for the RTC induction motor are built. Finally, effectiveness of the RTC induction motor is verified comparing open-loop speed control of both RTC and conventional induction motor.
KeywordsInduction motor Variable speed control Reaction torque compensation (RTC)
Damping of rotor, stator and system base
Initial deflection of tension spring at balance position
Force caused by tension spring
q-component of rotor and stator current
Inertia of rotor, stator and system base
Stiffness of tension spring
Stiffness of equivalent stator and system base springs
Undeformed length of tension spring
Magnetizing and rotor inductance
Number of poles
Distance from center of motor to pin of attached spring
Radius of the pins
Motor and load torque
Torque generated by spring between stator and base
Transmitted torque to the system base
d-component of rotor flux
Rotary angle of rotor, stator, system base
Rotating flux and rotor speed
AC induction motors are the most common motors in the world and used in industrial fields as well as home appliances [1, 2, 3, 4] due to their unique advantages such as simple and rugged design, low-cost, low maintenance and direction connection to an AC-power source .
Variable torque and speed load are most commonly found in the industry and variable speed operation of an induction motor allows to optimize the process under varying load conditions . However, rapid change of the rotating speed of an induction motor causes large reaction torque. The reaction torque of the induction motor may generate excessive vibration of the system base, which results in reduction of its life span or damage of the entire system .
A passive, Active and semi-active RFCs (reaction force compensation) to reduce the system vibration have been studied only for a linear motor motion stage [8, 9, 10, 11]. Although the passive RFC mechanism is compact and cost-effective, the passive RFC does not allow in situ modification of the dynamic characteristic of the RFC system. An active RFC mechanism using an additional coil can tune its dynamic characteristic and minimize the transmitted force against the motion profile variation . In addition, a semi-active RFC can modify the damping of the RFC by adjusting the external resistor or open–close time ratio of an additional coil [9, 10, 11].
Reaction torque compensations of an electric motor or driving system with additional motor or structure were proposed for mechanical stabilization [12, 13]. In addition, control algorithms were studied to cancel the reaction torques of the transmission system such gear or wire [14, 15].
This paper proposes an RTC induction motor considering dynamic characteristic of open-loop speed control with a variable frequency drive. The RTC induction motor has a rotary stator and torsion spring as well as rotor, bearing and housing. Through the torsion spring, only part of reaction torque is transmitted to the system base, while some reaction energy is dissipated as oscillating stator motion. First, dynamic equation of the RTC induction motor is introduced. A simulation model for the RTC induction motor is built and verified with experiments. Then, the acceleration response of an induction motor with variable frequency drive is approximated as first-order ordinary differential equation. The RTC mechanism such as spring and additional inertia are optimized under given performance indices considering derived acceleration or torque profile. Experimental set-up for the RTC induction motor is built and its control system is constructed using a DSP. Finally, effectiveness of the RTC induction motor is verified comparing step responses of both RTC and conventional induction motor.
2 RTC induction motor
2.2 Mathematical modeling
In this study, dynamics of the system base is neglected in designing the RTC induction motor. During the conceptual design of the RTC induction motor, the dynamics of the system base is not known and an iterative design between the RTC and the system base is necessary . In addition, the first step of the iterative design is to preliminarily determine the parameters of the RTC mechanism ignoring the base dynamics.
3 Design of RTC mechanism
3.1 Simulation model and motor validation
Parameters of the induction motor
Rotor inertia Jm (kg m2)
0.065 × 10−3
Rotor damping coef. cm (Nms/rad)
0.033 × 10−3
Rotor resistance Rr (Ω)
Stator resistance Rs (Ω)
Mutual inductance Lm (H)
Leakage inductance of stator winding Lls (H)
Leakage inductance of stator winding Llr (H)
3.2 RTC mechanism
3.3 Approximate acceleration during open-loop speed control
Since the speed response of the induction motor would not track accurately the speed command under open-loop control of the V/F method, it is necessary to find an approximated profile of the motor acceleration for proper design of the RTC mechanism.
3.4 Design of RTC mechanism
4.1 Experimental set-up
Parameters of the RTC mechanism
Stator inertia Js (kg m2)
2.28 × 10−3
Stator damping coef. cs (Nms/rad)
5.8 × 10−3
Tension spring stiffness K (N/m)
Initial deflection of the stator spring d0 (mm)
4.2 Performance of RTC induction motor
Speed responses of the induction motor with and without RTC mechanism are compared in Fig. 13. The RTC induction motor is investigated during acceleration or speed change from 200 to 2000 rpm in 0.17 s (about 1100 rad/s2). Although the rotor speed could not follow the speed profile perfectly, the rotor speed rapidly reaches its stable status in both cases of with and without RTC. Although the rotor speed of the RTC induction motor has very slow oscillation due to the stator rotation, the oscillation is so small to be ignored.
This paper proposed an RTC induction motor considering the dynamic characteristic of open-loop speed control with a variable frequency drive. The RTC induction motor has a rotary stator and torsion spring as well as rotor, bearing and housing. First, dynamic equation of RTC induction motor is introduced and a simulation model for the RTC induction motor is built. Then, the acceleration response of the induction motor with variable speed drive is approximated as a first-order ordinary differential equation. The RTC mechanism such as spring and additional inertia are determined considering the derived acceleration or torque profile. Experimental set-up for the RTC induction motor is built and its control system is constructed using a DSP. Finally, effectiveness of the RTC induction motor is verified with experiments.
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