Modelling and Simulation of Field-Oriented Control of Permanent Magnet Synchronous Motor

A permanent Magnet Synchronous Motor is an electric motor driven by permanent magnets, finding widespread use in industrial and robotic applications due to their high efficiency, low inertia and high torque to volume ratio. Various control techniques have been implemented to make drive systems control more precise and efficient. This paper presents a Field Oriented Control (FOC) as a novel method to effectively control motor torque and speed. The primary objective of this research is to develop a detailed model of FOC-PMSM and simulate its dynamic behaviour under various operating conditions. The system is simulated in MATLAB/Simulink to check the validity, reasonability and expected outcomes. Simulation results show that the designed control system can track speed and current references with minimum error. PMSM depicts better dynamic performances with FOC implementation.


Introduction:
DC motors dominated variable speed and drive systems ranging from low-power to high-power applications for decades due to their cheaper and simpler control mechanism.However, DC motors have significant limitations, including being uneconomical due to frequent maintenance, limited speed range of operation, lack of overload capacity and robustness, etc. [1].At that time, AC motors were operated under a fixed grid frequency.Nowadays, AC electric-drive control systems are more widely used in various applications than DC motor systems [2].Recent advancements in permanent magnet materials, solid-state devices and microelectronics have led to new energy-efficient and high-performance electric drives that use Brushless DC motors or PM synchronous motors.Performance comparison between these motors shows that PMSM reveals better efficiency, robustness, high power-to-weight ratio, and low noise than the BLDC motor [3].PMSMs is a type of synchronous motor with three-phase windings on the stator and rotor fitted with permanent magnets.
There is no need for slip rings and brushes as a permanent magnet in the rotor provides a magnetic field.Generally, a rare earth magnet is used as a permanent magnet of the rotor.PMSM has high performances, very good controllability in full-speed operating range, lower maintenance cost, high efficiency and low power-to-weight ratio compared to other motor types [4].This type of motor is widely used in industrial applications, robotics and hybrid vehicles.Various advanced control techniques are employed to optimise the performance of Permanent Magnet Synchronous Motors (PMSM) in variable speed drive applications.Some of the control techniques include field-oriented control (FOC), direct torque control (DTC), model predictive control (MPC), sliding mode control (SMC), and many more.The choice of this technique depends on the specific application, desired performance, and system complexity.The only drawback of these permanent magnet synchronous motors is the algorithms and electronics required to control the current in the motor are complex.Also, the drawback of cogging torque in PMSM can be eliminated through suitable design or electronic justification [5].The technique used in this work is field-oriented control simplifies complexity and makes motor control similar to DC motors.

Motor Model in "abc" Frame:
Three-phase AC fed to stator windings produces a rotating magnetic field.The rotor has a highperformance magnet to obtain a strong magnetic field such as neodymium iron boron or rare earth magnetic materials.The interaction between the rotor and stator magnetic field generates electromagnetic torque, which can be controlled by regulating the amplitude and phase of the three-phase currents.This can be achieved by using a three-phase inverter with Pulse Width Modulation (PWM) techniques.In order to facilitate analysis, the following assumptions are made: three-phase symmetrical stator winding, uniform air gap, ignoring the end effect, neglecting iron loss and magnetic saturation, linear magnetic circuit, converter provides ideal three-phase power, higher harmonics is ignored, ignoring rotor shaft friction.Motor voltage balance equations is given by: [6] (1) The motor flux balance equation is given by: Torque expression is given by: The equation of motion for the motor is given by:  =Electrical angular velocity Above analysis of motor in abc frame shows PMSM is a multi-variable coupled and non-linear time varying system.The direct use of traditional control cannot achieve effective control and as well system complexity is increased.

Field Oriented Control
FOC is a type of vector control in which phase and amplitude for a motor stator voltage or current vector is controlled at the same time.FOC simplifies the control of PMSM by making it to behave like a separately excited DC machine in which developed torque and magnetizing field can be controlled independently [7].For this three-phase time variant system (abc) is converted into time invariant system (dq).This causes decoupling of Torque and flux component to make control simple.Clarke and Park transformation helps to convert abc components into dq components.The mechanical equations are:  There is decoupling between these components i.e. both can be controlled independently.In this paper   = 0 is used to obtain maximum torque per ampere as similar to separately excited dc motor.Three PID controllers are tuned properly to track the reference commands under various operating conditions.These motor parameters are tested by applying FOC technique to observe the motor performances.The whole system is simulated in MATLAB/Simulink and shown in figure below.Since PMSM is a Multi-Input Multi-Output system, coupling exists between d-axis and q-axis.Decoupling block is used to remove the coupling between them and make system linear.This is shown in figure below.Error signals obtained by comparing speed and current references is regulated using PID controllers to obtain id and iq which eventually is fed to motor to obtain desired torque and speed.FOC method of PMSM uses three PID controllers, two of them are used to regulate d-axis and q-axis component and one is used to regulate speed.Frequency response method is used to tune PID controller with design margin=60 °and crossover frequency=

2𝜋𝑓 𝑠 10
Open loop transfer function is [7]   To simplify the design of speed PI controller, one can approximate the q-current close loop transfer function to be first order system (low pass filter).PI speed will be   =0.2769,   =107.87

Result and Discussion
The validity and Torque speed Response of Field Oriented Control of PMSM is examined.Motor is subjected to the variable speed at different instant of time.Reference input to the motor and output response at different instant is shown in Figure below     For the applied load torque the electromagnetic torque response of motor is shown below.

Figure 1 :]
Figure 1: Reference Frame The combined Clarke and Park Transformations can be written in Matrix form as:

Figure 2 :
Figure 2: Implementation of FOC on PMSM Above figure shows the general block diagram for implementation of FOC on PMSM.Motor is modelled in dq frame with use of transformations.The torque generated by motor depends on current vector..  =

Figure 3 :
Figure 3: modeling of PMSM in dq frame Motor is modelled in MATLAB/Simulink in dq frame using equations given as before.It is subjected to various load conditions.Motor parameters used in above model is shown in table below

Figure 11 :
Figure 11: Torque response of motor The transient torque response of motor with this control on varying load is given below

Table 1 :
Motor parameters

Table 2 :
Transient response analysis

Table 3 :
Motor load

Table 4 :
Torque response analysisSuccessful modelling of PMSM in dq coordinate frame and implementation of closed loop fieldoriented control of PMSM using MATLAB/Simulink shows better dynamic performances of motor.Upon the various changes in reference speed and load torque to the motor at different instant of time, speed overshoot of 2.068% and torque overshoot of 62.42% with minimum settling time was observed.Moreover, maximum torque per ampere can be obtained like DC motor by making direct axis current zero.This control techniques removes the coupling terms within motor and made PMSM motor control simple and equivalent to DC motor.Highly efficient and robust PMSM can be a suitable for variable speed drives ranging from high power applications to low power applications through this control technique5.AcknowledgementThis project was supported by the Department of Electrical Engineering at Pashchimanchal Campus.