System Descriptions and Block Diagram

Generally, a PMAC motor drive system with speed feedback control consists of control algorithm, PWM generator and driver circuit, as shown as Fig. 5.1. According to (3-1), the motor model with the parameters shown in Table 5.1 is built as a block in Simulink^®. Besides, the blocks of PWM driver and PI controller have also been built up. Connecting each block, a PMAC motor drive system, as Fig 5.1, is set up, as shown in Fig. 5.2. The simulation of speed control using PI controller is shown in Fig.

5.3. It is noted that the information of rotor position needed by driver is electrical angle, which is the product of mechanical angle and pole pairs.

Fig. 5.1 A PMAC motor drive system with speed feedback control

Speed ref.

Control algorithm

PWM generator

Driver

circuit Motor

Load

Angle feedback Speed

feedback

State vector

Parameter Symbol Value Unit stator resistance Ls 8.5 [mH]

stator inductance Rs 2.875 [Ω]

inertia Jm 4e-3 [k_g⋅m²]

pole pairs P 3

EMF constant KE 0.175 [Wb]

Table 5.1 Specifications of motor

Fig. 5.2 A PMAC motor drive system in Simulink^®

Fig. 5.3 Speed responses of the system shown in Fig. 5.2

command actual speed

Then, replacing above system with sensorless drive system by using the sliding observer and adaptive estimator designed before, as shown in Fig. 5.4. The sliding observer and the adaptive estimator blocks are built up with the parameters shown in Table 5.2. The position and velocity sensorless control system is modeling in Simulink^®, and the configuration of overall system as shown in Fig. 5.5. The sliding observer estimates the flux linkage from the phase voltages and currents. The rotor position can be obtained by using the estimated flux linkage. The velocity can be obtained by using the adaptive velocity estimation from the estimated flux linkage.

Parameter Symbol Value Unit

switching gain K -10000 feedback gain g₁ -8.5e-3 feedback gain g₂ 0.5*8.5e-3

feedback gain g′₁ ω_re

feedback gain g′₂ ω_re

adaptive gain KI 15000000 [rad/s/Wb/A]

Fig. 5.4 A PMAC motor sensorless drive system

Table 5.2 Parameters of observer and estimator Motor

Controller

Driver Circuit PWM

Generator

Sliding Observer Adaptive

Estimator

Motor Plant

voltage current

flux linkage velocity

position

Fig. 5.5 The position and velocity sensorless control system

5.2 Simulation Result and Analysis

In this section, several cases of different speed command are simulated. It is should be noted that the position and velocity sensorless estimation is switch on after the motor is started up successfully. Then, the information of feedback position and velocity is replaced with the estimation values while the motor is speeded up to 50 rpm. The method of start-up has been discussed in section 4.1, but it is not simulated here. Following simulations focus on the responses of the system at different speed commands and the robustness of the system to parameter deviations.

First, the acceleration and deceleration from 60 rpm to 2000 rpm with rectangular speed command will be simulated with 50µs step size. Second, the acceleration and deceleration sinusoidal speed command will be simulated.

Fig. 5.6 Information of the D-axis current in case (I)

Fig. 5.7 Information of the Q-axis current in case (I)

Fig. 5.8 Information of the D-axis flux linkage in case (I)

Fig. 5.9 Information of the Q-axis flux linkage in case (I)

Fig. 5.10 Information of the rotor position in case (I)

Fig. 5.11 Information of the rotor velocity in case (I)

Fig. 5.12 Information of the rotor position in case (II)

According to the simulation results as shown above, there are several conclusions can be made. Without any parameter variation, the current estimation fits the actual current rapidly with a near zero error. It should be noted that the magnitude of the estimation error is related to the sampling rate. It is clear that the error is smaller when the sample rate is faster. From Fig. 5.8 and Fig. 5.9, the estimation of the flux linkage is robust to the velocity variation so that the position estimation has high accuracy with only 1 degree error, as shown in Fig. 5.10. The simulation result of the acceleration and deceleration from 30 rpm to 2000 rpm is shown in Fig. 5.11. The feasibility of the proposed method is verified at low and high speed. The desirable performance is also obtained in the second case. Then, the parameter variations will

Fig. 5.13 Information of the rotor speed in case (II)

be considered in simulation. The 10% resistance variation and the 10% inductance variation will be put into the model. From Fig. 5.14 and Fig. 5.15, the steady flux linkage estimation and velocity estimation are not effected by the resistance variation, but the transient responses have bigger error. Comparing with the resistance variation, the inductance variation causes worse influence. The error of position estimation increases to 3 degree when the velocity is accelerated or decelerated, as shown in Fig.

5.16. In Fig. 5.17, a large error occurs in the velocity estimation at the instant of speed command changing. Summarily, the parameter variations cause the estimation error increasing. However, the magnitude of the error increment can still be tolerant due to the robustness.

Fig. 5.14 Information of the rotor position with resistance variation

Fig. 5.15 Information of the rotor speed with resistance variation

Fig. 5.16 Information of the rotor position with inductance variation

Fig. 5.17 Information of the rotor speed with inductance variation

Chapter 6

Conclusions and Future Works

In this thesis, the analysis of BLDC motor’s characteristics has been done by analytic and FEM based methods. After deriving the equation of energy conversion and the output torque equation with respect to back-EMF, the principle of motor driving has been realized clearly. Furthermore, employing results of FEM analysis, an explicit mathematic model can be established so that the unexpectable error of the actual control system can be reduced. Besides, an integrated sensorless drive method for PMAC motors has been proposed. The proposed sensorless drive method can be employed to drive a PMAC motor from standstill to desired speed with wide speed range. The fault of start-up, which exits in conventional sensorless drive method, has been overcome. It is different from conventional start-up method that the initial position of the rotor is detected to avoid the temporary reverse rotation. After starting up successfully, a sliding observer is designed to estimate the rotor position and velocity. Comparing with the actual value, the estimation has small estimated error and is robust to the back-EMF constant and parameter variation. The overall system is established and simulated in Matlab^®−Simulink^® to verify the feasibility.

However, there are several topics could be discussed. First, the implementation of the hardware using DSP or FPGA is worth proceeding. Second, the integration of Flux 2D and Matlab^®−Simulink^® is attractive due to the concept of full system simulation. Recently, the well-known FEM based software companies, such as Ansoft and Cedrat are devoted to popularize the FEM based simulation to every application.

The FEM analysis has high accuracy and fit the actual situation due to that all nonlinear conditions are considered. In motor application, the torque or speed ripple

can be analyzed efficiently by FEM analysis. All dynamic characteristics of the motor can be known well by using full system simulation. Besides, the fuzzy logic can be considered to increase the reliability of the proposed start-up procedure [6]. The reliability of the proposed start-up procedure is dependent on the resolution of the current sensors. The accuracy of the detection is influenced by the noise critically. The fuzzy logic may reduce the weight ratio of the sudden variation. Furthermore, the field-weakening control is worth studying. It is well known that the back-EMF is proportional to the speed. The provided phase voltages can not generated the phase currents to produce the torque at rapid speed due to the offset caused by back-EMF.

Considering the adjustable-speed motor drive without velocity constraint, the field-weakening control is needed.

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