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This paper focuses on the analysis, the modeling and the control of a linearswitched reluctance motor. The application under consideration is medical, and the actuator is to be used as a left ventricular assist device. The actuator has a cylindrical or tubular shape, with a mechanical unidirectional valve placed inside the mover, which provides a pulsatile flow of blood. The analytical expression of the effort based on the linear behavior of the actuator is given. The identification of the characteristics of the prototype actuator and the principle of position control is performed. A modeling of the actuator is proposed, taking into account the variation of inductance with respect to the position. The closedloop position control of the actuator is performed by simulation. A controller with integral action and anticipatory action is implemented in order to compensate the effects of disturbing efforts and tracking deviations. Moreover, a magic switch is performed in the controller to avoid overshoots. The results show that the closedloop response of the actuator is satisfactory.
Heart failure is one of the most common diseases in developed countries. In most of the cases, a left ventricular assist device (LVAD) is used to treat patients. The LVAD assists the failing left ventricle by providing an additional flow of blood in the body [
At the beginning of cardiovascular surgery, mechanical circulatory support (MCS), which is a pneumatic pump, mimics the function of the heart by providing a pulsatile flow of blood. The major limitations are the sheer size of the pump, limited mobility, because of a large drive console, and the need for constant anticoagulation solutions [
To prevent thrombosis, we propose to study a pulsatile flow pump for
The aims of the paper are to describe the characteristics and the modeling of this LSRM structure in order to control it and then to show the applicability of the motor for LVAD. The organization of the paper is as follows: the topology of the proposed LSRM and its basic operational principles are described in
For the application considered, the cylindrical LSRM is a good candidate. Its structure is simple and robust, and the mover part has no windings, as in [
The actuator studied is called Pulsamag and is presented in [
The coils are sequentially excited in order to create a magnetic field moving from one end to the other. Then the cylindrical magnetic mover performs an oscillatory movement. The closed aortic valve pushes the fluid in the flow direction, and when the cylinder comes back to its initial position, the valve is opened, so as not to interact with the fluid.
(
In this low speed application, because of low eddy current losses, the magnetic core does not have to be made of laminated steel. Moreover, due to the cylindrical shape, the normal forces are neutralized. The other advantages of this kind of actuator are its reliability, its simplicity of implementation, its ability to generate a linear motion directly (without mechanical processing),
According to [
The thrust of the mover is:
The physiological needs for a ventricular assist device are a flow of 3 L/min and a pressure of 120 mmHg (16kPa) under a frequency of 2 Hz (120 bpm). Therefore, with a 25 mm diameter valve, the stroke is
According to Equation (1), the control of the position of the mover at a given frequency will fix the blood flow. By setting a value of supply voltage, a current is injected in each phase. Thus, the driving force required is produced and, in accordance with Equation (2), blood pressure is imposed.
From the actuator presented in
The radial dimensions (
(
The sizing and the twodimensional finite element analysis of the actuator are presented in [
We can notice in
The stroke of the actuator depends on: the tooth pitch length,
The total length of the stator,
The total length of the mover,
By assuming a linear model of the basic pattern, the analytical expression of the traction or propulsion force can be obtained using the principle of conversion of energy [
It is to be noted that the lateral force will be high if the air gap length,
The actuator presented in
The prototype dimensions and a picture of the LSRM are given, respectively, in
Prototype dimensions.
Name  Abbreviation  Value (mm) 

Valve radius 

12.5 
Mover yoke thickness 

2 
Mover tooth length 

1.5 
Air gap length 

0.2 
Air gap radius 

16.1 
Stator tooth length 

9 
Stator yoke thickness 

1.5 
External radius 

26.7 
Tooth width 

2.9 
Slot width 

2.9 
Nonmagnetic ring thickness 

1.45 
Total length of the stator 

80 
Total length of the mover 

140 
For the application considered, the desired stroke and the thrust are, respectively, 50 mm and 8 N. According to the above dimensions, the stroke is available.
The winding characteristics of the prototype are given in
Winding characteristics.
Name  Abbreviation  Value 

Number of phases 

4 
Number of coils per phase 

2 
Number of turns per slot 

155 
Turn diameter 

0.335 mm 
Slot area  26.1 mm²  
Coil area  13.66 mm²  
Slot fill factor  52.30% 
The expression of the mmf,
Therefore, for a current supply of
By measurements, it was determined that the prototype had the parameters and characteristics given in
Prototype characteristics.
Characteristic  Value 

Mass of the mover  
Static dry friction force  
Winding resistance (average value)  
Unaligned Position inductance (average value)  
Aligned Position inductance (average value)  
Winding inductance (average value)  
Rate of change of inductance (average value) 
The output power,
By supplying one phase after the other, the average speed can be expressed according to the desired frequency,
In this low speed application (the frequency is low, typically under 3 Hz), the iron losses can be neglected compared to the copper losses. Therefore, the efficiency, η, is given by:
The Joule losses for one energized phase (constituted of
Finally, the Joule losses can be expressed by:
One dimensioning factor for switched reluctance motors is the maximization of the mean torque per copper loss. In [
If we neglect the stator yoke thickness,
By supplying one phase after the other, we can calculate the output power, the input power and the efficiency at different frequencies (
Input power, output power and efficiency
The motor is controlled using a dSPACE system with a DS1005 PWM card and a DS2202 acquisition card. A Mitutoyo LGF550L position sensor with the EH10P signal conditioner is used to obtain the real position of the mover. The power supply of the prototype has been developed by the Novatem SAS Company and consists of four independent Hbridges (one Hbridge per phase).
In this pump application, the functioning of the motor requires a back and forth motion. The motor is to be controlled in position with a sinusoidal variation of the position:
Test bench of Pulsamag prototype.
The control of the motor has been developed using Matlab Simulink software in discrete mode with a sampling period:
Open loop control of the motor. PWM, pulsewidth modulation.
The elements that are inside the dotted box in
By setting a reference signal for the position with a sinusoidal variation, the desired speed has a sinusoidal variation. It is obtained simply by using a derivation block.
To control the motor, we must provide duty cycles for the four Hbridges of the inverter to the “PWM & power supply” block. To do this, the “Motor simplified electric model” block receives the currents,
We assume that the magnetic circuit of the motor has a linear behavior without saturation and that the phases are independent (no mutual inductance). This equation is commonly used in the works dealing with modeling and control of SRM [
The values of R, L and dL/dx are given in
The generation of currents,
Generation of the phase currents according to the reference position.
We can see that when the reference position increases (positive speed), the current supply sequence generated is in the order
The current amplitude is function of the desired force and is determined by:
It is assumed here that only one phase is energized at a time, and only the phase supplied contributes to generating the desired force. Previous assumptions on the linearity, the nonsaturation of the magnetic material and the independence of the phases are maintained. This equation is also used in work [
The desired total force,
Preliminary test in order to determine
The determination of the slope of the curve,
The modeling of the motor is done in two steps. First, from the electrical equation, we construct the estimated currents,
Principle of modeling.
To model the motor phase number,
To simplify, we assume that the rate of change of inductance with respect to the position,
Electrical modeling of one phase of the motor.
The “LSRM Electrical model” block of
Each phase of the motor supplied by an input current,
The sum for
The mechanical equation governing the motion of the mover is given by:
The dry friction force,
Mechanical modeling of the motor.
In order to have a realistic model, the rate of change of inductance is not taken with respect to the position
The rate of change of inductance with respect to the position when supplying one single phase can be modeled by the inductance profile given in
Inductance profiles of the four phases with respect to the position.
When the phases are supplied one after the other, taking care to supply one single phase at a time, the variations of inductances of phases 2, 3 and 4, namely
Values of the functions,
0 < 


10/2.9  10/2.9  
10/2.9  10/2.9  10/2.9  
10/2.9  10/2.9  10/2.9  10/2.9  10/2.9  
10/2.9  10/2.9  10/2.9  10/2.9 
Finally, the mechanical modeling of the motor,
Content of the block diagram “LSRM (linearswitched reluctance motor) Mechanical model”.
The “Matlab Function” calculates the values of
The entire modeling of the motor can be improved by taking into account the values of
The motor being modeled,
Open loop configuration: input (position
The steady state error requires setting up a closed loop control with an integral and derivative terms controller.
From
Closed loop control of the motor.
Thus, a block called “Force Controller” is implemented. From the reference position,
The output of the “Force Controller” block is called the control force,
“Force Controller” block.
(
The flow chart of the Sfunction is presented in
In this paper, we have presented a tubular linearswitched reluctance motor for a medical application. This actuator must provide a pulsatile pump operation for a ventricular assistance device. After describing the operating principle of this actuator, we presented the characteristics of the prototype actuator and the principle of position control. This control is based on a dSPACE control system associated with Matlab Simulink. A dedicated power supply based on a Hbridge inverter for the four phases of the machine has been developed.
A simplified model of the actuator was proposed, which can be generalized to a linearswitched reluctance motor for all applications. This modeling takes into account the variation of inductance with respect to the position and assumes an independence of the phases (and a linear behavior of the magnetic materials).
After this modeling, we present the open and closedloop position control of the actuator in Matlab Simulink. For the closedloop control, a controller with an integral action and anticipatory action, called feedforward, is implemented. We provide the implementation of a magic switch that prevents the integral action to inflate the command and that avoids overshoots of the output. The results obtained show that the use of a simplified model is satisfactory.
In the perspective of this work, a real control of the prototype under dSPACE based on the Simulink models already developed must be carried out.