Electromechanical Machines Simulation Toolkit - Ovak Technologies

Electromechanical Machines Simulation Toolkit User Manual Ovak Technologies 2015

Contents 1. 2. 3. Introduction . 3 1.1. Definitions and acronyms.3 1.2. Purpose .3 1.3. Scope .3 1.4. Overview .3 Structure . 3 2.1. Brushed DC motor .3 2.2. BLDC motor .5 2.3. Stepper motor .7 2.4. Asynchronous AC motor .8 2.5. Synchronous AC motor .9 Examples . 12 3.1. Angular position control system.12 3.2. Stepper motor manual control .13 3.3. BLDC motor hall sensor six steps control system.14 4. Palettes items . 17 5. System requirements . 18 6. LabVIEW features sand concepts used . 18 7. Support information . 19 8. References . 19 2

1. Introduction 1.1. Definitions and acronyms EMMSim – Electromechanical Machines Simulation LV – LabVIEW BL – Brushless DC – Direct current AC – Alternating current EMF – Electromotive force BLDC – Brushless direct current electric motor 1.2. Purpose This document is designed to provide necessary information to LabVIEW developers in order to create applications using EMMSim toolkit. The document describes the architecture of the toolkit and provides the necessary information about how to use it. 1.3. Scope EMMSim is a set of electrical motors' models that is designed to help user to create systems simulations where electrical engines are needed. The user can choose the motor type, its parameters, connect it to any other system and follow the way it works. 1.4. Overview EMMSim is a palette of different types of motors and additional subsystems, which will help user to simulate motors’ controls. 2. Structure 2.1. Brushed DC motor The brushed DC motor is a classic motor, which is widely used in control systems. The main principle is based on Fleming's left-hand rule. In order to understand this rule, please see the picture below. Figure 1 Fleming’s left-hand rule The forces cause a turning effect on the coil, which rotates it. 3

The motor parameters supposed to be constant during the simulation are the following: J – motor inertia, kg.m 2; B – viscous damping coefficient; R – internal resistance, Ohm; L – internal inductance, mH; Kt – torque constant, N-m/A; 𝐾𝑒𝑚𝑓 – back EMF constant, V/rad/s; Omega (t 0) – angular speed of the motor right before it was started, rad/sec. Figure 2 Brushed DC Motor Front Panel Motor input signals are the following: Vapp – voltage applied, V; Mc – load torque, N-m. The user can follow transient phenomena. The following differential equations were used to create the model: [1] 1 (𝐼(𝑡)𝐾𝑇 𝜃𝐵̇) ( ) 𝜃̈ 𝐽 [𝑉𝑎𝑝𝑝 𝜃̇ 𝐾𝑒𝑚𝑓 𝑅𝐼(𝑡)] 1 𝑑𝑖 𝐿 𝑑𝑡 The angular speed is the following: 𝜔 𝑑𝜃 𝑑𝑡 (rad/sec) The torque equation is the following: 𝑀 𝐽 𝑑𝜔 𝑀𝑐 𝑑𝑡 The purpose is to calculate motor angular speed and torque. 4

2.2. BLDC motor Brushless motors are synchronous motors, which are powered by DC electric source. They are permanent magnet motors where the function of commutator and brushes were implemented by solid-state switches. There are single-phase, two-phase and three-phase BLDC motors. However, the most popular and widely used are three-phase motors. They produce a trapezoidal back EMF, and motor current generates a pulsating torque. The motor parameters supposed to be constant during the simulation are the following: R – stator resistances per phase are equal for all phases. Ra Rb Rc R; L – stator inductances per phase are equal for all phases. La Lb Lc L; M – the mutual inductances are equal too. M Mab Mac Mbc Mba Mca Mcb; B – damping constant; J – inertia of the motor; 𝐾𝑒𝑚𝑓 – back EMF constant. The motor input signals are: Va, Vb, Vc (V) voltage inputs on phases; Mc (N-m) load torque. Figure 3 Brushless DC motor Front Panel The purpose is to calculate motor angular speed and rotor angle θ. Three-phase BLDC motor equations are the following: 𝑉𝑎 𝑖𝑎 𝑅 𝐿 𝑑𝑖𝑎 𝑑𝑖𝑏 𝑑𝑖𝑐 𝑀 𝑀 𝑑𝑡 𝑑𝑡 𝑑𝑡 𝑉𝑏 𝑖𝑏 𝑅 𝐿 𝑑𝑖𝑏 𝑑𝑖𝑎 𝑑𝑖𝑐 𝑀 𝑀 𝑑𝑡 𝑑𝑡 𝑑𝑡 𝑉𝑐 𝑖𝑐 𝑅 𝐿 𝑑𝑖𝑐 𝑑𝑖𝑏 𝑑𝑖𝑎 𝑀 𝑀 𝑑𝑡 𝑑𝑡 𝑑𝑡 When a BLDC motor rotates, each winding generates a back EMF voltage. It opposes the main voltage supplied to the windings according to Lenz's Law. The speed increases, back EMF also increases and the polarity of the back EMF is opposite to the energized voltage. The back EMF is a function of rotor position (θ) and has the amplitude E 𝐾𝑒𝑚𝑓 * ω (𝐾𝑒𝑚𝑓 is the back EMF constant). 5

The respective back EMF in the windings is represented by the following equations: [2] 6𝐸 𝜋 ) 𝜃 (0 𝜃 ) 𝜋 6 𝜋 5𝜋 𝐸( 𝜃 ) 6 6 6𝐸 5𝜋 7𝜋 𝑒𝑎 ( ) 𝜃 6𝐸 ( 𝜃 ) 𝜋 6 6 7𝜋 11𝜋 𝐸 ( 𝜃 ) 6 6 6𝐸 11𝜋 𝜃 12𝐸 𝜃 2𝜋) ( ) ( { 𝜋 6 𝜋 𝐸 (0 𝜃 ) 2 6𝐸 𝜋 5𝜋 ( ) 𝜃 4𝐸 ( 𝜃 ) 𝜋 2 6 5𝜋 9𝜋 𝐸( 𝜃 ) 𝑒𝑏 6 6 6𝐸 9𝜋 11𝜋 ( ) 𝜃 10𝐸 ( 𝜃 ) 𝜋 6 6 11𝜋 𝐸 𝜃 2𝜋) ( { 6 𝜋 𝐸 (0 𝜃 ) 6 6𝐸 𝜋 𝜋 ( ) 𝜃 2𝐸 ( 𝜃 ) 𝜋 6 2 𝜋 7𝜋 𝐸 ( 𝜃 ) 𝑒𝑐 2 6 6𝐸 7𝜋 9𝜋 ( ) 𝜃 8𝐸 ( 𝜃 ) 𝜋 6 6 9𝜋 𝐸 ( 𝜃 2𝜋) { 6 ( The generated electromagnetic torque is the following: 𝑇𝑒 𝐾𝑒𝑚𝑓 {𝑓𝑎 (𝜃)𝑖𝑎 𝑓𝑏 (𝜃)𝑖𝑏 𝑓𝑐 (𝜃)𝑖𝑐 }(Nm) 𝑓(𝜃) 𝑒 𝐸 The simple system equation of motion is: 𝐽 𝑑𝜔 𝐵𝜔 𝑇𝑒 𝑀𝑐 𝑑𝑡 Where, Mc is the load torque. 6

2.3. Stepper motor Stepper motors are usually used in positioning problems via digital control. There are two, four and eight phase motors. The current motor is two-phase stepping motor and is controlled by two impulse voltage signals. The physically constant parameters for the motor are the following: R – active resistance of a stator wind, Ohm; L, L0, M, M0 – to calculate L1, L2, M which are correspondingly first and second phase inductions and their mutual induction; D – viscous damping coefficient; 𝐽𝑠𝑢𝑚 – rotor complete moment of inertia, kgm 2; 2p – number of rotor poles; λ – angle between two phases, rad; 𝛹𝑚 – maximum flux linkage, weber; Omega (t 0) – angular speed right before motor starts. Figure 4 Stepper motor Front Panel Motor input signals are the following: U1, U2 (V) voltage inputs on phases; Mc (N-m) load torque. The purpose is to have the following outputs: Omega out (rad/sec) – motor angular speed; Theta (rad) – rotor angular position. The following equations are used to create dynamic characteristics of the system:[4] 𝑈1 𝑖1 𝑅 𝐿1 𝑈2 𝑖2 𝑅 𝐿2 𝑑𝑖1 𝑑𝑖2 𝑑𝑖𝑐 𝑑 (𝜓 sin 𝑝𝛳) 𝑀 𝑀 𝑑𝑡 𝑑𝑡 𝑑𝑡 𝑑𝑡 𝑚 𝑑𝑖2 𝑑𝑖1 𝑑𝑖𝑐 𝑑 (𝜓 sin 𝑝(𝛳 𝜆)) 𝑀 𝑀 𝑑𝑡 𝑑𝑡 𝑑𝑡 𝑑𝑡 𝑚 7

Where, 𝐿1 𝐿0 𝐿 cos 2𝑝𝜃 𝐿2 𝐿0 𝐿 cos 2𝑝(𝜃 𝜆) 𝜆 𝑀 𝑀0 𝑀 cos 2𝑝 (𝜃 ) 2 The equation of torques on the rotor: Me h𝜓𝑚 𝑖1 sin p 𝛳 𝜓𝑚 𝑖2 sin 𝑝(𝛳 𝜆) 𝐽𝑠𝑢𝑚 𝑑 2 𝛳 𝐷𝜔 𝑀𝑒 𝑀𝑐 𝑝 𝑑𝑡 Where i1 and i2 currents are calculated in “Stepper motor subsystem 1.vi”. 2.4. Asynchronous AC motor The second name of this motor is “Induction motor”. This motor’s rotor and generated magnetic field are rotating with different frequencies. The rotating torque is generated as a result of interaction between stator’s rotating magnetic field and current in the rotor. The motor's parameters which are supposed to be constant during the simulation are in the "Parameters" cluster [5]. J – inertia moment of the rotating parts; r1 – resistance; x1 – inductive resistance of the rotor; x’2 – inductive resistance of the rotor; r’2 – resistance; c – coefficient; Phase num – number of phases; Pole pairs num – number of pole pairs. The input signals of the motor are: Amplitude – input AC voltage amplitude; Frequency – input AC voltage frequency; Load torque – external torque influencing on the rotor. This VI is designed to calculate output angular speed and generated torque. 8

Figure 5 Asynchronous AC motor Front Panel The rotating torque is: M m1 I ′ 2 2( R′ 2 S) ω1 This equation can be transformed using replacement diagram. Thus, the current can be calculated in the following way: I′ 2 U1 ′ 2 (r1 cR 2 ) (xs1 cx ′ S2 )2 S As ω1 2πn1 60 2πf p Assuming that p, m1 , r1 , R′ 2 , xs1 , x ′ S2 , U1 , f are constant we have M 2.5. m1 pU1 2 r2 ′ 2πf[(r1 cr2 ′ )2 (xs1 cxS2 ′ )2 ] Synchronous AC motor The synchronous motors are AC motors which rotation speed is synchronized with rotation of the magnetic field generated in stator. In order to have a mathematical model of a pole synchronous motor we use d-q coordinate system. Let us have a look on that system equations after explaining the main principles of synchronous motor’s work. Just like the other motors, synchronous motors have stator and rotor. The stator of synchronous motor and stator of induction motor are similar in construction. The rotor is either a permanent magnet or an electrical magnet with DC power supply. DC power either is given to rotor with external supply or is transformed from main AC power. As the field is generated in the stator, it is relating with the rotor field and rotates it. The main feature of this motor is that its speed does not depend on the load. Now let us discuss the mathematical model of this motor. 9

The equations are given as vector equation [6]. ⃗ 𝑅𝑖 𝐿 𝑑𝑖 𝜔𝑟 𝐿𝑧 𝑖, 𝑈 𝑑𝑡 Where, ⃗ 𝑈𝑑 , 𝑈𝑞 , 𝑈𝑓 , 0, 0 𝑡 , 𝑈 𝑖 𝑖𝑑 , 𝑖𝑞 , 𝑖𝑓, 𝑖𝑑𝑟 , 𝑖𝑞𝑟 , 𝑅𝑠 𝑅 0 𝐿𝑑 𝐿𝑧 0 0 0 𝑅𝑓 𝑅𝑑𝑟 𝐿𝑑 0 𝐿 𝑀𝑑 𝑀𝑑 0 𝑅𝑠 𝑅𝑞𝑟 0 𝐿𝑞 0 0 𝑀𝑞 𝑀𝑑 0 𝐿𝑓 𝑀 0 𝑀𝑑 0 𝑀𝑑 𝐿𝑑𝑟 0 0 𝑀𝑞 0 0 𝐿𝑞𝑟 𝐿𝑞 0 0 0 0 0 𝑀𝑑 0 0 0 0 𝑀𝑑 0 0 0 𝑀𝑞 0 0 0 0 𝜔𝑟 – rotor rotation speed; 𝑅𝑑 , 𝑅𝑞 , 𝑅𝑓 , 𝑅𝑑𝑟 , 𝑅𝑞𝑟 – stator active resistances by d-q axes, energizing and damper resistances by d-q axes; 𝐿𝑑 , 𝐿𝑞 , 𝐿𝑓 , 𝐿𝑑𝑟 , 𝐿𝑞𝑟 – own inductances by d-q axes, energizing and damper inductances by d-q axes; 𝑀𝑑 , 𝑀𝑞 – mutual inductances between winds by d-q axes; 𝑈𝑑 , 𝑈𝑞 – stator voltages by d-q axes; 𝑖𝑑 , 𝑖𝑞 , 𝑖𝑓 , 𝑖𝑑𝑟 , 𝑖𝑞𝑟 – stator currents by d-q axes, energizing and damper currents by d-q axes. The electromagnetic torque 𝑀𝑒 is 𝑀𝑒 𝑈𝑑 𝑖𝑑 𝑈𝑞 𝑖𝑞 𝑅𝑠 (𝑖𝑑 2 𝑖𝑞 2 ) The rotor movement equation is 𝑇𝑗 𝑑𝑠 𝑀𝑐 𝑀𝑒 𝑑𝑡 𝜔𝑟 (1 𝑠)𝜔𝑠 10

Where, 𝑇𝑗 – inertia constant; 𝑀𝑐 – load torque; 𝜔𝑠 – synchronous rotation speed. The discussed matrix equation is equal to a multi circuit diagram. Where, 𝐸𝑑1 𝜔𝑟 𝐿𝑞 𝑅𝑞 𝐸𝑑2 𝜔𝑟 𝑀𝑞 𝑖𝑟𝑞 𝐸𝑞1 𝜔𝑟 𝐿𝑑 𝑖𝑑 𝐸𝑞2 𝜔𝑟 𝑀𝑑 𝑖𝑓 𝐸𝑞3 𝜔𝑟 𝑀𝑑 𝑖𝑑𝑟 Figure 6 Equivalent circuit The mathematical model is built according to these circuits. 11

Figure 7 Synchronous AC motor Front Panel 3. Examples 3.1. Angular position control system An angular position control system is shown in this example. Control system is implemented with Brushed DC motor and PID Subsystem. There are random disturbance torques influencing in the controlled object. User can follow control process on the front panel. Clicking on “Slow” button you can follow the process in slow motion. [3] Figure 8 Angular position control “Description” tab 12