Modelling and Simulation of engineering systems - Essay Example

The main advantage of SIMULINK over other programming softwares is that, instead of compilation of program code, the simulation model is built up systematically by means of basic function blocks. Through a convenient graphical user interface (GUI), the function blocks can be created, linked and edited easily using menu commands, the keyboard and an appropriate pointing device (such as the mouse). A set of machine differential equations can thus be modelled by interconnection of appropriate function blocks, each of which performing a specific mathematical operation.

Programming efforts are drastically reduced and the debugging of errors is easy. Since SIMULINK is a model operation programmer, the simulation model can be easily developed by addition of new sub-models to cater for various control functions. As a sub-model the induction motor could be incorporated in a complete electric motor drive system (Wade 495-505; Shi 231-235). A generalized dynamic model of the induction motor consists of an electrical sub-model to implement the three-phase to two-axis transformation of stator voltage and current calculation, a torque sub-model to calculate the developed electromagnetic torque, and a mechanical sub-model to yield the rotor speed.

In addition, a stator current output sub-model is needed for calculating the voltage drop across the supply cables. Multiple line equation(s) cannot be represented in ASCII text. ASCII text where Vas, Vbs, and Vcs are the three-phase stator voltages, while Vds and Vqs are the two-axis components of the stator voltage vector Vs. Torque sub-model of induction motor In the two-axis stator reference frame, the electromagnetic T is given by: T = PLm/3(idriqs - iqrids) Mechanical sub-model of induction motor From the torque balance equations and neglecting viscous friction, the rotor speed omega0 may be obtained as follows: Multiple line equation(s) cannot be represented in ASCII text where J is the moment of inertia of the rotor and load and TL is the load torque.

Stator current output sub-model The stator current output sub-model is used to calculate the stator current amplitude according to the following equation: |is| = 2/3 square root of (ie, sub ds)2 + (ie, sub qs)2 A SIMULINK Fcn' block is used to implement the above equation. Simulation System Of Induction MotorThe complete simulation system of the induction motor includes the induction motor model in a power supply sub-model. Power supply sub-model The voltage supply block consists of a three-phase sinusoidal voltage generator and a terminal-voltage calculation block which accounts for the voltage drop in the supply cable.

Simulation ResultsThe induction motor chosen for the simulation studies has the following parameters: Type: three-phase, 7.5 kW, 6-pole, wye-connected, squirrel-cage induction motor Rs = 0.288 OMEGA/ph Rr = 0.158 OMEGA/ph Ls = 0.0425 OMEGA/ph Lm = 0.0412 OMEGA/ph Lr = 0.0418 OMEGA/ph J = 0.4 kg m2 JL = 0.4 kg m2To illustrate the transient operation of the induction motor, a simulation study of direct-on-line starting is demonstrated. At t = 0, the motor, previously