PERMANENT MAGNET DC MOTOR ANALYSIS USING MATLAB

HELLO FRIENDS!!!!!

I am here to share my project work with you. in this project, i have done a comparative analysis of PMDC motor  to  show the variation in response by changing its parameters. we'll start with PMDC introduction....

1-Permanent Magnet DC motors

PMDC machines are found in a wide variety of low-power applications. the field winding is a permanent magnet. they do not require external excitation, less space requirement and they are cheaper.

PMDC motors have found their applications in the robotic systems requiring small actuators that can easily be tested and formulated.

Basic Theory

The stator magnetic field is generated by permanent magnets; no power is used in the field structure. The stator magnetic flux remains essentially constant at all levels of armature current and, therefore, the speed torque curve of the PM motor is linear over an extended range (see fig 1).

Fig. 1. Permanent Magnet DC motor

Fig. 2. Variation of current and speed with Torque

With modern ceramic magnets, the stalled torque will tend to be more linear than for a comparable wound field motor.

The linear speed torque curve is a result of use of permanent magnets, since in the case of these motors, the armature reaction flux stays orthogonal to the permanent magnet flux, since the permeability of ceramic magnetic material is very low (almost equal to that of air). In addition the high coercive force of the magnetic materials resists an change in flux whenever the armature field enters, thus the result is the linear torque characteristics.

Advantages of the PM DC motors:

1. The electrical power need not be supplied to generate the stator magnetic flux. And hence reducing the power losses. Thus, the Pm motor thus simplifies power supply requirements, while at the same time it requires less cooling.
2. They had linear torque-speed characteristics.
3. High stall (accelerating) torque.
4. A small frame and lighter motor for a given output power. This is because their radial dimension is typically one forth that of the wound field for a given air gap.
   
   
   2-Motor Equations and Transfer Function
   
   
   In PM DC the permanent magnets produce a constant field flux, Φ_f. in steady state the electromagnetic torque, T_em is given by;
   
   
   Tem = k_T Ia …(1)
   Where, k_T is the torque constant of the motor. In the armature circuit a back emf, E_a is generated by the rotation of the armature conductors at speed wm in the presence of field flux, and in given by;
   Ea = k_E w_m …(2)
   When a controllable voltage V_i is applied to the armature terminals to establish I_a. Thus I_a is determined by the V_i, the back-emf E_a, the armature winding resistance R_a, and the armature winding inductance L_a, as;
   
   
   Vi = Ea +Ia Ra + La di/dt …(3)
   The interaction of T_em (electromagnetic torque generated) with the load torque, T_L(t) is given by;
   
   
   Tem = J dw_m/dt ₊ B w_m + T_L(t) …(4)
   Where, J and B are total equivalent inertia and damping, of the motor load combination and T_L(t) is the total working torque of the load.
   
   Fig. 3. DC Motor Equivalent Circuit
   
   
   
   
   The equation (3) and (4) are termed as the electrical and the dynamic equations respectively.
   Motor Transfer Function
   Equation (1), (3) and (4) provide a model for the motor which describes a relation between its variables. Now for the motor to be used as a component in a system, it is described in a transfer function between motor voltage and its velocity.
   For this purpose we can assume that T_L equals zero for the time being, and then apply the laplace transforms to the motor equations, we obtain;
   
   
   Tem(s) = k_T Ia(s) … (5)
   Vi(s) = k_E w_m(s) + Ra Ia (s)+ sLa (s)Ia(s) … (6)
   Tem (s) = sJ w_m(s) ₊ B w_m (s) … (7)
   Solving these equations;
   
   
   
   
   Fig.4. Block diagram representation of the Motor and Load