Project - Speed Control of a Direct Current (DC) motor

Aim: Speed Control of a Direct Current (DC) motor.

Objective :

In this project, a Simulink model for the DC motor will be first developed per the schematic shown in Figure 1.

Use the Proportional, Integral, and Derivative (PID) control design knowledge gained in the training to design, develop and test a controller to maintain a desired speed for the motor.

Ans:

A common actuator in control systems is the DC motor. It directly provides rotary motion and, coupled with wheels or drums and cables, can provide translational motion. The electric circuit of the armature and the free-body diagram of the rotor are shown in the following figure:

For this example, we will assume that the input of the system is the voltage source () applied to the motor's armature, while the output is the rotational speed of the shaft . The rotor and shaft are assumed to be rigid. We further assume a viscous friction model, that is, the friction torque is proportional to shaft angular velocity.

The physical parameters for our example are:

(J)     moment of inertia of the rotor     0.01 kg.m^2

(b)     motor viscous friction constant    0.1 N.m.s

(Ke)    electromotive force constant       0.01 V/rad/sec

(Kt)    motor torque constant              0.01 N.m/Amp

(R)     electric resistance                1 Ohm

(L)     electric inductance                0.5 H

ω(s)/Vs(s) = Kt / J⋅La⋅s2+(J⋅Ra+B⋅La)⋅s+(B⋅Ra+kt⋅km)

• Here the Speed control of a DC motor is either done manually by the operator or by means of an automatic control device.
• This is different to speed regulation where the speed is trying to be maintained or regulated against the natural change in speed due to a change in the load on the shaft

• so the speed can be varied by changing:

  1. The terminal voltage of the armature V
  2. The external resistance in armature circuit R_a
  3. The flux per pole

• So Terminal voltage and external resistance involve a change that affects the armature circuit while flux involves a change in the maginetic field

• so Therefore speed control of DC motor can be classified into:

  1. Armature Control Methods
  2. Field Control Methods

Simulink model :

• Here first we need to creat simulink model of the DC motor and make it as subsytem called the DC motor
• So next the subsytem of DC motor is connected to the discrete PID controller which helps in maintaining the desired speed
• So after the PID controller we need to start with the kp ki kd such as 1.0 1.0 0 after tunin accordingly so by this we can adjust the kp ki kd values
• Which is used to obtaine the control design objectives

Matlab script to define modeling and control design parameters:

M-file to make subplots:

Without using PID block Simulation model:

Without using PID block result:

Simulink model using PID block:

PID Tune:

PID tuning we set kp ki kd which is used to obtaine the control objectives of the settling time , overshoot time and steady state error

Prameters:

Value of overshoot, rise time, settling time, and steady-state error.

The DC motor is getting stable.

PID controller is needed to design with a gain value of kp,kd, ki.

Now For maintaing the stabilty of a dynamic system :

Out put results:

Case : 1 When maintaining a desired speed of the motor at 30:

Case : 2 When maintaining a desired speed of the motor at 100 :

Case : 3 When maintaining a desired speed of the motor at 230 :

In above cases,we change desired speed as 30 in case 1 ,100 in case 2 and 230 in case 3 , since all the case, Plotting Remains same. Hence, we maintain desired Speed For a Dc Motor.

Conclusion:

we have desined In this project a Simulink model for the DC motor as shown in Figure 1.and also we Use the Proportional Integral and Derivative PID control design knowledge gained in the training to design develop and test a controller to maintain a desired speed for the motor.