abdul haseeb
TRANSCRIPT
MODELING OF DC MOTOR SPEED CONTROL
Control Systems Lab
DC MOTOR SPEED
System Modeling Physical Setup 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.
Input of a system is the voltage source (V)
Output is the rotational speed of the shaft dθ/dt.
SYSTEM REQUIREMENTS
we will require that the steady-state error of the motor speed be less than 1%.
it must accelerate to its steady-state speed as soon as it turns on. In this case, we want it to have a settling time less than 2 seconds.
A speed faster than the reference may damage the equipment, we want to have a step response with overshoot of less than 5%.
In short Settling time less than 2 seconds Overshoot less than 5% Steady-state error less than 1%
PHYSICAL PARAMETERS
Physical Parameter Description
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 1Ω
L electric inductance 0.5 H
SYSTEM EQUATIONS
Motor torque is proportional to only the armature current Ia by a constant factor Kt
Τ=KtIa The back emf, ε, is proportional to the angular velocity of the shaft by a
constant factor Ke.
ε=Kes θ By using Kirchhoff's voltage law
Ia = (V – ε)/(Ls+R) Mechanical torque is sum of inertia and friction
Τ=Js2 θ+Ds θ Rotational speed is considered the output and the armature voltage is
considered the input.
θ/V = Kt/[(Ls+R)(Js2+Ds)+ KtKes]
MATLAB REPRESENTATION
• OPEN LOOP RESPONSEJ = 0.01; b = 0.1; K = 0.01; R = 1; L = 0.5; s = tf('s'); P_motor = K/((J*s+b)*(L*s+R)+K^2)
P_motor = 0.01 --------------------------- 0.005 s^2 + 0.06 s + 0.1001
Continuous-time transfer function.
CONTROLLER DESIGN
PID Controller Design : Proportional controlFrom the plot we see that both the steady-state error and the overshoot are too large. When we increase the proportional gain Kp , steady-state error will reduce . When we increase Kp results in increased overshoot, therefore, it appears that not all of the design requirements can be met
with a simple proportional controller.
TUNING THE GAINS
Kp = 100; Ki = 200; Kd = 1;As expected, the steady-state error is now eliminated much more quickly
than before. However, the large Ki has greatly increased the overshoot. Let's increase Kd in an attempt to reduce the overshoot.
SIMULINK
COMBINE REPRESENTATION
Modeling Equations
Controller design
Simulink design
PID controller
DESIGN REQUIREMENTS
FLOW DIAGRAM
State space