ME 335 Boğaziçi University A Study on Motor Speed Control

ME 335 Boğaziçi University System Equations KVL and Newton’s 2’nd law gives : Let : Output : y = Input : u = v a Disturbance w = T l Laplace transforming, we obtain :

ME 335 Boğaziçi University Transfer Functions Where:

ME 335 Boğaziçi University System Parameters For this example, the following values for the physical parameters will be assumed. moment of inertia of the rotor (J) = kg.m 2 /s 2 * damping ratio of the mechanical system (b) = 0.0 Nms * electromotive force constant (K=K e =K t ) = 0.01 Nm/Amp * electric resistance (R) = 0.1 ohm * electric inductance (L) = H * input (V): Source Voltage * output ( ): angular velocity of shaft * disturbance (T l ) : Load torque * The rotor and shaft are assumed to be rigid Reference :

ME 335 Boğaziçi University Numerical Values J=0.0001; b=0.0; Ke=0.01; Kt=0.01; R=0.1; L=0.0005; A=Kt/(b*R+Kt*Ke); A=100 B=1/(b*R+Kt*Ke); B=10000 den=[J*L/(b*R+Kt*Ke) (J*R+b*L)/(b*R+Kt*Ke) 1]; r = roots(den); tau1= -1/r(1); tau2=-1/r(2); tau1 = s.: mech. time constant tau2 = s.: electrical time constant.

ME 335 Boğaziçi University Open Loop Step Response step(A,den,0:.05:1.5) title('Step Response for the Open Loop System')

ME 335 Boğaziçi University Steady State Model y ss = 100 u w where y is in rad/s, u is in Volts and w is in N/m. For example, u = v a = 1.5 Volts gives  ss = 150 rad/s = 1432 rpm. If w = T l = N m., then  ss = = 130 rad/s = 1241 rpm. Result : Without control, the speed decreases (or increases) proportional to w. Controller must increase (or decrease) u, to compensate for the effect of disturbance.

ME 335 Boğaziçi University Feedback Control Measurement : Tachometer gain : Volts/rad/s Simulink block diagram Input saturation : Input voltage v a can be between 0 and 2.5 volts Reference signal : 150 rad/s * Volts/rad/s = 4.2 Volts; is compared with tachometer output.

ME 335 Boğaziçi University Proportional Control y ref is increased from 150 to 160 rad/s. There is ss. error, ss. error decreases as K P is increased

ME 335 Boğaziçi University Disturbance Rejection A step torque disturbance of T l = Nm. is applied Compared to no control (130 rad/s), there is improvement, still there is ss. error.

ME 335 Boğaziçi University PID Controller Control signal is a linear combination of error, integral of error and time rate of change of error.

ME 335 Boğaziçi University PID Control of DC Motor No steady state error, good response.