servo_motor - SERVO MOTOR DYNAMICS Rajesh Rajamani...

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Unformatted text preview: SERVO MOTOR DYNAMICS Rajesh Rajamani Department of Mechanical Engineering University of Minnesota PRINCIPLES Conductor of length L in a magnetic field of flux density B carrying a current I Force on the conductor = BIL When a conductor moves in a magnetic field with flux =BA , a current is induced in it e d dt equal to called back-emf: it is in such a direction as to produce a current that sets up magnetic fields which tend to neutralize the change in magnetic flux 1 SERVO MOTOR DYNAMICS L V (t ) em i R Electrical system: di V (t ) L Ri em 0 dt J em K m Mechanical system: J d T K mi dt T K mi SERVO MOTOR DYNAMICS L V (t ) i R em J 1 s I ( s) L J H ( s) V (s) R K 2 s s m L J JL Km Km ( s ) R JL G ( s) 2 V (s) L J R K s 1 s 1 s s m L J JL R 2 SERVO MOTOR DYNAMICS V (t ) + Motor Amplifier Encoder Motor: G ( s) ( s ) G V ( s ) Te s 1Tm s 1 Te L R Tm J Including amplifier and encoder dynamics: G Te s 1Tm s 1 Ka Ta s 1 V (s ) K enc s (s ) SERVO MOTOR DYNAMICS V (t ) V (s ) + Motor Amplifier Ka Ta s 1 G Te s 1Tm s 1 Encoder K enc s (s ) Tm 8.8ms Assume Tm Te Ta { Ta 2 ms Te 2.27 ms Good approximation: V (s ) K s Tm s 1 (s ) 3 SERVO MOTOR DYNAMICS K s Tm s 1 V (s ) K (s ) -20 dB/dec | G ( j ) | -40 dB/dec 1 10 m SYSTEM IDENTIFICATION IN LAB 6 Transfer function relation between input and output Y (s) G(s) X (s) If x(t ) is a sinusoid at any one frequency G ( j ) amplitude of y amplitude of x Find the Bode magnitude plot of G ( j ) by using the above relation and having sinusoidal inputs, one frequency at a time 4 SYSTEM IDENTIFICATION IN LAB 6 Procedure Send a sinusoidal analog voltage to motor (input) Read encoder signal which measures rotational motor motion High pass filter the encoder signal (output) Find the ratio of output amplitude to input amplitude Set frequency to 2.5 Hz This provides magnitude of transfer function at that frequency Repeat at other frequencies (up to 75 Hz) SYSTEM IDENTIFICATION IN LAB 6 Schematic of C-code for loop (while !kbhit) { Send analog voltage to motor Read signal from encoder Store encoder signals in array Wait until 1 ms is up } High pass filter the encoder signals In Matlab Find peak to peak amplitude of motor angular motion 5 SYSTEM IDENTIFICATION IN LAB 6 C program tips Start with sine_io.cpp We don’t need to read any analog voltages in this lab (the motor motion is read from an encoder) Remove the a2d portion of the program Add code from encoder.cpp to read the encoder Outside the real-time loop, use the high pass filter function provided to you void high_pass_filter(int *original_data, double *processed_data, int element_number); This function also generates a Matlab file called enc_plot.m that plots both the original encoder data and the high pass filtered data SYSTEM IDENTIFICATION IN LAB 6 Why do we need to use a high pass filter ? What is a high pass filter ? These topics will be discussed in detail in the next lecture 6 SYSTEM IDENTIFICATION IN LAB 6 K s Tm s 1 V (s ) (s ) | G ( j ) | K -20 dB/dec -40 dB/dec 1 10 m Need to fit a transfer function to the experimental data Need to find gain and corner frequency 7 ...
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This note was uploaded on 02/07/2012 for the course ME 4231 taught by Professor Staff during the Fall '08 term at Minnesota.

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