Digital Control System

Transcription

1 Digital Control System Digital Computer Command + Controller D/A Control Signal Plant A/D T Sampler Sensor

2 Digital Controller Design Design by Emulation-Approximation Euler s Method Tustin s Method Discrete Design (Direct Digital Design) Root Locus Bode Plot

3 Design by Emulation

4 Design by Emulation U() s 1 = Ds () = Es () s kt kt T kt ukt ( ) = etdt () = etdt () + etdt () 0 0 kt = ukt ( T) + etdt ( ) kt T kt T

5 Backward Rectangular Rule (Euler s Method) uk ( ) = uk ( 1) + T ek ( ) 1 ( ) = ( ) + ( ) U z z U z T E z U( z) T 1 = = Ez ( ) 1 z 1 z T 1 1 a a Ds () =, Dz () = s 1 z T 1 1 z s T + 1 a + a

6 Backward Rectangular Rule(Euler s Method) Es () = sus () et () = ut () ut () ut ( T) et () T ut () ut ( T) + T et () ukt ( ) ukt ( T) + T ekt ( )

7 Forward Rectangular Rule (Euler s Method) uk ( ) = uk ( 1) + T ek ( 1) U z z U z T z E z 1 1 ( ) = ( ) + ( ) 1 U( z) Tz T 1 = = = 1 Ez ( ) 1 z z 1 z 1 T a a Ds () =, Dz () = s+ a z 1 + T z 1 s T a

8 Forward Rectangular Rule(Euler s Method) Es () = sus () et () = ut () ut ( + T) ut ( ) et () T ut ( + T) ut () + T et () uk ( + 1) uk ( ) + T ek ( ) zu( z) = U( z) + TE( z) U( z) T = Ez ( ) z 1

9 Tustin s Method (Trapezoidal Rule, Bilinear Transform) T uk ( ) = uk ( 1) + [ ek ( 1) + ek ( )] 2 1 T 1 U( z) = z U( z) + [ z E( z) + E( z)] 2 1 U( z) T 1+ z 1 = 1 = 1 Ez ( ) 2 1 z T 1 z z a a Ds () =, Dz () = 1 s+ a T 1 z a z T 1 z s z

10 1st Order Digital Filter Gs () Gz ( ) Y() s 1 = = U() s 1 + s/ ω Y( z) 1 Tω = = = U( z) 1 z T 1 z 1+ Tω c c 1 1 ωc + c

11 1st Order Digital Filter 1 ( Tωc + 1 z ) Y( z) = TωcU( z) 1 ( Tωc + 1) Y( z) z Y( z) = TωcU( z) 1 Y z z Y z T U z 1 ( ) = ( ) + ωc ( ) ( Tωc + 1) 1 yk ( ) = yk ( 1) + T cuk ( ) ( Tω + 1) c [ ω ]

12 2nd Order Dynamic System Y() s ω = U() s s 2 s 2 n ζωn + ωn 2 d y dy ζω 2 n + ωny = ωn dt 1 2 dy x () t = x () t x () t = ω x () t 2 ζω x () t + ω u() t n 1 n 2 n yt () = x() t 1 u

13 2nd Order Dynamic System x () t = x ( τ) dτ t t = 0 n 1 n 2 + n x () t ω x ( τ ) 2 ζω x ( τ) ω u( τ) dτ x ( t) = x ( t T) + T x ( t T) x2() t = x2( t T) + T ωnx1( t T) 2 ζωnx2( t T) + ωnu( t T)

14 2nd Order Dynamic System ω = 2π 10,2π 20 n ζ = 0.2, 1

15 Interrupt Main Program Interrupt Service Routine

16 PC Interrupt

17 PC Interrupt

18 PC Interrupt

19 PC bus AD board IRQ5 AD Converter Timer AD conversion start AD conversion end Timer AD Converter IRQ Interrupt Request T (Sampling Period)

20 AD Conver Board PCI-1711

21 AD Conver Board PCI-1711

22 AD Conver Board PCI-1711

23 AD Conver Board PCI-1711

24 DA Converter Board PCI-1720

25 DA Converter Board PCI-1720

26 DA Converter Board PCI-1720

27 PCI Devices

28 sine.c #include "C:\Tornado\target\h\fppLib.h #include "math.h" #define AD_BASE 0x1800 #define AD_LOW_BYTE AD_BASE #define AD_HIGH_BYTE AD_BASE+1 #define AD_RANGE AD_BASE+2 #define AD_START_CHANNEL AD_BASE+4 #define AD_STOP_CHANNEL AD_BASE+5 #define AD_CONTROL AD_BASE+6 #define AD_STATUS AD_BASE+7 #define AD_CLEAR_INTERRUPT AD_BASE+8 #define AD_CLEAR_FIFO AD_BASE+9 #define DIO1 AD_BASE+16 #define DIO2 AD_BASE+17 #define COUNTER0 #define COUNTER1 #define COUNTER2 #define COUNTER_CONTROL #define DA_BASE #define DA_CHANNEL0_LOW #define DA_CHANNEL0_HIGH #define DA_RANGE AD_BASE+24 AD_BASE+26 AD_BASE+28 AD_BASE+30 0x1840 DA_BASE DA_BASE+1 DA_BASE+8

29 sine.c #define ONMASK 0xdf /* Turn IRQ5 On */ #define OFFMASK 0x20 /* Turn IRQ5 Off */ #define ONMASK2 0xfb /* Turn IRQ10 On */ #define OFFMASK2 0x04 /* Turn IRQ10 Off */ #define PICMASK 0x21 /* 8259 Mask Register */ #define PICEOI 0x20 /* 8259 EOI Instruction */ #define IRQ5 0x25 /* IRQ5 interrupt number */ #define PIC2MASK 0xA1 /* 8259 Mask Register */ #define PIC2EOI 0xA0 /* 8259 EOI Instruction */ #define IRQ10 0x2A /* IRQ10 interrupt number */ /* VxWorks 5.4 Programmer's Guide page 444 */ /* By default, vector number 0x20 to 0x2f are mapped to IRQlevel 0 to 15 */

30 sine.c void initialize_timer_interrupt(void) { unsigned short count; /* Initilize the timer */ count=100; sysoutbyte(counter_control,0x74); /* */ sysoutbyte(counter1,(count & 0xff)); sysoutbyte(counter1,((count >> 8) & 0xff)); count=50; sysoutbyte(counter_control,0xb4); /* */ sysoutbyte(counter2,(count & 0xff)); sysoutbyte(counter2,((count >> 8) & 0xff)); /* count=100,count=50 : 2KHz for 10MHz clock input : PCI-1711 */ sysoutbyte(picmask,(sysinbyte(picmask) & (ONMASK))); /* enable IRQ5 interrupt */ } /* initialize_timer_interrupt */

31 sine.c void interrupt_service_routine(void) { fppsave(pfpcontext); int_counter++; x=sysinword(ad_low_byte); x=x-2048; y=204.8*2*sin(2.0* *100.0*(float)int_counter/2000.0); y=y+2048; sysoutword(da_channel0_low,y); sysoutbyte(ad_clear_interrupt,0); /* clears interrupt */ sysoutbyte(ad_clear_fifo,0); /* clears FIFO */ fpprestore(pfpcontext); sysoutbyte(pic2eoi,0x20); /* end of interrupt */ } /* interrupt_service_routine */

32 sine.c void initialize_ad_converter(void) { sysoutbyte(ad_start_channel,0); sysoutbyte(ad_stop_channel,0); sysoutbyte(ad_range,0x0); /* single-ended bipolar */ sysoutbyte(ad_control,0x12); /* AD conversion mode : Timer Trigger, Interrupt */ /*sysoutbyte(ad_control,0x01);*/ /* AD conversion mode : Software Trigger, No Interrupt */ sysoutbyte(da_range,0xff); } /* initialize_ad_converter */

33 sine.c void app( void ) { int i; initialize_ad_converter(); connect_interrupt_service_routine(); initialize_timer_interrupt(); sysoutbyte(ad_clear_interrupt,0); /* clears interrupt */ sysoutbyte(ad_clear_fifo,0); /* clears FIFO */ } /* application main */

34 Two s complement 입력전압 10*(2047/2048) 10*(1/2048) 0-10*(1/2048) -10 입력값 0xfff 0x801 0x800 0x7ff 0x0 Two s complement (long integer: 4 bytes) 0x000007ff 0x xffffffff 0xfffff800