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chap09 - 9 Controller Design 9.1 INTRODUCTION In all...

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9 Controller Des i gn 9.1 INTRODUCTION In all sw i tch i ng converters, the output voltage v ( t ) i s a funct i on of the i nput l i ne voltage the duty cycle d ( t ), and the load current as well as the converter c i rcu i t element values . In a dc–dc con- verter appl i cat i on, i t i s des i red to obta i n a constant output voltage v ( t ) = V , i n sp i te of d i sturbances i n and and i n sp i te of var i at i ons i n the converter c i rcu i t element values . The sources of these d i stur- bances and var i at i ons are many, and a typ i cal s i tuat i on i s i llustrated i n F i g . 9 . 1 . The i nput voltage of an off-l i ne power supply may typ i cally conta i n per i od i c var i at i ons at the second harmon i c of the ac power system frequency (100 Hz or 120 Hz), produced by a rect i f i er c i rcu i t . The magn i tude of may also vary when ne i ghbor i ng power system loads are sw i tched on or off . The load current may con- ta i n var i at i ons of s i gn i f i cant ampl i tude, and a typ i cal power supply spec i f i cat i on i s that the output voltage must rema i n w i th i n a spec i f i ed range (for example, 3 . 3 V ± 0 . 05 V) when the load current takes a step change from, for example, full rated load current to 50% of the rated current, and v i ce versa . The values of the c i rcu i t elements are constructed to a certa i n tolerance, and so i n h i gh-volume manufactur i ng of a converter, converters are constructed whose output voltages l i e i n some d i str i but i on . It i s des i red that essent i ally all of th i s d i str i but i on fall w i th i n the spec i f i ed range ; however, th i s i s not pract i cal to ach i eve w i thout the use of negat i ve feedback . S i m i lar cons i derat i ons apply to i nverter appl i cat i ons, except that the output voltage i s ac . So we cannot expect to s i mply set the dc dc converter duty cycle to a s i ngle value, and obta i n a g i ven constant output voltage under all cond i t i ons . The i dea beh i nd the use of negat i ve feedback i s to bu i ld a c i rcu i t that automat i cally ad j usts the duty cycle as necessary, to obta i n the des i red output voltage w i th h i gh accuracy, regardless of d i sturbances i n or or var i at i ons i n component values . Th i s i s
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332 Controller Design a useful th i ng to do whenever there are var i at i ons and unknowns that otherw i se prevent the system from atta i n i ng the des i red performance . A block d i agram of a feedback system i s shown i n F i g . 9 . 2 . The output voltage v ( t ) i s measured, us i ng a sensor w i th ga i n H ( s ). In a dc voltage regulator or dc ac i nverter, the sensor c i rcu i t i s usually a voltage d i v i der, compr i sed of prec i s i on res i stors . The sensor output s i gnal H ( s ) v ( s ) i s compared w i th a reference i nput voltage The ob j ect i ve i s to make H ( s ) v ( s ) equal to so that accurately follows regardless of d i sturbances or component var i at i ons i n the compensator, pulse-w i dth modu- lator, gate dr i ver, or converter power stage .
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