Forbidden State Space Trajectories of Pwm Converters: Implication to Digital Control

A b s t r a c t T h e p o s s i b l e t r a j e c t o r i e s o f t h e s t a t e v e c t o r v a l u e s ( i L(t) and vC (t) ) o f B u c k a n d B o o s t PWM converters under large transients are examined and evaluated . The forbidden trajector ies , detected b y e x a m i n i n g t h e s t a t e s p a c e t r a c e s , i m p o s e s e v e r l i m i t a t i o n o n t h e c o n t r o l d e s i g n . T h e s e l i m i t a t i o n s are bes t demonstrated by i n v e s t i g a t i o n o f large s i g n a l transient response o f c o n v e n t i o n a l l inear c o n t r o l l e r s . B a s e d o n t h i s i n v e s t i g a t i o n , a s i m p l e d i scre te contro l ru le i s proposed. Based on i t , a p r e l i m i n a r y s i m p l e d i s c r e t e c o n t r o l f u n c t i o n f o r a Boost converter was tested and compared to a l inear Peak Current Mode (PCM) control.