Application of neural networks and state space averaging to a DC/DC PWM converter in sliding mode operation

A Fixed-Frequency Pulsewidth Modulation Based Quasi-Sliding-Mode Controller for Buck Converters

“…In two other related papers [14], [15] the state space averaging technique is incorporated into the controller's modeling. By doing so, PWM duty cycle control can be directly applied to the implementation of SM controllers.…”

“…However, while these papers provided encouraging evidence on the feasibility of developing such SM controllers, they failed to study the technical aspects of the implementation, which is equally important for engineering practices. For a deeper understanding of the topic, interested readers may refer to [3], [10], [11], and [13]- [15].…”

Indirect Sliding Mode Control of Power Converters Via Double Integral Sliding Surface

“…To ensure the existence of SM operation, the local reachability condition 0 must be satisfied. This can be expressed as (20) Case 1-Buck Converter: For the DISM voltage controlled buck converter, the existence condition for steady-state operations (equilibrium point) [8], [18], [34], can be derived by substituting (8) eration of the system's dynamics (10) as (21), shown at the bottom of the page, where denotes the minimum input voltage; denotes the expected steady-state output, i.e., approximately the desired reference voltage ; and are, respectively, the maximum and minimum capacitor currents at full-load condition; and are respectively the maximum and minimum steady-state voltage errors, which in this case are basically the inverse functions of the output voltage ripples; and and are respectively the maximum and minimum integrals of the steady-state voltage error, which is the time integral of the inverse functions of the output voltage ripples with a negligible dc shift. All these parameters can be calculated from the design specification of the converter.…”

“…Thus, the compliance of the inequalities in (21) through the substitution of the state variables' parameters assures the existence of the SM operation to occur at least in the small region of the origin for all input and output operating conditions. Case 2-Boost Converter: For the DISM current controlled boost converter, the existence condition for steady-state operations can be derived by substituting (8) and its time derivative into (20) with the consideration of the system's dynamics (14) as (22), shown at the bottom of the page, where and denote the maximum and minimum input voltages respectively; denotes the expected steady-state output, i.e., approximately the desired reference voltage ; and , and are respectively the maximum and minimum inductor and capacitor currents at full-load condition; and are respectively the maximum and minimum steady-state current errors; and are respectively the maximum and minimum (21) (22) steady-state voltage errors, which in this case are basically the inverse functions of the output voltage ripples; and and are respectively the maximum and minimum integrals of the combination of steady-state voltage and current errors. Fig.…”

“…Our investigation shows that this is due to the imperfect steady-state error correction method of the PWM-based ISM controllers. The problem is common to all types of indirect ISM controllers derived from the equivalent control method [14], [17], [20], [29], [32], [34]. It is also found that the steady-state error increases as the converter's switching frequency decreases and that the error can be quite large at a low switching frequency.…”