ISR develops, applies and teaches advanced methodologies of design and analysis toAbstract Sampled-data analysis of converters has been a topic of investigation for the past two decades. However, this powerful tool is not widely used in control loop design or in closed-loop performance validation. Instead, averaged models are typically used for control loop design, while detailed simulations are used for validating closed-loop performance. This paper makes several contributions to the sampled-data modeling and analysis of closed-loop PWM DC-DC converters, with the aim of increasing appreciation and use of the method. General models are presented in a unified and simple manner, while removing simplifying approximations present in previous work. These models apply both for current mode control and voltage mode control. The general models are nonlinear. They are used to obtain analytical linearized models, which are in turn employed to obtain local stability results. Detailed examples illustrate the modeling and analysis in the paper, and point to situations in which the sampled-data approach gives results superior to alternate methods. For instance, it is shown that the sampled-data approach will reliably predict the (local) stability of a converter for which averaging or simulation predicts instability.
A general and exact critical condition of saddle-node bifurcation is derived in closed form for the buck converter. The critical condition is helpful for the converter designers to predict or prevent some jump instabilities or coexistence of multiple solutions associated with the saddle-node bifurcation. Some previously known critical conditions become special cases in this generalized framework. Given an arbitrary control scheme, a systematic procedure is proposed to derive the critical condition for that control scheme.
SUMMARYExact and approximate sampled-data models in closed forms are derived for switching DC-DC converters under peak/valley current-mode control. The corresponding sampled-data poles and zeros in closed forms are also derived. The location and stability conditions of the poles and zeros, boundary conditions of subharmonic instability, and nulling of the audio-susceptibility are also derived. It is proved that the stable operating range of the source voltage is linearly proportional to the ramp slope. The sampled-data models agree with previous experiment results and accurately predict the subharmonic instability. The different view from the sampled-data model about the number and stability (minimum phase) of pole and zero does not necessarily invalidate the traditional continuous-time averaged model. However, this different view gives better prediction about converter dynamics and is useful for the analog or digital controller design for DC-DC converters.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.