Design of feedback gain vector of two-state basic PWM multifeedback regulators for large-signal stability

Abstract

A method for determining boundaries on the feedback gains in a switching regulator with multiple feedback, in order to ensure stability for large changes in the load values, is developed. Using an original approach for time-domain analysis, a large-signal, nonlinear, discrete-time model of the closed-loop converter is obtained; the model's equations are expressed in disturbances of the state variables due to disturbance in the load. The first step toward a global stability design is to find the constraint that ensures local stability around the operating point: the nonlinear terms (products of disturbances) are neglected in the model, the z-transform is applied to the linearized equations, and the condition that the eigenvalues are situated inside the unit circle is imposed. The nonlinear model, including the nonlinearity of the pulsewidth modulation (PWM), due to possible saturation, is then considered. A new constraint in terms of feedback gains is found in order to ensure that one and only one real equilibrium point (i.e., the quiescent operating point) exists. Putting together the constraints, boundaries on the feedback gains are found. The method is developed for converters containing two reactive elements, operating in continuous conduction mode. An example of a boost converter with inductor current and output voltage feedback is presented in detail. The large-signal stability of the design is checked by using the state-plane portrait and timedomain simulation.Index Terms-Large signal stability design, modeling technique, power electronics.

Optimal PWM Control of Switched-Capacitor DC–DC Power Converters via Model Transformation and Enhancing Control Techniques

“…Among them, PWM control methods are the common method for both minimizing the output ripple magnitude and regulating the output load voltage subject to the change in the input voltage and the load resistance. This is because these methods exploit both the switching and the nonlinear phenomena of the switched-capacitor DC/DC power converters [21]- [25], [32]. The implementations of the PWM control methods can also be simple [23].…”

“…This problem is not trivial and has not been completely solved yet. The conventional PWM control methods [21]- [25] are based on small signal approximation. That is, the switched-capacitor DC/DC power converter is modeled as a linear time invariant system via perturbating the equations around a fixed point or employing a state space averaging model.…”

“…There are some existing methods for minimizing the output ripple magnitude of a switched-capacitor DC/DC power converter, such as multirate control method [16], LQR control methods [17]- [19], intelligent control method [20], and PWM control methods [21]- [25], etc. On the other side, some methods have been proposed for regulating the output load voltage, such as PWM control method [32], noise shaping method [33], pseudo-continuous control method [34], interleaved discharging method [35], and constant frequency charge pump method [36], etc.…”

Large-signal stability-oriented design of boost regulators based on a Lyapunov criterion with nonlinear integral

“…In [9] and [10] the feedback gain vector is designed for guaranteeing large-signal stability. In [9], the Lyapunov method is used: the feedback gain matrix is calculated, in an iterative process, by solving, in successive approximations, a Riccati equation for which a positive definite solution of a Lyapunov expression is found.…”

“…As the previously mentioned papers [1] and [8], this one also makes use of the average models of the switching-mode converter. In [10], the feedback vector is designed for assuring the large-signal stability for a restricted class of converters: ones operating in two switching stages per cycle (for example, basic hard-switching PWM converters operating in continuous conduction mode).…”