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

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 time-domain simulation.