Feedback linearization of fixed frequency PWM converters

State space averaging applied to the two switch configurations in a switching converter usually yields a nonlinear state space system. The state space averaging and linearization methods of Cuk and Middlebrook allow for a linear systems analysis although local in nature. In this dissertation, we first construct an input-state feedback transformation for the boost and buck-boost converters taking the state space averaged nonlinear system to a controllable linear system. This transformation is globally one-to-one on our domain and is exact. Furthermore, it is independent of any operating point (that determines the output voltage) chosen for the nonlinear system. We are able to perform excellent control design through a formula we provide for the control d, the duty ratio. First, we take a second-degree monic polynomial s2 + K2s + K, and choose the parameters K1 and K 2 so that the roots of the polynomial are in the open left half plane. Then we take an operating point for the nonlinear system and incorporate it into our formula for d. We prove that the nonlinear state space operating point is asymptotically stable with this d as input. This is true for the same values of K1 and K2 regardless of the operating point. Next we model the PWM switching process. To provide robustness we add Proportional (P) or Proportional-Integral (PI) control loop after applying our control d to the nonlinear system. The use of d greatly simplifies our analysis. We provide Simulink simulations that indicate the performance of our control technique. In one experiment we choose operating points for which the buck-boost acts first as a buck converter and then as a boost converter. In both cases the corresponding equilibrium points in state space are asymptotically stable without having to change the feedback gains.; Secondly, we construct an input-output feedback transformation for the boost and buck-boost converters which again takes the state space averaged nonlinear system to a controllable linear system. Parameters are chosen so that the nonlinear system is locally asymptotically stable for a given operating point (x10, x20). We focus only on the switched model and we use leading-edge modulation instead of trailing-edge modulation as has been done up until now. Previously, we used input-state linearization because the system zero dynamics associated with the boost and buck-boost converters in continuous conduction mode with trailing-edge modulation are unstable. Input-output linearization cannot be used under such conditions. However, with leading-edge modulation, the zero dynamics are stable, and input-output linearization can be applied. To asymptotically stabilize an operating point, we only need to stabilize a linear system with transfer function denominator s + k, which only requires k > 0. We again derive a formula for the duty ratio d and use it to provide Simulink simulations to prove the performance of our control technique. Proportional (P) and Proportional-Integral (PI) loops can be added for robustness. We perform the same type of experiments as before. A Spice analysis of the buck-boost converter using input-output linearization is provided in an appendix.