# Control of non-minimum phase power converters

#### Abstract

The inner structural characteristics of non-minimum phase DC-DC converters pose a severe limitation in direct regulation of voltage when addressed from a control perspective. This constraint is reflected by the presence of right half plane zeros or the unstable zero dynamics of the output voltage of these converters. The existing controllers make use of one-to-one correspondence between the voltage and current equilibriums of the non-minimum phase converters and exploit the property that when the average output of these converters is the inductor current, the system dynamics are stable and hence they indirectly regulate the voltage. As a result, the system performance is susceptible to circuit parameter and load variation and require additional controllers, which in turn increase the system complexity. In this thesis, a novel approach to this problem is proposed for second order non-minimum phase converters such as Boost and Buck-Boost Converter. Different solutions have been suggested to the problem based on whether the converter is modeled as a linear system or as a nonlinear system. For the converter modeled as a linear system, the non-minimum phase part of the system is decoupled and its transfer function is converted to minimum phase using a parallel compensator. Then the control action is achieved by using a simple proportional gain controller. This method accelerates the transient response of the converter, reduces the initial undershoot in the response, and considerably reduces the oscillations in the transient response. Simulation results demonstrate the effectiveness of the proposed approach. When the converter is modeled as a bilinear system, it preserves the stabilizing nonlinearities of the system. Hence, a more effective control approach is adopted by using Passivity properties. In this approach, the non-minimum phase converter system is viewed from an energy-based perspective and the property of passivity is used to achieve stable zero dynamics of the output voltage. A system is passive if its rate of energy storage is less than the supply rate i.e. the system dissipates more energy than stores. As a result, the energy storage function of the system is less than the supply rate function. Non-minimum phase systems are not passive, and passivation of non-minimum phase power converters is an attractive solution to the posed problem. Stability of non-minimum phase systems can also be investigated by defining the passivity indices. This research approaches the problem by characterizing the degree of passivity i.e. the amount of damping in the system, from passivity indices. Thus, the problem is viewed from a system level rather than from a circuit level description. This method uses feed-forward passivation to compensate for the shortage of passivity in the non-minimum phase converter and makes use of a parallel interconnection to the open-loop system to attain exponentially stable zero dynamics of the output voltage. Detailed analytical analysis regarding the control structure and passivation process is performed on a buck-boost converter. Simulation and experimental results carried out on the test bed validate the effectiveness of the proposed method.

#### Degree

M.S.E.C.E.

#### Advisors

Li, Purdue University.

#### Subject Area

Electrical engineering

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