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This paper proposes the new cascaded series parallel design for improved dynamic performance of DC-DC buck boost converters by a new Sliding Mode Control (SMC) method. The converter is controlled using Sliding Mode Control method that utilizes the converter’s duty ratio to determine the skidding surface. System modeling and simulation results are presented. The results also showed an improved overall performance over typical PID controller, and there was no overshoot or settling time, tracking the desired output nicely. Improved converter performance and robustness were expected.

Power electronics is the process and control of the flow of electric energy from a given source to a load in a shape that is optimally suited for its use. Modern electric systems demand high quality, reliable, efficient and light weight power supplies.

Higher power converters, such as the ones used in Electrified Vehicles (EVs) and aircraft power units, are also in increase demand as a result of the green acts taken on by many countries. The improvement in power switching devices such as the IGBTs and MOSFETs made the power electronics more appealing to many applications. Higher switching frequency, higher power capability and improved efficiency are the main reasons for the expanded application [

Paralleled DC-DC converters are used in telecommunication industry widely and operated under closed loop control to regulate the output voltage [

For paralleled DC-DC converters control, [

In this paper, we will introduce a concept to improve the output quality and simplify the paralleled converters control to a simple single like converter. We will use a Sliding Mode Controller (SMC) with the Variable Structure Surface Design concept developed in [

In this section a model for N paralleled buck boost converters to supply a common load is developed.

This paper will introduce a new approach to controlling the converter to reduce the output harmonics and simplify the control to an equivalent of a single converter. First a single converter model is given by the following equations:

The above equations show the model that the first section of the converter associated with, the switch takes on the values. The current is the inductor current associated with the first inductor and is the capacitor voltage as a result of the contribution of all other converters. For multi converters the output current is the sum of all individual inductor currents and is given by the following equation.

The states are the inductor currents and capacitor voltage as shown in Equation (4).

m: number of converters Using Equation (3) and based on Equations (1) and (2) we can formulate the following relation. Given that the capacitor voltage is the same as the output voltage.

The derivative of the output current given by Equation (3) is shown in Equation (5)

Substituting Equation (1) into Equation (5) and collecting the terms we get Equation (6) interim of the derivative of the load and capacitor currents.

where is the state of the n^{th} switch.

We determine from

Taking the derivative of Equation (7) we get the following relation

With the advancement in switches and their higher switching frequency capabilities we assume an infinite switching frequency. With this assumption we can assume that the rate of change in the capacitor voltage and current are zero, solving Equation (8) we get the following Equation (9)

It can be seen that the second term of Equation (9) is related to the duty ratio for the buck boost converter. The duty ration is defined as the turn on time as a percentage of the period defined as.

Substituting the expression for into Equation (9) we determine the switching time as follows

The above equation shows the distribution of the switching time for the converters, the sum of all the switches contribution is equivalent to the duty ratio or the required on time of an equivalent single switch to provide the desired output. The contribution of each leg is an equal portion of the required output voltage and current.

The control methodology can vary from PID, VSC, Fuzzy logic, SMC or other methods, but the end results is the same as to determine the turn ON time for the switches.

Next an improved performance of the converter to reduce harmonics content is presented. It is proposed to do a harmonic cancelation by shifting the switching sequence of the converters, by imposing on the subsequent converter legs using the following relation

: Delayed time factor (e.g. 10)

: The specific converter

: Total number of converters

In this section we propose a new converter control design to simplify the overall control and improve performance. In DC-DC converters control, the principle is to eliminate the error between the actual output and the desired output value. The control action is taking by switching the control device in this case a MOSFET to apply the input DC voltage to the converter periodically and proportional to the error. In this paper we propose separating the converter into two stages as discussed next.

The design consists of two cascaded stages where the first stage is the control stage shown in

The performance stage represents m number of parallel converters to be controlled to reduce the harmonics contents of the output. This separation gives the designer the freedom to choose the switching frequency to optimize the performance of the converter. This frequency is

independent of the control stage and can be optimized.

The converters switching time is determined in advance and the frequency can be optimized to reduce switching losses or improve EMI performance. The simulation will show the performance of the converter with synchronized switching time and also the enhanced performance with the shifted switching time as suggested above in Equation (12).

The control stage as shown enclosed in the dashed line in

The control of the first stage through, as shown in

In this section we will use sliding mode control to control the converter. The sliding surface used is a unique duty cycle dependent surface developed in [

Consider the linear time invariant system given by

Equation (13).

where,

;

The states are defined as the inductor current and the capacitor voltage which the same as the output voltage.

Given the surface as defined in [14,15].

taking the derivative of (14).

Using Equation (13) to Equation (15) we get the equivalent control discussed by Utkin [16,29]. It is developed to derive the sliding mode equations into the manifold and then the solution to is called the equivalent control.

The method in [

where

Are the errors between the actual values and the desired one. Taking the derivative of Equation (17) we find the value of C, the surface coefficients, as

Using the value of C in Equation (18) and the given A and B coefficients of the system and evaluating Equation (16) to get the equivalent control.

The total control of the system consists of two components the equivalent control and corrective control, where the equivalent control is used to reach the surface while the corrective is to keep the system on the surface.

For system stability, we need to guarantee the system ends up and stays at the surface regardless of the initial conditions. Using the following Lyapunov function:

We need to grantee that the derivative of Equation (21) is negative definite that is for all, that from any initial condition. Taking the derivative of (21):

With

and

to grantee Equation (22) holds the corrective control is chosen as follow.

where is appositive number. Hence the complete control is given by Equation (20) is:

where and are the coefficients derived in [

: Inductor value

: Capacitor value

: Load Resistor Value

: Associated Jordan value associated with the selected eigen values.

and l: Arbitrary positive numbers

: Duty ratio In the next section we will show the results of the application of the hyper plane coefficients in the proposed two stage converter and compare to the results to a conventional PID controller. Although a comparison will show an improvement over the conventional method in term of overshoot and settling time, the main purpose of the application to test the feasibility of the method developed in [

In the next section will show and compare the results of using a single converter, parallel converters, paralleled converters with the enhanced mode and the developed hyper plain coefficients method [

The converter shown in

In the second part of the simulation, the converters are paralleled and the new two mode design is implemented.

The same values as the single converter are used with a mismatch of 10% to represent a more realistic situation. However for sensitive applications more precise value components can be chosen.

First part of the simulation is of the single converters with the values given above. The results are shown below in

delayed switching time in the performance stage as suggested by Equation (12) has shown a great deal of improvement. Examining the switched input voltages, it can be seen that the proposed two stage converter has reduced the switching frequency hence reducing the switching losses of the converter in the input stage. The performance stage switching frequency and duty cycle can be optimized to improve the overall efficiency of the system.

This paper develops a paralleled Buck Boost DC-DC converter with two stages named the control and the performance stages. The control stage performed a manipulation of the input voltage whereas the performance stage was designed to improve further the quality of the output. The quality is measured by reducing the ripples, hence reducing power lost and increasing system reliability.

The converter is controlled using Sliding Mode Control method. The sliding surface in the controlled is developed to be dynamic and duty cycle dependent. This dynamic hyper plane or sliding surface showed an expected improved performance. The results also showed an improved overall performance over typical PID controller, and there was no overshoot or settling time, tracking the desired output nicely. The enhanced mode in combination

with the sliding mode control has shown a reduction in harmonics in comparison to the SMC without the delayed enhanced mode.

With the increasing demand of large power load and the development of distributed power supply system, the importance of research on paralleled power supply modules is increasing, while achieving an equivalent current sharing between the modules is the key element. In future work, the current-sharing control will be presented and compared with other existing ones.