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Sliding mode control is a discontinuous control technique that is, by its nature, appropriate for controlling variable structure systems, such as the switch regulated systems employed in power electronics. However, when designing control laws based on the average models of these systems a modulator is necessary for their experimental implementation. Among the most widely used modulators in power electronics are the pulse width modulation (PWM) and, more recently, the sigma-delta-modulator (

Sliding mode control is a well-known discontinuous feedback control technique which has been exhaustively explored in many books and journal articles by various authors. The technique is naturally suited for controlling variable structure systems. A complete account of the history and fundamental results of sliding modes is found in books, such as those presented by Emelyanov [

In the aforementioned literature, several applications of sliding modes have been introduced. However, it is often necessary to design control laws based on the average models of switched systems. When designing control laws based on such models, particularly DC/DC power converters, a modulator is required for their experimental implementation. Thus, based on [

Nowadays modulators have a wide variety of applications which include, among others, communications, audio, power delivery, and voltage regulation. In particular, this research is focused on their application to the proper handling of the switches associated with DC/DC power converters. Among the most popular modulators used in power electronics, the most prominent are the pulse width modulation (PWM) and, more recently, the sigma-delta-modulator (

On the one hand, the PWM has been extensively used for switching DC/DC power converters. For the regulation of the Buck power converter output voltage, the study in [

On the other hand, switched implementation of average controllers for power converters via the

The literature provided herein shows that both modulators, PWM and

Until now, none of the publications that compare the PWM with the

This paper is structured as follows. Section

This section presents a general description of the DC/DC Buck switching converter and its average model associated with the continuous conduction mode. Then, following the differential flatness approach provided in [

The DC/DC Buck power converter, shown in Figure

DC/DC Buck power converter.

Electronic circuit

Ideal circuit

Assuming that the converter is operating under continuous conduction mode, that is, the average value of the inductor current never drops to zero due to load variations (as stated in [

Regarding the Buck converter matematical model used herein, it should be remarked that despite being a model where energy losses are not considered it has been extensively used in the literature [

The converter

Considering the aforementioned representation, the average model of the DC/DC Buck converter will be described by

According to [

In this subsection, an average flatness-based controller is obtained for the DC/DC Buck converter. The principle of this approach is to find an output, referred to as

The flat output of the DC/DC Buck converter is determined by

Introducing (

The average control determined by (

Flatness-based control developed.

The PWM’s characteristics, operation principles, and applications to power electronics have been widely documented, for example, [

This section describes the experimental switched implementation, via either a PWM or a

In order to accomplish the controller implementation on the converter, a DS1104 electronic card from dSPACE, along with its application software, and Matlab-Simulink were used. A diagram of the connections employed to develop the experiments is shown in Figure

Connection diagram used for the experimentation.

The

The

Control block adapted to Matlab-Simulink.

This section presents the experimental results associated with the trajectory tracking task, as well as a discussion of the obtained results. The approach used in this section is meant to assess the tracking performance of the DC/DC Buck converter when the average control law is implemented through either the PWM or the

The experimental results associated with

The first one is when the system’s nominal parameters, defined by (

The second one is when there is an abrupt change in the load

The third one is when there is a perturbation associated with the supply voltage

The fourth one is when there is an abrupt change in the dynamics of the system, which was not considered while designing the average controller. In this case, the system’s dynamics was modified via the parallel connection of

Case (i) via PWM.

Case (i) via

Case (ii) via PWM.

Case (ii) via

Case (iii) via PWM.

Case (iii) via

Case (iv) via PWM.

Case (iv) via

In order to observe in detail the performance of the average controller implemented through the PWM and the

In the experimental results obtained, it can be observed how the implementation of the average controller via the

To evaluate the experimental results, the ISE index is used to quantify the performance achieved in the trajectory tracking task when the average controller is implemented through each modulator. The ISE performance indices obtained in the experimental results are shown in Figure

Values of the modulators’ ISE performance indices.

The following aspects of the experimental results should be taken into consideration.

Since the implementation of the average controller via the

Albeit the controller based on differential flatness is robust against parametric uncertainties, it is important to note that its implementation may be less feasible and applicable, since it leads to a long mathematical controller (see (

In this research, an average trajectory tracking controller was implemented for a DC/DC Buck converter via either a PWM or a

Assessing the experimental results presented in Figures

Finally, as a possible direction for future research, this methodology can be used in other DC/DC power converter topologies, to determine whether the

Consider the basic block diagram of Figure

First order

Consider the

From Figure

An estimate of the hitting time

The average

Suppose a smooth nonlinear system of the form

If an additional implementation requirement entitles now that the control input

The answer is clearly given by the average features of the previously considered

Then the following general result concerning the control of nonlinear systems through sliding modes synthesized on the basis of an average feedback controller and a

Consider the following smooth nonlinear single input,

The proof of this theorem is immediate upon realizing that, under the hypothesis on the average control input,

Note that the

The authors declare that the research was conducted in the absence of any commercial, financial, or personal relationships that could be construed as a potential conflict of interests.

The authors wish to thank the anonymous reviewers for their helpful comments and critical review. Likewise, the authors would like to thank M. Antonio-Cruz for her technical support in this research. R. Silva-Ortigoza, M. Marcelino-Aranda, and H. Taud acknowledge financial support from the Secretaría de Investigación y Posgrado del Instituto Politécnico Nacional (SIP-IPN), SNI-Mexico, and the IPN programs EDI and COFAA. Also, M. Marcelino-Aranda acknowledges financial support from IPN through the