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This paper presents the design of a smooth starter for a DC motor that uses a full-bridge Buck inverter powered by renewable energy. For this aim, a renewable energy power supply is considered in the mathematical model of the “full-bridge Buck inverter–DC motor” system. Whereas, for the design of the smooth starter, a control based on sliding-mode and proportional-integral control is proposed. The performance of the developed control scheme is experimentally validated using the system prototype, the TDK-Lambda G100-17 renewable energy emulator source, the DS1104 board, and the Matlab-Simulink software. Experimental tests are conducted with two different power supply scenarios: 1) a time-varying input voltage and 2) a commercial photovoltaic panel emulator. The obtained experimental results show the robustness of the controller proposed here to abrupt disturbances in the system parameters and torque.

This work addresses the control problem related to the bidirectional velocity of a DC motor fed by a DC/DC Buck converter–inverter as power amplifier. While various power electronic topologies have been proposed in the literature, this research focuses on one that was previously disregarded due to its delivery of pulse width modulated voltage signals instead of smooth voltage signals to the DC motor. However, in this paper it is demonstrated that by appropriately controlling the power electronic converter it is indeed possible to deliver the desired smooth voltage signals to the motor. Moreover, the proposed control strategy is robust, employing multiple proportional-integral loops, and a sliding mode controller. A formal proof of asymptotic stability is provided and the robustness is verified through experimental validation.

In this investigation, a tracking control is designed for the angular velocity of the DC/DC Boost converter–DC motor system. To this end, the dynamics of the power supply, generated through a renewable energy power source, is considered in both the mathematical model and the designed control. This latter is proposed by using a two-level hierarchical approach, where the dynamics of the DC/DC Boost converter and the one associated with the DC motor not only are treated as two independent subsystems, but also they exploit their differential flatness property. For the DC/DC Boost converter, an alternative first-order mathematical model is obtained for designing the low-level voltage control. Whereas, the well known second order mathematical model of the DC motor is used for developing the high-level angular velocity control. The robustness and performance of the hierarchical tracking control are verified via realistic numerical simulations and experimental results by using Matlab-Simulink, a prototype of the system, the DS1104 board, and the renewable energy emulator TDK-Lambda G100-17. The results demonstrate and validate the effectiveness of the proposed approach.

A sensorless control based on the exact tracking error dynamics passive output feedback (ETEDPOF) methodology is proposed for executing the angular velocity trajectory tracking task on the “full-bridge Buck inverter–DC motor” system. When such a methodology is applied to the system, the tracking task is achieved by considering only the current sensing and by using some reference trajectories for the system. The reference trajectories are obtained by exploiting the flatness property associated with the mathematical model of the “full-bridge Buck inverter–DC motor” system. Experimental tests are developed for different desired angular velocity trajectories. With the aim of obtaining the experimental results in closed-loop, a “full-bridge Buck inverter–DC motor” prototype, Matlab-Simulink, and a DS1104 board from dSPACE are employed. The experimental results show the effectiveness of the proposed control.

This paper is concerned with velocity control in a permanent magnet synchronous motor (PMSM) when it is fed by an inverter-DC/DC Buck power converter system as power amplifier. We present, for the first time, a formal local asymptotic stability proof to solve this control problem. We stress that this is the first time that this problem is solved for an AC motor. Our control scheme is simple when compared to differential flatness- and backsteping-based proposals in the literature to solve this problem for DC motors. The key for these achievements is the employment of a novel passivity-based approach which takes advantage of the natural energy exchange among the electrical and mechanical subsystems that compose the inverter-DC/DC Buck power converter-PMSM system. The main features of this novel passivity-based approach are summarized in this paper.

With the intention of delivering an intuitive and simple platform to plan, generate, and track trajectories with a WMR, this paper presents a technological integration of hardware and software. This technological integration consists of a mobile computing device with an app developed by authors for the trajectory planning and a differential drive WMR that possesses an embedded system, in which a trajectory generation algorithm and a trajectory tracking control algorithm -both proposed by authors - are programmed. The mobile computing device wirelessly drives the WMR through the embedded system. The app is developed on the basis of the sketch approach, since it allows drawing sketches of the trajectory intuitively on the mobile device. Also, the app geometrically scales the sketch coordinates to match them with the real WMR workspace. For the trajectory generation, these scaled coordinates are wirelessly sent to the embedded system, where the trajectory generation algorithm joins them by using Bézier polynomials and concatenation of straight-lines. Hence, the tracking task is carried out with the control algorithm, which is proposed departing from the dynamic model of the WMR and whose asymptotic stability proof is performed with the Lyapunov method. Experimental results verify that the technological integration successfully plans, generates, and tracks trajectories, even when the WMR is far from the initial coordinate of the desired trajectory. These results, corroborate the good performance and robustness of the proposed control algorithm. Thus, the introduced technological integration is intuitive and simple since users only have to draw a sketch on the mobile device to carry out the trajectory tracking task.

By designing a robust control, for the first time in literature, the tracking task associated with the MIMO DC/DC Boost converter-inverter-DC motor system is solved. Such robustness is achieved through the exploitation of the differential flatness property related to the system and by a suitable design of auxiliary controls. With the aim of verifying the performance of the robust control, a platform of the system along with MATLAB-Simulink and a DS1104 board are used. The experimental results show the good performance of the system in closed-loop even when electrical abrupt changes are considered in some parameters of the Boost converter and when a mechanical load perturbation is applied.

This paper presents a passivity-based control for the DC/DC Buck-Boost converter-inverter-DC motor system. Such control exploits the energy structure associated with the system error dynamics. This in order to solve the trajectory tracking task for both the converter voltage and motor bidirectional angular velocity, without using electromechanical sensors. The successful experimental validation of the proposed control is performed in a built prototype of the system, using Matlab-Simulink and a DS1104 board.

This paper presents the design of a linear state feedback controller for the stabilization of two inverted pendulums, namely, Furuta pendulum and pendubot. Such a controller design allows eliminating the limit cycle that appears in the systems due to the effect of a nonlinearity, that is, dead-zone, which is induced by static friction at the motor shaft. To do this, the differential flatness approach is applied to the linear approximate model of the inverted pendulums under study. Then, the resulting flat systems are translated to the frequency domain for which a control scheme is proposed. Subsequently, the dead-zone nonlinearity is treated off-line as an approximation obtained through the describing function method. Since this is an approach intrinsically based on frequency response, the frequency response-based approach is suitable for tuning the gains of the proposed control scheme. An advantage of using the frequency response-based approach along with the describing function method is that they allow obtaining precise formulas that simplify the tuning of the proposed control scheme, so that the limit cycle caused by the dead-zone is eliminated. This must be contrasted with a time response-based approach, proposed recently by the authors, where precise formulas were not obtained and intuitive ideas have to be used to eliminate limit cycle. Finally, the procedure of the controller design herein proposed is verified via experimental tests.

Different educational and didactic papers that allow students to experimentally validate linear controllers have been reported. However, generally, in those papers, procedure followed to select controller gains is not discussed. This lack of information renders difficult experimental implementation of controllers by students who, in general, do not have enough experience on controller tuning. Motivated by this situation, this paper introduces a methodology that provides important information on how to select controller gains for regulation in a Furuta pendulum. This methodology allows improving closed-loop system performance in a desired direction. Differential flatness is the Furuta pendulum property that is exploited. The main idea is to translate a linear state feedback control design problem into a scenario, where classical tools such as root locus can be used. As an example, controller design is directed toward reduction or even elimination of limit cycle effects. The proposal is experimentally tested on a built Furuta pendulum. These experimental results show that the closed-loop system performance is improved, and hence, the proposed methodology is successfully validated.

Through the development of a three-level hierarchical controller, this study proposes a solution to the obstacle avoidance task in wheeled mobile robots (WMRs). The proposed controller takes into consideration the dynamics of the three subsystems that typically compose a WMR (mechanical structure, actuators, and power electronics). At the high level, a control based on input-output linearization that uses the artificial potential fields technique is used and a Lyapunov-like function is proposed for stability analysis purposes. At the medium level, two controls based on differential flatness are employed and a Hurwitz-stable-type polynomial is defined with the aim of locating the poles on the left-hand-side of the complex plane. Finally, at the low level, two cascaded controls are implemented using sliding modes and PI control. The performance of the three-level hierarchical controller is evaluated through a co-simulation using Matlab-Simulink and PSpice software. The obtained results are assessed with a two-level controller that does not take into account the dynamics of the power stage. Such results demonstrate that both controllers accomplish the obstacle avoidance task when no kind of perturbations are considered. However, and unlike the two-level controller, the three-level hierarchical controller successfully achieves the obstacle avoidance task even when disturbances in some parameters of the system are introduced.

We present the Shannon entropy of the Schrödinger equation with an asymmetric rectangular multiple well, in which the potential well width is equal but the barrier width is in an arithmetic sequence. When the confined potential is small, we notice that the wave function of the particle is distributed inside the entire interval, but its distribution is mainly confined inside the wells as the confined potential increases. For the higher excited state, we find that the magnitude inside the barrier is always bigger than that inside the well. However, in the double-well case the magnitude is the biggest in the leftmost second barrier for Vconf=1000meV, but it is in the rightmost barrier in the triple well case. For large confined potential, the momentum entropy density (MED) will be concentrated to the center of the total rectangular multiple well with the increasing confined potential. Likewise, we see that the momentum entropy densities of the ground, first and second excited states are overlapped in the triple well case, but they are all overlapped in the four well case. Particularly, in the double well case, the position entropy densities of ground state and 2nd excited state as well as the 1st and 3rd excited states occupy each well. In the triple well case, however, the position entropy densities of ground state and 2nd excited state occupy each one of three wells, but the 1st and 3rd excited states occupy one of four wells. The position entropy density (PED) of each state in four well case is distributed in each well of them as the confined potential is very large. When the number of wells increases, there exist some additional oscillations in the PED. For the higher excited state, the oscillator frequency of the PED increases inside the well but decreases inside the barrier as the confined potential depth increases. For the lower states, as the potential well depth increases the MED extends outward from the original central distribution, but the main distribution is concentrated to the center of the total system for the higher excited state. We also note that both the position entropy Sxand the momentum entropy Spdo not decrease or increase as the parameter Vconfincreases, but their sum always satisfies the BBM inequality.

By developing a robust control strategy based on the differential flatness concept, this paper presents a solution for the bidirectional trajectory tracking task in the “full-bridge Buck inverter–DC motor” system. The robustness of the proposed control is achieved by taking advantage of the differential flatness property related to the mathematical model of the system. The performance of the control, designed via the flatness concept, is verified in two ways. The first is by implementing experimentally the flatness control and proposing different shapes for the desired angular velocity profiles. For this aim, a built prototype of the “full-bridge Buck inverter–DC motor” system, along with Matlab–Simulink and a DS1104 board from dSPACE are used. The second is via simulation results, i.e., by programming the system in closed-loop with the proposed control algorithm through Matlab–Simulink. The experimental and the simulation results are similar, thus demonstrating the effectiveness of the designed robust control even when abrupt electrical variations are considered in the system.

The efficiency in the controller performance of a BLDC motor in an uncertain environment highly depends on the adaptability of the controller gains. In this paper, the chaotic adaptive tuning strategy for controller gains (CATSCG) is proposed for the speed regulation of BLDC motors. The CATSCG includes two sequential dynamic optimization stages based on identification and predictive processes, and also the use of a novel chaotic online differential evolution (CODE) for providing controller gains at each predefined time interval. Statistical comparative results with other tuning approaches evidence that the use of the chaotic initialization based on the Lozi map included in CODE for the CATSCG can efficiently handle the disturbances in the closed-loop system of the dynamic environment.

The design of a robust flatness-based tracking control for the DC/DC Buck converter-DC motor system is developed in this paper. The design of the control considers the dynamics of a renewable energy power source that plays the role of the primary power supply associated with the system. The performance and robustness of the control is verified through simulations via MATLAB-Simulink when abrupt changes in some parameters of the system are taken into account. Also, experiments are performed by using a built prototype of the DC/DC Buck converter-DC motor system, a TDK-Lambda G100-17 programmable DC power supply, MATLAB-Simulink, and the DS1104 board from dSPACE. In this regard, the TDK-Lambda G100-17 is implemented with the aim of emulating photovoltaic panels through the solar array mode for generating the power supply of the system. Thus, both simulations and experiments show the effectiveness of the proposed control scheme.

In this paper, we solve the problem of position regulation in a magnetic levitation system that is fed by a DC/DC Buck power electronic converter as a power amplifier. We present a formal asymptotic stability proof. Although this result is local, the merit of our proposal relies on the fact that this is the first time that such a control problem is solved for a magnetic levitation system, a nonlinear electromechanical plant. In this respect, we stress that most works in the literature on control of electromechanical systems actuated by power electronic converters are devoted to control brushed DC motors which are well known to have a linear model. Furthermore, despite the plant that we control in the present paper is complex, our control law is simple. It is composed by four nested loops driven by one sliding mode controller, two proportional-integral controllers, and a nonlinear proportional-integral-derivative position controller. Each one of these loops is devoted to control each one of the subsystems that compose the plant: electric current through the converter inductor, voltage at the converter capacitor, electric current through the electromagnet, and position of the ball. Thus, our proposal is consistent with the simple and intuitive idea of controlling each subsystem of the plant in order to render robust the control scheme. We stress that such a solution is complicated to derive using other control approaches such as differential flatness or backstepping. In this respect, our proposal relies on a novel passivity-based approach which, by exploiting the natural energy exchange between the mechanical and electrical dynamics, renders possible the design of a control scheme with the above cited features.

In this paper, a new linear feedback controller for synchronization of two identical chaotic systems in a master-slave configuration is presented. This controller requires knowing a priori Lipschitz constant of the nonlinear function of the chaotic system on its attractor. The controller development is based on an algebraic Riccati equation. If the gain matrix and the matrices of Riccati equation are selected in such a way that a unique positive definite solution is obtained for this equation, then, with respect to previous works, a stronger result can be guaranteed here: the exponential convergence to zero of the synchronization error. Additionally, the nonideal case is also studied, that is, when unmodeled dynamics and/or disturbances are present in both master system and slave system. On this new condition, the synchronization error does not converge to zero anymore. However, it is still possible to guarantee the exponential convergence to a bounded zone. Numerical simulation confirms the satisfactory performance of the suggested approach.

A frequency response-based linear controller is implemented to regulate the inverted pendulum on a cart at the inverted position. The objective is to improve the performance of the control system by eliminating the limit cycle generated by the dead-zone, induced by static friction, at the actuator of the mechanism. This control strategy has been recently introduced and applied by the authors to eliminate the limit cycle in the Furuta pendulum and the pendubot systems. Hence, the main aim of the present paper is to study the applicability of the control strategy to eliminate the limit cycle in the inverted pendulum on a cart. The successful results that are obtained in experiments corroborate that the approach introduced by the authors to eliminate the limit cycle in the Furuta pendulum and pendubot is also valid for the inverted pendulum on a cart.

This paper is concerned with path-tracking control of a wheeled mobile robot. This robot is equipped with two permanent magnet brushed DC-motors which are fed by two inverter-DC/DC Buck power converter systems as power amplifiers. By taking into account the dynamics of all the subsystems we present, for the first time, a formal stability proof for this control problem. Our control scheme is simple, in the sense that it is composed by four internal classical proportional-integral loops and one external classical proportional-derivative loop for path-tracking purposes. This is the third paper of a series of papers devoted to control different nonlinear systems, which proves that the proposed methodology is a rather general approach for controlling electromechanical systems when actuated by power electronic converters.

In order to solve the trajectory tracking task in a wheeled mobile robot (WMR), a dynamic three-level controller is presented in this paper. The controller considers the mechanical structure, actuators, and power stage subsystems. Such a controller is designed as follows: At the high level is a dynamic control for the WMR (differential drive type). At the medium level is a PI current control for the actuators (DC motors). Lastly, at the low level is a differential flatness-based control for the power stage (DC/DC Buck power converters). The feasibility, robustness, and performance in closed-loop of the proposed controller are validated on a DDWMR prototype through Matlab-Simulink, the real-time interface ControlDesk, and a DS1104 board. The obtained results are experimentally assessed with a hierarchical tracking controller, recently reported in literature, that was also designed on the basis of the mechanical structure, actuators, and power stage subsystems. Although both controllers are robust when parametric disturbances are taken into account, the dynamic three-level tracking controller presented in this paper is better than the hierarchical tracking controller reported in literature.

Two differential flatness-based bidirectional tracking robust controls for a DC/DC Buck converter-DC motor system are designed. To achieve such a bidirectional tracking, an inverter is used in the system. First control considers the complete dynamics of the system, that is, it considers the DC/DC Buck converter-inverter-DC motor connection as a whole. Whereas the second separates the dynamics of the Buck converter from the one of the inverter-DC motor, so that a hierarchical controller is generated. The experimental implementation of both controls is performed via MATLAB-Simulink and a DS1104 board in a built prototype of the DC/DC Buck converter-inverter-DC motor connection. Controls show a good performance even when system parameters are subjected to abrupt uncertainties. Thus, robustness of such controls is verified.

The trajectory tracking task in a wheeled mobile robot (WMR) is solved by proposing a three-level hierarchical controller that considers the mathematical model of the mechanical structure (differential drive WMR), actuators (DC motors), and power stage (DC/DC Buck power converters). The highest hierarchical level is a kinematic control for the mechanical structure; the medium level includes two controllers based on differential flatness for the actuators; and the lowest hierarchical level consists of two average controllers also based on differential flatness for the power stage. In order to experimentally validate the feasibility of the proposed control scheme, the hierarchical controller is implemented via a Σ–Δ-modulator in a differential drive WMR prototype that we have built. Such an implementation is achieved by using MATLAB-Simulink and the real-time interface ControlDesk together with a DS1104 board. The experimental results show the effectiveness and robustness of the proposed control scheme.

By using the hierarchical controller approach, a new solution for the control problem related to trajectory tracking in a differential drive wheeled mobile robot (DDWMR) is presented in this paper. For this aim, the dynamics of the three subsystems composing a DDWMR, i.e., the mechanical structure (differential drive type), the actuators (DC motors), and the power stage (DC/DC Buck power converters), are taken into account. The proposed hierarchical switched controller has three levels: the high level corresponds to a kinematic control for the mechanical structure; the medium level includes two controls based on differential flatness for the actuators; and the low level is linked to two cascade switched controls based on sliding modes and PI control for the power stage. The hierarchical switched controller was experimentally implemented on a DDWMR prototype via MATLAB-Simulink along with a DS1104 board. With the intention of assessing the performance of the switched controller, experimental results associated with a hierarchical average controller recently reported in literature are also presented here. The experimental results show the robustness of both controllers when parametric uncertainties are applied. However, the performance achieved with the switched controller introduced in the present paper is better than, or at least similar to, performance achieved with the average controller reported in literature.

This paper has two aims. The first is to develop a robust hierarchical tracking controller for the DC/DC Buck-Boost–inverter–DC motor system. This controller considers a high level control for the inverter–DC motor subsystems and a low level control for the DC/DC Buck-Boost converter subsystem. Such controls solve the tracking task associated with the angular velocity of the motor shaft and the output voltage of the converter, respectively, via the differential flatness approach. The second aim is to present a comparison of the robust hierarchical controller to a passive controller. This, with the purpose of showing that performance achieved with the hierarchical controller proposed in this paper, is better than the one achieved with the passive controller. Both controllers are experimentally implemented on a prototype of the DC/DC Buck-Boost–inverter–DC motor system by using Matlab-Simulink along with the DS1104 board from dSPACE. According to experimental results, the proposal in the present paper achieves a better performance than the passive controller.

In this paper, the modeling and the experimental verification of the “bidirectional DC/DC boost converter–DC motor” system are presented. By using circuit theory along with the model of a DC motor, the mathematical model of the system is derived. This model was experimentally tested under time-varying duty cycles obtained via the system differential flatness property. The experimental verification was carried out using Matlab-Simulink and a DS1104 board in a built prototype of the system.