Ramón Silva-Ortigoza

DC/DC Buck Power Converter as a Smooth Starter for a DC Motor Based on a Hierarchical Control

In this paper a smooth starter, based on a dc/dc Buck power converter, for the angular velocity trajectory tracking task of a dc permanent magnet motor is presented. To this end, a hierarchical controller is designed, which is integrated by a control associated with the dc motor based on differential flatness at the high level, and a control related with the dc/dc Buck converter based on a cascade control scheme at the low level. The control at the high level allows the dc motor angular velocity to track a desired trajectory and also provides the desired voltage profile that must be tracked by the output voltage of the dc/dc Buck power converter. In order to assure the latter, a cascade control at the low level is designed, considering a sliding mode control for the inner current loop and a proportional-integral control for the outer voltage loop. The hierarchical controller is tested through experiments using MATLAB-Simulink and the DS1104 board from dSPACE. The obtained results show that the desired angular velocity trajectory is well tracked under abrupt variations in the system parameters and that the controller is robust in such operation conditions, confirming the validity of the proposed controller.

Two-Stage Control Design of a Buck Converter/DC Motor System without Velocity Measurements via a-Modulator

This paper presents a two-stage control design for the “Buck power converter/DC motor” system, which allows to perform the sensorless angular velocity trajectory tracking task. The differential flatness property of the DC-motor model is exploited in order to propose a first-stage controller, which is designed to achieve the desired angular velocity trajectory. This controller provides the voltage profiles that must be tracked by the Buck converter. Then, a second-stage controller is meant to assure the aforementioned. This controller is based on flatness property of the Buck power converter model, which provides the input voltage to the DC motor. Due to the fact that the two-stage controller proposed uses the average model of the system, as a practical and effective implementation of this controller, a -modulator is employed. Finally, in order to verify the control performance of this approach, numerical simulations are included.

Trajectory Tracking in a Mobile Robot without Using Velocity Measurements for Control of Wheels

In this paper we present a solution for the trajectory tracking problem in a newt mobile robot. We exploit the differential flatness property of the robot kinematic model to propose an input-output linearization controller which allows both the position and the orientation to track a desired trajectory. An important assumption is that robot has to be initially placed at a point on such a desired trajectory. This controller provides the velocity profiles that the robot wheels have to track and a second controller has to be designed in order to ensure the latter. This is accomplished by means of another differential flatness based control scheme which does not require measurements of any mechanical variables, i.e. velocities, to control the DC motors used as actuators at the wheels. We verify our findings through numerical simulations.

A New Tuning Procedure for PID Control of Rigid Robots

This paper is concerned with classical PID control of rigid robots. We introduce a tuning procedure for selection of the PID gains ensuring asymptotic stability in a domain which can be enlarged arbitrarily. The novelty of our approach relies on the fact that conditions for stability are formulated as expressions that have to be satisfied at each joint instead of conditions on norms of gain and parameter matrices as reported previously. This allows better performances than those obtained using tuning procedures previously reported in the literature.

PI Control Plus Electric Current Loops for PM Synchronous Motors

We present a solution for velocity control in permanent magnet synchronous motors. We formally prove that velocity converges to the constant desired value from any initial condition. Our controller is so simple that it only differs from the linear control strategy commonly implemented in commercial drives by two simple adaptive terms. Moreover, identical velocity responses are obtained with both controllers. Hence, our results explain how the linear control strategy implemented in most commercial drives works and also provide tuning guidelines for that control strategy. We remark that this has been a long standing unsolved problem.

Hierarchical Velocity Control Based on Differential Flatness for a DC/DC Buck Converter-DC Motor System

This paper presents a hierarchical controller that carries out the angular velocity trajectory tracking task for a DC motor driven by a DC/DC Buck converter. The high level control is related to the DC motor and the low level control is dedicated to the DC/DC Buck converter; both controls are designed via differential flatness. The high level control provides a desired voltage profile for the DC motor to achieve the tracking of a desired angular velocity trajectory. Then, a low level control is designed to ensure that the output voltage of the DC/DC Buck converter tracks the voltage profile imposed by the high level control. In order to experimentally verify the hierarchical controller performance, a DS1104 electronic board from dSPACE and Matlab-Simulink are used. The switched implementation of the hierarchical average controller is accomplished by means of pulse width modulation. Experimental results of the hierarchical controller for the velocity trajectory tracking task show good performance and robustness against the uncertainties associated with different system parameters.

An exact tracking error dynamics passive output feedback controller for a Buck-Boost-converter driven DC motor

This article deals with the trajectory tracking problem for the angular velocity of a DC-motor shaft using a buck-boost-converter as the switch regulated electronic drive. The main result of our proposed control scheme is that a linear time-varying controller results from the consideration of the exact tracking error dynamics and static passive output feedback controller design. The measuring of the angular velocity is not really necessary and the control law is synthesized using only a linear time-varying combination of the converter current and voltage variables. The voltage reference trajectory for the converter is generated exploiting a partial differential flatness property of the combined system. The reference trajectories of the average control and the input current are calculated via stored energy considerations and planning for the initial and final stationary regimes. The discrete switching control realization of the designed continuous feedback control law is accomplished by means of a traditional PWM-modulation scheme. Experimental results are provided

Describing the structure of ronchigrams when the grating is placed at the caustic region: the parabolical mirror

In this work we use the geometrical point of view of the Ronchi test and the caustic-touching theorem to describe the structure of the ronchigrams for a parabolical mirror when the point light source is on and off the optical axis and the grating is placed at the caustic associated with the reflected light rays. We find that for a given position of the point light source the structure of the ronchigram is determined by the form of the caustic and the relative position between the grating and the caustic. We remark that the closed loop fringes commonly observed in the ronchigrams appear when the grating and the caustic are tangent to each other. Furthermore, we find that the caustic locally has singularities of the purse or hyperbolic umbilic type, and the ronchigram obtained when the grating is located at certain specific positions at the caustic locally is of the serpentine type. The main motivation of this work is that nowadays a quantitative analysis of the Ronchi test is applied only when the grating is outside the caustic, and we claim that by working at the caustic, the sensitivity of the Ronchi test will be improved. Therefore, a clear understanding of the properties of the ronchigrams when the grating is placed at the caustic will be needed to extend the Ronchi test to that region.

Wavefronts and caustic of a spherical wave reflected by an arbitrary smooth surface

The aim of the present work is to obtain expressions for both the wavefront train and the caustic associated with the light rays reflected by an arbitrary smooth surface after being emitted by a point light source located at an arbitrary position in free space. To this end, we obtain an expression for the k-function associated with the general integral of Stavroudis to the eikonal equation that describes the evolution of the reflected light rays. The caustic is computed by using the definitions of the critical and caustic sets of the map that describes the evolution of an arbitrary wavefront associated with the general integral. It is shown that the expression for the caustic is the same as that--reported in the literature--obtained by using an exact ray tracing. The general results are applied to a parabolic mirror. For this case, we find that when the point light source is off the optical axis, the caustic locally has singularities of the hyperbolic umbilic type while the reflected wavefront at the caustic region locally has singularities of the cusp ridge and swallowtail types.

Wavefronts, caustic, ronchigram, and null ronchigrating of a plane wave refracted by an axicon lens.

The aim of this work is threefold: first we obtain analytical expressions for the wavefront train and the caustic associated with the refraction of a plane wavefront by an axicon lens, second we describe the structure of the ronchigram when the ronchiruling is placed at the flat surface of the axicon and the screen is placed at different relative positions to the caustic region, and third we describe in detail the structure of the null ronchigrating for this system; that is, we obtain the grating such that when it is placed at the flat surface of the axicon its associated pattern, at a given plane perpendicular to the optical axis, is a set of parallel fringes. We find that the caustic has only one branch, which is a segment of a line along the optical axis; the ronchigram exhibits self-intersecting fringes when the screen is placed at the caustic region, and the null ronchigrating exhibits closed loop rulings if we want to obtain its associated pattern at the caustic region.