Josep M. Olm

Stable inversion of Abel equations

Stable inversion plays a key role in the solution of the exact tracking control problem in nonminimum phase systems. However, the general methods developed so far for the computation of stable inverses require backwards time numeric integration of the internal dynamics equation, which yields high sensitivity to external disturbances and/or structured uncertainties. This article introduces an iterative technique that provides periodic, closed-form analytic expressions uniformly convergent to the exact periodic solution of a certain class of Abel ODE written in the normal form. The method is then applied to the output voltage tracking of periodic references in DC-DC boost power converters through a state feedback indirect control scheme. The procedure lies on a number of assumptions for which sufficient conditions involving system parameters and reference candidates are derived. It also allows one to attenuate the effect of bounded, piecewise constant load disturbances using dynamic compensation. Simulation results validate the proposed algorithm.

Generation of signals in a buck converter with sliding mode control

Time-dependent sliding surfaces are used in the generation of signals at the load resistance of a buck converter. Restrictions on these signals are derived from the condition of existence of sliding regime. The use of two sliding zones in the generation of a specified signal is studied.<<ETX>>

Discrete-time minimal control synthesis adaptive algorithm

This article proposes a discrete-time Minimal Control Synthesis (MCS) algorithm for a class of single-input single-output discrete-time systems written in controllable canonical form. As it happens with the continuous-time MCS strategy, the algorithm arises from the family of hyperstability-based discrete-time model reference adaptive controllers introduced in (Landau, Y. (1979), Adaptive Control: The Model Reference Approach, New York: Marcel Dekker, Inc.) and is able to ensure tracking of the states of a given reference model with minimal knowledge about the plant. The control design shows robustness to parameter uncertainties, slow parameter variation and matched disturbances. Furthermore, it is proved that the proposed discrete-time MCS algorithm can be used to control discretised continuous-time plants with the same performance features. Contrary to previous discrete-time implementations of the continuous-time MCS algorithm, here a formal proof of asymptotic stability is given for generic n-dimensional plants in controllable canonical form. The theoretical approach is validated by means of simulation results.

Switching Frequency Regulation in Sliding Mode Control by a Hysteresis Band Controller

Fixing the switching frequency is a key issue in sliding mode control implementations. This paper presents a hysteresis band controller capable of setting a constant value for the steady-state switching frequency of a sliding mode controller in regulation and tracking tasks. The proposed architecture relies on a piecewise linear modeling of the switching function behavior within the hysteresis band, and consists of a discrete-time integral-type controller that modifies the amplitude of the hysteresis band of the comparator in accordance with the error between the desired and the actually measured switching period. For tracking purposes, an additional feedforward action is introduced to compensate the time variation of the switching function derivatives at either sides of the switching hyperplane in the steady state. Stability proofs are provided, and a design criterion for the control parameters to guarantee closed-loop stability is subsequently derived. Numerical simulations and experimental results validate the proposal.

Design and analysis strategies for digital repetitive control systems with time-varying reference/disturbance period

This article analyses stability and performance features of different design schemes for digital repetitive control systems subject to references/disturbances that exhibit non-uniform frequency. Aiming at maintaining a constant value for the ratio T p /T s , T p being the period of the reference/disturbance signal and T s being the sampling period, two approaches are proposed. The first one deals with the real-time adaptation of T s to the actual changes of T p ; stability is studied by means of an LMI gridding method and also using robust control techniques. The second one propounds the introduction of an additional compensator that annihilates the effect of the time-varying sampling in the closed-loop system and forces its behaviour to coincide with that of an a priori selected nominal sampling period; the internal stability of the compensator-plant subsystem is checked by means of LMI gridding. The theoretical results are experimentally tested and compared through a mechatronic plant model.

Discrete-Time MRAC with Minimal Controller Synthesis of an Electronic Throttle Body

The electronic throttle body (ETB) is a fundamental actuator for regulating the air mass coming into an internal combustion engine; hence, it is used to control the engine torque in any modern drive-by-wire configuration. To cope with the nonlinear and discontinuous dynamics of this automotive device, in this paper a novel discrete-time model reference adaptive control (MRAC) method is designed and experimentally tested on an ETB installed on a 2-L engine. The control strategy extends the class of the minimal control synthesis (MCS) algorithms for discrete-time systems by adding an explicit discrete-time adaptive integral action and an adaptive robust term. An in-depth experimental investigation shows that the proposed control method is a viable solution as it is robust with respect to nonlinear torques acting on the plant, and it guarantees better performance than those provided by other MRAC strategies especially for small reference signals around the limp-home position where plant nonlinearities strongly affect the ETB dynamics.

Digital repetitive control under time-varying sampling period: An LMI stability analysis

Digital repetitive control is a technique which allows to track periodic references and/or reject periodic disturbances. Repetitive controllers are usually designed assuming a fixed frequency for the signals to be tracked/rejected, its main drawback being a dramatic performance decay when this frequency varies. A usual approach to overcome the problem consists of an adaptive change of the sampling time according to the reference/disturbance period variation. This article presents a stability analysis of a digital repetitive controller working under time-varying sampling period by means of an LMI gridding approach. Theoretical developments are illustrated with experimental results.

Discrete-time integral MRAC with minimal controller synthesis and parameter projection

Model reference adaptive controllers with Minimal Control Synthesis are effective control algorithms to guarantee asymptotic convergence of the tracking error to zero not only for disturbance-free uncertain linear systems, but also for highly nonlinear plants with unknown parameters, unmodeled dynamics and subject to perturbations. However, an apparent drift in adaptive gains may occasionally arise, which can eventually lead to closed-loop instability. In this paper, we address this key issue for discrete-time systems under L-2 disturbances using a parameter projection algorithm. A consistent proof of stability of all the closed-loop signals is provided, while tracking error is shown to asymptotically converge to zero. We also show the applicability of the adaptive algorithm for digitally controlled continuous-time plants. The proposed algorithm is numerically validated taking into account a discrete-time LTI system subject to parameter uncertainty, parameter variations and L-2 disturbances. Finally, as a possible engineering application of this novel adaptive strategy, the control of a highly nonlinear electromechanical actuator is considered

Periodic solutions with nonconstant sign in Abel equations of the second kind

Abstract The study of periodic solutions with constant sign in the Abel equation of the second kind can be made through the equation of the first kind. This is because the situation is equivalent under the transformation x ↦ x − 1 , and there are many results available in the literature for the first kind equation. However, the equivalence breaks down when one seeks for solutions with nonconstant sign. This note is devoted to periodic solutions with nonconstant sign in Abel equations of the second kind. Specifically, we obtain sufficient conditions to ensure the existence of a periodic solution that shares the zeros of the leading coefficient of the Abel equation. Uniqueness and stability features of such solutions are also studied.

A functional iterative approach to the tracking control of nonminimum phase switched power converters

In this article, we introduce a methodology that, under appropriate assumptions, provides exact output voltage tracking of smooth periodic references in a class of nonminimum phase, single-input, basic DC-to-DC nonlinear switched power converters by means of a stable inversion approach. Firstly, a