252 research outputs found
Analysis of explicit and implicit discrete-time equivalent-control based sliding mode controllers
Different time-discretization methods for equivalent-control based sliding
mode control (ECB-SMC) are presented. A new discrete-time sliding mode control
scheme is proposed for linear time-invariant (LTI) systems. It is error-free in
the discretization of the equivalent part of the control input. Results from
simulations using the various discretized SMC schemes are shown, with and
without perturbations. They illustrate the different behaviours that can be
observed. Stability results for the proposed scheme are derived
Comparisons between implicit and explicit discrete-time implementations of equivalent-control-based sliding mode controllers: input and output chattering suppression via the implicit method
This paper presents a set of experimental results concerning the sliding mode control of an electro-pneumatic system. The controller is implemented via a micro-processor as a discrete-time input. Three discrete-time control strategies are considered for the implementation of the discontinuous part of the sliding mode controller: explicit discretizations with and without saturation, and an implicit discretization (that is very easy to implement with a projection on the interval [−1, 1]). While the explicit implementation is known to generate numerical chattering, the implicit one is expected to significantly reduce chattering while keeping the accuracy. The experimental results reported in this work remarkably confirm that the implicit discrete-time sliding mode supersedes the explicit ones, with several important features: chattering in the control input is almost eliminated (while the explicit and saturated controllers behave like high-frequency bang-bang inputs), the input magnitude depends only on the perturbation size and is independent of the controller gain and sampling time. On the contrary the explicit controller shows obvious chattering for all sampling times, its magnitude increases as the controller gain increases, and it does not reduce when the sampling period augments. The tracking errors arecomparable for both methods, though the implicit method keeps the precision when the control gain increases, which is not the case for the explicit one. Introducing a saturation in the explicit controller does not allow to significantly improve the explicit controller behaviour
Discrete-time twisting controller without numerical chattering: analysis and experimental results with an implicit method
International audienceIn this note, we present an implementation of the twisting controller on an electropneumatic plant for a tracking control problem. Implicit and explicit discrete-time twisting controllers are considered, and some implementation details are provided. Experimental results are provided and analyzed. They sustain the theoretical superiority of the implicitly discretized version, as shown in previous work. The main advantages of the implicit method are better tracking and drastic reduction in the input and output chattering. This is achieved without modifying the controller structure compared to its continuous-time version
Multivalued robust tracking control of fully actuated Lagrange systems: Continuous and discrete–time algorithms
International audienceIn this paper the robust trajectory tracking problem of a class of nonlinear systems described by the Euler–Lagrange equations of motion is studied. We start considering a plant under the effects of an unknown external perturbation and also with uncertainties on its parameters. After that a class of passivity-based multivalued control laws is proposed and the well–posedness together with the stability of the closed–loop are established in the continuous–time setting. The discrete–time version of the plant and the controller are studied and well–posedness together with stability results are obtained, using the so-called implicit discretization approach introduced in [1, 2]. Numerical simulations are presented and demonstrate the effectiveness of the proposed discrete-time controller
Comparison between explicit and implicit discrete-time implementations of sliding-mode controllers
International audienceDifferent time-discretization methods for sliding mode control (SMC) are presented. A new discrete-time sliding mode control scheme is proposed for linear time-invariant (LTI) systems. It is error-free in the discretization of the equivalent part of the control input. Results from simulations using the various discretized SMC schemes are shown, with and without perturbations. They illustrate the different behaviours that can be observed
Adaptive Discrete Second Order Sliding Mode Control with Application to Nonlinear Automotive Systems
Sliding mode control (SMC) is a robust and computationally efficient
model-based controller design technique for highly nonlinear systems, in the
presence of model and external uncertainties. However, the implementation of
the conventional continuous-time SMC on digital computers is limited, due to
the imprecisions caused by data sampling and quantization, and the chattering
phenomena, which results in high frequency oscillations. One effective solution
to minimize the effects of data sampling and quantization imprecisions is the
use of higher order sliding modes. To this end, in this paper, a new
formulation of an adaptive second order discrete sliding mode control (DSMC) is
presented for a general class of multi-input multi-output (MIMO) uncertain
nonlinear systems. Based on a Lyapunov stability argument and by invoking the
new Invariance Principle, not only the asymptotic stability of the controller
is guaranteed, but also the adaptation law is derived to remove the
uncertainties within the nonlinear plant dynamics. The proposed adaptive
tracking controller is designed and tested in real-time for a highly nonlinear
control problem in spark ignition combustion engine during transient operating
conditions. The simulation and real-time processor-in-the-loop (PIL) test
results show that the second order single-input single-output (SISO) DSMC can
improve the tracking performances up to 90%, compared to a first order SISO
DSMC under sampling and quantization imprecisions, in the presence of modeling
uncertainties. Moreover, it is observed that by converting the engine SISO
controllers to a MIMO structure, the overall controller performance can be
enhanced by 25%, compared to the SISO second order DSMC, because of the
dynamics coupling consideration within the MIMO DSMC formulation.Comment: 12 pages, 7 figures, 1 tabl
Modified Implicit Discretization of the Super-Twisting Controller
In this paper a novel discrete-time realization of the super-twisting
controller is proposed. The closed-loop system is proven to be globally
asymptotically stable in the absence of a disturbance by means of Lyapunov
theory. Furthermore, the steady-state error in the disturbed case is computed
analytically and shown to be independent of the parameters. The steady-state
error only depends on the sampling time and the unknown disturbance. The
proposed discrete-time controller is compared to previously published
discrete-time super-twisting controllers by means of the controller structure.
In extensive simulation studies the proposed controller is evaluated
comparative to known controllers. The continuous-time super-twisting controller
is capable of rejecting any unknown Lipschitz-continuous perturbation.
Furthermore, the convergence time decreases, if any of the gains is increased.
The simulations demonstrate that the systems closed in the loop with each of
the known controllers lose one of these properties, introduce
discretization-chattering effects, or do not yield the same accuracy level as
with the proposed controller. The proposed controller, in contrast, is
beneficial in terms of the above described properties of the continuous-time
super-twisting controller
Experimental Comparisons Between Implicit and Explicit Implementations of Discrete-Time Sliding Mode Controllers: Toward Input and Output Chattering Suppression
International audienceThis brief presents a set of experimental results concerning the sliding mode control of an electropneumatic system. Two discrete-time control strategies are considered: an explicit and an implicit (that is very easy to implement with a projection on the interval [−1, 1]) Euler discretizations. While the explicit implementation is known to generate numerical chattering , the implicit one is expected to significantly reduce chattering while keeping the accuracy. The experimental results reported in this brief remarkably confirm that the implicit discrete-time sliding mode supersedes the explicit ones, with several important features: chattering in the control input is almost eliminated (while the explicit and saturated controllers behave like high-frequency bang–bang inputs), the input magnitude depends only on the perturbation size and is independent of the controller gain and sampling time
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