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

A solution to the stick slip problem for an electropneumatic drive

International audienceThis paper describes a solution to the problem of "stick-slip" for an electro-pneumatic system. The phenomenon of "stick-slip" may appear during the mechanical static state when the position is fixed but the pressures continue to evolve in each actuator chamber, until exceeding the dry friction zone. The system is then in partial equilibrium. The idea to avoid this phenomenon is a switching control law between the tracking position control and the pressure regulation

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

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

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

Implicit discrete-time twisting controller without numerical chattering: analysis and experimental results

International audienceIn this paper, we present an implementation of the sliding mode twisting controller on an electropneumatic plant for atracking control problem. To this end, implicitly and explicitly discretized twisting controllers are considered. We discusstheir structure, properties and implementations, as well as the experimental results. The analysis of the performancesustains the theoretical superiority of the implicitly discretized version, as shown in previous works. The main advantagesof the implicit method are better tracking performance and drastic reduction in the input and output chattering. This isachieved without modifying the structure of the controller compared to its continuous-time version. The tracking errorcannot be used as the sliding variable: it has a relative degree 3 w.r.t. the control input. The tuning of the sliding surfacehas well as some other parameters in the control loop was instrumental in achieving good performance. We detail theselection procedure of those parameters and their influence on the closed-loop behaviour. Finally we also present someresults with an implicitly discretized EBC-SMC controller

Robust output feedback sampling control based on second order sliding mode

International audienceThis paper proposes a new second order sliding mode output feedback controller. This latter is developped in the case of finite sampling frequency and is using only output information in order to ensure desired trajectory tracking with high accuracy in a finite time in spite of uncertainties and perturbations. This new strategy is evaluated in simulations on an academic example

Experimental results on implicit and explicit time-discretization of equivalent-control-based sliding-mode control

International audienceThis chapter presents a set of experimental results concerning the sliding mode control of an electro-pneumatic system. The controller is implemented {\em 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 as 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 are comparable 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 if one does not take care of the saturation width