Reset Rule Research Articles

Stick–slip oscillations in the low feed linear motion of a grinding machine due to dry friction and backlash

This paper deals with mechanical modelling and numerical bifurcation analysis of stick–slip oscillations that plague extremely low feed grinding operations. Based on experimental observations, a novel two degree of freedom mechanical model of a grinding machine feed drive system is formulated, which incorporates Stribeck-type dry friction, position and velocity controller dynamics, and actuator backlash. Loss and re-establishment of contact between the feed drive elements is modelled through both rigid-body impacts and a contact-stiffness model. The resulting piecewise-smooth equations of motion are subjected to detailed stability and bifurcation analysis with the help of shooting and collocation based numerical continuation tools. Major focus is attributed to the influence of the feed velocity and the control-loop parameters as well as the identification of stable, stick–slip free parameter regimes. Finally, a controller enhancement strategy is proposed, based on event-driven integrator reset rules, to help limit the amplitude of arising limit-cycle oscillations.

Robust Global Attitude Control: Random Reset Rule

In this paper, we propose a new random reset rule for attitude control systems, where a new Lyapunov-Foster function implies the robust global attitude control without adding any constraints on the random reset rule, except the support domain for the involved random variables. Compared with deterministic binary logic variables, random variables introduce an automatically adjusted hysteresis half-width for each reset process, thus bring a flexible tradeoff between the hysteresis-induced inefficiency for avoiding unwinding phenomenon and the robustness to measurement noise. A benchmark case for the attitude tracking control of a miniature quadrotor prototype verifies the designed random reset rule.

Event-triggered control for a class of nonlinear systems with random reset controllers

By taking into account a communication strategy in the state-feedback control law, this paper considers the stability of a class of nonlinear systems, where the controller contains a reset variable satisfying certain reset rule and the reset values are driven by random processes. Randomness enters exclusively through the reset of the controller in terms of certain forced reset condition, yet the framework covers forced and spontaneous transitions through the communication strategy composed of the Zeno-free event-triggered strategy (ETS) and the random reset rule of the reset controller variable. A threshold-based forced ETS is designed depending on system states and the random reset variable, and a clock-based spontaneous ETS is also designed neither depending on system states directly nor depending on the random reset variable. The Lyapunov–Foster conditions ensure the feasibility of the designed communication strategy, which is verified via a benchmark case for the attitude tracking control of a miniature quadrotor prototype.

An approach to the stability of reset switched systems using dynamics without reset

In this paper, we consider switched linear systems that have jumps in the state (determined by a reset rule) at each switching instant. Those systems are called switched systems with state reset. We show that it is possible to analyze the state trajectories of a switched system with state reset by considering suitable switched systems without state resets, that is, with continuous state trajectories. We establish sufficient conditions for the stability of switched systems with state reset using the associated systems without reset. Moreover, introducing some restrictions, we also derive simple algebraic stability conditions. The obtained results are used in numerical examples to show the effectiveness of the proposed approach.

Reset control and ℒ2-gain analysis of piecewise-affine systems

This paper is concerned with reset controller design and L 2 -gain stability of piecewise-affine systems under the framework of hybrid systems. Firstly, stability conditions of piecewise-affine systems under dynamic state-feedback control are established through bilinear matrix inequality conditions. Secondly, a reset controller with reset rules under the hybrid systems framework is proposed in the sense of Lyapunov and sufficient conditions for exponential and L 2 -gain stability of the closed-loop systems are provided. Different from the piecewise-affine systems with the dynamic state-feedback controller, the reset controller is designed such that the L 2 -gain performance of piecewise-affine systems can be enhanced. Thirdly, an LMI approach is proposed to avoid the difficulty of solving the bilinear matrix inequalities. Furthermore, robustness to inflations of the flow and jump sets is established, and robustness to the norm-bounded uncertainties is proposed. Finally, numerical simulations including a robot arm system, an inverted pendulum system and the Chua's circuit system are provided to illustrate the results.

Study of distributed model predictive control for radiant floor heating systems with hydraulic coupling

Radiant floor heating (RFH) is an advanced technology that can couple with renewable low-temperature sources and improve occupant thermal comfort. However, due to the large thermal inertia, the conventional control strategies based on heuristic rules have difficulty handling a room temperature response to changes in weather or set-points. Because of the excellent coping ability, model predictive control (MPC) has aroused increasing attention as a promising solution to manage RFH. This research is focused on the MPC scheme for RFH systems, especially large-scale RFH systems with hydraulic coupling. First, we develop a novel control-oriented thermodynamic model for an RFH system. A new calculating method for the floor surface temperature is adopted to avoid defining the thermal resistance and thermal capacity of the virtual core temperature layer, and the heat transfer along water flow and weather elements like solar radiation and wind are considered. Then an experiment is conducted to validate that the accuracy can be adequate for the prediction of MPC. Next, we design a distributed MPC scheme for RFH systems with hydraulic coupling. A supply reset rule for central equipment is improved, and a hierarchical optimization algorithm is proposed to implement the distributed MPC scheme. Then a simulation test is carried out with results showing that the scheme can achieve hydraulic decoupling between occupants, thus avoiding room temperature fluctuations and decreasing the root-mean-square error by 0.24 °C. An appropriate supply set-point is recommended that meets thermal comfort demands with minimum energy consumption.

Extended hybrid control scheme for asynchronous switching

This paper is devoted to the problem of extended hybrid control for asynchronous switching between system modes (we call each subsystem a mode) and controller candidates. Such undesirable behavior is caused by mismatch delay. Since asynchronous switching is relevant in many switched systems, this paper presents highly impressive results in stabilizing and controlling a switched linear system infected by mismatch delay. In this technical note, an asynchronous switched system is considered as a switched system with new stable and unstable subsystems.Through piecewise Lyapunov-like function (LLF) approach, two different mode-dependent dwell time (MDT) structures are designed. These dwell time structures satisfy a lower bound and an upper bound for stable and unstable part of each controlled subsystem respectively. In this regard, a hybrid control scheme with L2-gain stability analysis is provided for the mentioned system to cover the mismatch defect. The obtained boundary conditions can be incorporated with the synthesis problem in convex formation. Besides, to have more satisfying results, a rest supervisor is also considered to enforce the reset rules to the controller candidates. By determining acceptable dwell time parameters, the controller gain matrices of the new approach will be calculated to solve linear matrix inequality (LMI) optimization. Finally, the effectiveness of the obtained theoretical results is demonstrated via a numerical example.

On global mechanisms of synchronization in networks of coupled chaotic circuits and the role of the voltage-type coupling

A model for synchronization of coupled Nakano’s chaotic circuits is studied. The Nakano circuit consists of a simple RLC circuit with a switch voltage-depending reset rule which generates a discontinuous dynamics. Thus, the model that we study is a network of identical spiking oscillators with integrate-and-fire dynamics. The coupling between oscillators is linear, but the network is subject to a common regime of reset depending on the global state of the oscillator population. This constitutes the simplest way of build pulse-coupled networks with arbitrary topology for this type of oscillators, and it allows the emergence of synchronous states and different reset regimes. The main result is that under certain hypothesis over the weight matrix (that represents the network topology) the different reset regimes match and the formalism of the master stability function can be generalized in order to study the stability of the synchronous state and the discontinuous dynamic of the network. Also, the low dimensionality of the Nakano’s circuit allows to implement the saltation-matrix method and numerical simulations can be performed in order to analyze the role of the coupling mode in the synchronization regime of the network and the influence of the voltage-type variables.

Bemessungshilfen für biegedruckbeanspruchtes unbewehrtes Mauerwerk – Teil 2: Anwendung von Bemessungshilfen für die Bemessung nach DIN EN 1996‐1‐1/NA

AbstractThe semi‐probabilistic safety concept of divided safety factors for action and resistance of DIN EN 1990 [1] in combination with the structural design codes DIN EN 1996‐1‐1 [2] and DIN EN 1996‐1‐1/NA [3] include the requirement that acting normal forces NEd may not exceed the normal force resistances NRd for the structural design of masonry under bending compression. According to [3], fully plastic material behaviour can be assumed and the stress block used as the material law for masonry.Building on this, design aids and their theoretical basis were presented in Part 1 of this scientific paper [4], which are comparable with the ω tables (called the ɸ table here) and the general design diagram for massive construction.The application of the design aids is described in this second part of this scientific paper through calculation examples and the connection with the calculation approaches of [3] is made clear.The relation to the reduction factor ɸm, which covers effects of 2nd order theory, is also obtained. With known values of the load eccentricities according to 1st and 2nd order theory, the design task becomes the analysis of the loadbearing capacity of the masonry section at half wall height. Knowing ɸm, the load eccentricity e2 and the additional moment according to 2nd order theory can subsequently be determined, which does not ensue from the calculation equations of [3].With the general design diagram, the values of compression zone height and the assumed load eccentricities of the acting normal forces, which result from the reset rule for masonry sections with high load eccentricities, can be directly read off, greatly improving the clarity of this procedure.

Synchronization of Electrically Coupled Resonate-and-Fire Neurons.

Electrical coupling between neurons is broadly present across brain areas and is typically assumed to synchronize network activity. However, intrinsic properties of the coupled cells can complicate this simple picture. Many cell types with electrical coupling show a diversity of post-spike subthreshold fluctuations, often linked to subthreshold resonance, which are transmitted through electrical synapses in addition to action potentials. Using the theory of weakly coupled oscillators, we explore the effect of both subthreshold and spike-mediated coupling on synchrony in small networks of electrically coupled resonate-and-fire neurons, a hybrid neuron model with damped subthreshold oscillations and a range of post-spike voltage dynamics. We calculate the phase response curve using an extension of the adjoint method that accounts for the discontinuous post-spike reset rule. We find that both spikes and subthreshold fluctuations can jointly promote synchronization. The subthreshold contribution is strongest when the voltage exhibits a significant post-spike elevation in voltage, or plateau potential. Additionally, we show that the geometry of trajectories approaching the spiking threshold causes a "reset-induced shear" effect that can oppose synchrony in the presence of network asymmetry, despite having no effect on the phase-locking of symmetrically coupled pairs.

Design aids for unreinforced masonry under bending compression – Part 1: Basics

AbstractThe semi‐probabilistic safety concept of divided safety factors for action and resistance of DIN EN 1990 [1] led in Germany to a comparison of resisting bending moments and normal forces with the corresponding acting section forces and moments in the structural design of masonry building elements.Regarding the material properties for masonry under bending compression, fully plastic material behaviour is assumed in DIN EN 1996‐1‐1/NA [2]. The use of a stress block has been introduced as a material law, which results in the reduction factor ϕ for the determination of the loadbearing capacity of the section. This describes the ratio of the normal force resistance of the reduced (due to the bending effect) part of the design section under compression and the resistance value related to the total area.Building on this, design aids are presented here, which are comparable with the ν tables (called ϕ table here) and the ”general structural design program“ of massive building, since common mechanical basics permit this.The user‐friendly handling of the design diagram and design tables is demonstrated through examples in the second part of the scientific paper [3] and the relation to the calculation approaches of DIN EN 1996‐1‐1/NA [2] is made clear. The relation to the reduction factor ϕm, which takes into account the effects of second order theory, is also described in [3], like the use of the reset rule for masonry sections with normal forces acting with large load eccentricities.

A solution for enhancement of transient performance in nonlinear adaptive control: Optimal adaptive reset based on barrier Lyapunov function

In this paper, an adaptive controller based on barrier Lyapunov function combined with an optimal reset rule is devised in order to improve the transient performance of nonlinear adaptive control. A novel reset rule is designed such that the estimated parameters of the adaptive controller jump to the optimal values in a way that optimizes a cost function representing the transient performance index. It is proved that asymptotic tracking is achieved and the output remains in a desired bound by ensuring boundedness of the barrier Lyapunov function. Besides, the convergence rate is increased by resetting the estimated parameters to optimal values. A regularly referred example is simulated to demonstrate the effectiveness of the proposed method and the results are compared with the existing investigations.

An Optimal Investment Strategy and Multiperiod Deposit Insurance Pricing Model for Commercial Banks

We employ the method of stochastic optimal control to derive the optimal investment strategy for maximizing an expected exponential utility of a commercial bank’s capital at some future date T>0. In addition, we derive a multiperiod deposit insurance (DI) pricing model that incorporates the explicit solution of the optimal control problem and an asset value reset rule comparable to the typical practice of insolvency resolution by insuring agencies. By way of numerical simulations, we study the effects of changes in the DI coverage horizon, the risk associated with the asset portfolio of the bank, and the bank’s initial leverage level (deposit-to-asset ratio) on the DI premium while the optimal investment strategy is followed.

On [formula omitted] gain performance improvement of linear systems with Lyapunov-based reset control

This paper considers reset rules design for linear systems for the purpose of improving L2 gain performance. Novel Lyapunov-based reset rules are proposed such that the L2 gain performance of reset control systems can be improved compared with the stable base systems, and the proposed method is then extended to observer-based design. Moreover, reset rules design for stabilizing unstable base systems are proposed such that prespecified L2 gain performance can be achieved. Illustrative examples are given to support our results.

Reset strategy for consensus in networks of clusters

This paper addresses the problem of consensus in networks structured in several clusters. The clusters are represented by fixed, directed and strongly connected graphs. They are composed by a number of agents which are able to interact only with other agents belonging to the same cluster. To every agent we associate a scalar real value representing its state. The states continuously evolve following a linear consensus protocol and approach local agreements specific to each cluster. In order to enforce a global agreement over the whole network, we consider that each cluster contains an agent that can be exogenously controlled. The state of this agent, called leader, will be quasi-periodically reseted by a local master controller that receives information from some neighboring leaders. In order to control the consensus value we have to firstly characterize it. Precisely we show that it depends only on the initial condition and the interaction topologies. Secondly, we provide sufficient Linear Matrix Inequality (LMI) conditions for the global uniform exponential stability of the consensus in presence of a quasi-periodic reset rule. The study of the network behavior is completed by a decay rate analysis. Finally we design the interaction network of the leaders which allows to reach a prescribed consensus value. Numerical implementation strategy is provided before illustrating the results by some simulations.

Hybrid Control for Switched Linear Systems With Average Dwell Time

This technical note presents a hybrid control scheme for the output-feedback control of switched linear systems with average dwell time. The proposed hybrid controller consists of a standard switching output-feedback control law and a supervisor enforcing a reset rule for the switching controller states at each switching instant. This hybrid control scheme provides an efficient and systema tic way for designing average dwell time switched linear control systems in the sense that the boundary condition can be incorporated into the synthesis problem in a convex formulation. Specifically, bo th full-order and reduced-order controllers with guaranteed stability and optimal weighted H1 performance will be solved by linear matrix inequality (LMI) optimizations. Simulation studies are included to illustrate the effectiveness of the proposed approach. Index Terms—Switching control; average dwell time; controller state reset; full-order and reduced-order controllers; LMI.

Improving ℒ2 Gain Performance of Linear Systems by Reset Control

In this paper, new Lyapunov-based reset rules are constructed to improve ℒ2 gain performance of linear-time-invariant (LTI) systems. By using the hybrid system framework, sufficient conditions for exponential and finite gain ℒ2 stability are presented. It is shown that the ℒ2 gain of the closed loop system with resets can be improved compared with the base system. Numerical example supports our results.

Anti‐windup strategy for reset control systems

AbstractThis paper proposes an anti‐windup strategy to deal with stability and performance requirements for a class of hybrid systems, such as those including a reset controller and subject to input saturation. The computation of the anti‐windup compensator aiming at ensuring both ℒ︁2 input‐to‐state stability and internal stability of the closed‐loop system is carried out from the solution of matrix inequalities. Depending on the way chosen to describe reset rules, the conditions for designing the anti‐windup compensator are expressed through nonlinear matrix inequalities or linear matrix inequalities. Some optimization criteria in both cases are considered for the synthesis purpose: maximization of the ℒ︁2‐norm upper bound on the admissible disturbances for which the trajectories are assured to be bounded; minimization of the ℒ︁2‐gain of the disturbance to the system‐to‐be‐controlled output; and the maximization of an estimate of the domain of attraction of the origin. Copyright © 2011 John Wiley & Sons, Ltd.

Control of neuromuscular stimulation for ambulation by complete paraplegics via artificial neural networks

The paper describes the application of a neural network (ANN) for controlling a functional neuromuscular stimulation (FNS) system to facilitate patient-responsive ambulation by paralyzed patients with traumatic, thoracic-level spinal cord injuries. The particular ANN that is employed is a modified Adaptive-ResonanceTheory (ART-1) network. It serves as a controller in an FNS system (the Parastep system) that is presently in use by approximately 500 patients worldwide (but still without ANN control) and which was the first and only FNS system approved by FDA. The proposed neural network discriminates above-lesion upper-trunk electromyographic (EMG) time series to activate standing and walking functions under FNS and controls FNS stimuli levels using response-EMG signals. For this particular application, several modifications are introduced into the standard ART-1 ANN. First, a modified on-line learning rule is proposed. The new rule assures bi-directional modification of the stored patterns and prevents noise interference. Second, a new reset rule is proposed, which prevents 'exact matching' when the input is a subset of the chosen pattern. A single ART-1-based structure is being applied to solving two problems, namely (1) signal pattern recognition and limb function determination, and (2) control of stimulation levels. This also facilitates ambulation of paraplegics under FNS, with adequate patient interaction in initial system training, retraining the network when needed, and in allowing patient's manual over-ride in the case of error, where any manual over-ride serves as a re-training input to the neural network. The ANN control facilitates continuous update of control settings during normal use, without formal retraining. [Neurol Res 2001; 23: 472-481]

Artificial neural network control of FES in paraplegics for patient responsive ambulation.

This paper describes an ART-1-based artificial neural network (ANN) adapted for controlling functional electrical stimulation (FES) to facilitate patient-responsive ambulation by paralyzed patients with spinal cord injuries. This network is to serve as a controller in an FES system developed by the first author which is presently in use by 300 patients worldwide (still without ANN control) and which was the first and the only FES system approved by the FDA. The proposed neural network discriminates above-lesion upper-trunk electromyographic (EMG) time series to activate standing and walking functions under FES and controls FES stimuli levels using response-EMG signals. For this particular application, we introduce several modifications of the binary adaptive resonance theory (ART-1) for pattern recognition and classification. First, a modified on-line learning rule is proposed. The new rule assures bidirectional modification of the stored patterns and prevents noise interference. Second, a new reset rule is proposed which prevents "exact matching" when the input is a subset of the chosen pattern. We show the applicability of a single ART-1-based structure to solving two problems, namely, 1) signal pattern recognition and classification, and 2) control. This also facilitates ambulation of paraplegics under FES, with adequate patient interaction in initial system training, retraining the network when needed, and in allowing patient's manual override in the case of error, where any manual override serves as a retraining input to the neural network. Thus, the practical control problems (arising in actual independent patient ambulation via FES) were all satisfied by a relatively simple ANN design.