Feedback Switching Research Articles

Feedback switching control of a walking piezoelectric actuator for trajectory tracking

Abstract This paper proposes a feedback switching control (FSC) scheme for a Walking Piezoelectric Actuator (WPA) to track a time-varying trajectory. A WPA has two feet with each foot integrated with a clamp and shear Piezoelectric Stack Actuators (PSAs). The first foot pushes the stage translator a step forward when clamped while the second foot is reset and retracted; subsequently, ‘foot switching’ occurs; as a result, the second foot is clamped to push the translator to make a next step forward and the first foot is reset and retracted. To make sure that the translator is always controlled in closed-loop no matter which foot is clamped, the FSC scheme is proposed. It consists of a clamping waveform generator which converts the trajectory into control signals for the clamp PSAs of the two feet and a feedback controller which provides control signals for the two shear PSAs of the feet. Experimental results show that the proposed control scheme achieves a tracking error of 0.028 µm for a constant velocity trajectory, which is a 75% reduction compared to the 0.113 µm of waveform-based control with ILC compensation in literature.

Dynamic output feedback robust MPC hybrid fault-tolerant control for discrete uncertain systems: a switching control strategy

To guarantee the control performance of the discrete system under unmeasurable state and partial actuator failure, a robust dynamic output feedback predictive fault-tolerant control method derived from switching strategy is developed. A new iterative error switching model is established, which both ensures tracking performance and lays the foundation for the development of the next switching controller. Based on this model, output feedback switching fault-tolerant controller is developed. Compared with conventional fault-tolerant control methods, the designed controller can be used under the case of unmeasurable states, and it is more fault tolerant and less conservative. According to the Lyapunov stability theory, the robust stability analysis is carried out under normal and fault conditions, respectively. Then, depending on the findings of the stability analysis, sufficient conditions to guarantee the stability of the closed-loop normal and faulty system are derived. Finally, the suggested method's efficacy is confirmed using the injection moulding process as an example.

Safety-Critical Stabilizing Design of Switched Linear Autonomous Systems

For continuous-time switched linear autonomous systems, this work addresses the stabilization problem under safety-critical constraints. Given an origin-symmetric region that any state trajectory should be stayed, we seek to design a switching law to achieve both stability and safety. The main approach is to characterize, both theoretically and algorithmically, the safe initial set that any initial state within the set could stay in the given safety region with a properly designed switching law. Technically, we develop a design procedure that could approximate the safe initial set with the help of the pathwise state feedback switching strategy. A third-order example is presented to validate the effectiveness of the proposed methodology.

Optimization of transient performance for continuous-time switched linear autonomous systems

For the general class of continuous-time switched linear autonomous systems, this work presents a constructive design scheme to estimate and optimize the transient response in terms of state overshoot and settling time. Based on the pathwise state feedback switching strategy, we present theoretical characterizations of the transient performance, and develop a computational design procedure that optimizes the state overshoot and settling time in a constructive manner. A numerical example is presented to show the effectiveness of the proposed design scheme.

Asynchronous Fault Detection for Memristive Neural Networks With Dwell-Time-Based Communication Protocol.

This article studies the asynchronous fault detection filter problem for discrete-time memristive neural networks with a stochastic communication protocol (SCP) and denial-of-service attacks. Aiming at alleviating the occurrence of network-induced phenomena, a dwell-time-based SCP is scheduled to coordinate the packet transmission between sensors and filter, whose deterministic switching signal arranges the proper feedback switching information among the homogeneous Markov processes (HMPs) for different scenarios. A variable obeying the Bernoulli distribution is proposed to characterize the randomly occurring denial-of-service attacks, in which the attack rate is uncertain. More specifically, both dwell-time-based SCP and denial-of-service attacks are modeled by means of compensation strategy. In light of the mode mismatches between data transmission and filter, a hidden Markov model (HMM) is adopted to describe the asynchronous fault detection filter. Consequently, sufficient conditions of stochastic stability of memristive neural networks are devised with the assistance of Lyapunov theory. In the end, a numerical example is applied to show the effectiveness of the theoretical method.

Stabilization of discrete-time switched systems with constraints by dynamic logic-based switching feedback

A switching feedback has more flexibility in stabilizing systems compared to a feedback being continuous in state. In practice, a system controlled by a state-triggered switching law exhibits more robustness than by a time-triggered one. However, designing an admissible switching law in the static feedback form is difficult or even impossible when the switching sequence is subjected to certain constraints, such as the minimum dwell-time constraints. This study proposes a class of switching feedbacks with dynamic switching logic for discrete-time switched systems with constrained switching. First, a logic dynamic generator (LDG) is constructed to generate all admissible switching sequences. By combining the switched system with the LDG, the original switched system is transformed into a switched system without constraint on switching. Then, the logic and the continuous states are merged by using the theories of the semi-tensor product (STP) of matrices and the vector-representation of logic. Using this technique, the problem considered is then transformed into a problem of designing a state-triggered switching feedback for a merged switched system without constraints, and then to a problem of solving a set of bilinear matrix inequalities. Examples show that the proposed switching law with dynamic logic can stabilize certain switched systems that cannot be stabilized by existing switching laws in the static feedback form.

Nonlinear feedback switching rule design for sector‐bounded switched systems

AbstractThis article presents a robust switching rule design technique for a class of nonlinear and uncertain switched systems. The approach is based on a state transformation that allows for nonlinear state feedback. The results are given in terms of linear matrix inequality problems and they guarantee global asymptotic stability of the closed‐loop system even if sliding modes occur on any switching surface. The class of systems considered is general enough to include multiple time varying sector‐bounded nonlinearities associated with real‐time changes in the operation point. The potential of the method is illustrated through photovoltaic systems, in which the nonlinear I–V characteristic of the modules is treated as a sector‐bounded function. As the slope of the sectors depend on the environmental conditions, robust sectors containing the nonlinearities for any uncertain uniform operation condition are derived.

Necessary and sufficient conditions for quadratic stabilizability of switched systems on non-uniform time domains

In this paper, we consider the quadratic stabilizability via state feedback for a particular class of switched systems that evolve on a non-uniform time domain by introducing time scales theory. The system considered switches between a continuous-time subsystem with variable lengths and a discrete-time subsystem with variable discrete step sizes. Necessary and sufficient conditions are derived to guarantee the quadratic stability of this class of switched systems via a switching state feedback law based on the existence of a common positive definite matrix satisfying the quadratic stabilizability condition by considering that the two subsystems are unstable. By state feedback, we mean that the switching among subsystems depends on the system states. Current results for this kind of state switching feedback control are derived only for switched systems evolving on a continuous time domain or a discrete time domain with fixed step’s size. These results are not applicable for the particular class of switched systems where there is a mixing between the continuous and discrete dynamics. This motivates the derivation of a new and more general state feedback control law for switched systems in this work. A numerical example illustrating the results is presented.

Transport of coupled particles in fractional feedback ratchet driven by Bounded noise

In this paper, the transport of coupled particles in fractional feedback potential driven by two bounded noises is investigated. The mean velocity of coupled particles is calculated versus the fractional order, barrier height, noise intensity, coupling intensity and static length. The results suggest that compared with the integer order feedback potential, the fractional order situation can affect the switching frequency of the feedback potential, and thereby regulate the transport speed of coupled particles. Therefore, a new quantity Cf is specially introduced to quantify the feedback switch frequency. In addition, the superposition of bounded noises on the coupled particles will lead to the increase of mean velocity. It is worth noting that for a definite noise intensity, an optimal fractional order can be found to bring the particles reach the maximum velocity. Once the fractional order is greater than the optimal value, the mean velocity will drop sharply to near zero. Furthermore, our results also show that the optimal static length can increase the transport velocity when the coupling coefficient is properly selected. This can provide theoretical basis for the treatment of diseases caused by neurotransmitter transport disorder.

The human MRS2 magnesium-binding domain is a regulatory feedback switch for channel activity.

Mitochondrial RNA splicing 2 (MRS2) forms a magnesium (Mg2+) entry protein channel in mitochondria. Whereas MRS2 contains two transmembrane domains constituting a pore on the inner mitochondrial membrane, most of the protein resides within the matrix. Yet, the precise structural and functional role of this obtrusive amino terminal domain (NTD) in human MRS2 is unknown. Here, we show that the MRS2 NTD self-associates into a homodimer, contrasting the pentameric assembly of CorA, an orthologous bacterial channel. Mg2+ and calcium suppress lower and higher order oligomerization of MRS2 NTD, whereas cobalt has no effect on the NTD but disassembles full-length MRS2. Mutating-pinpointed residues-mediating Mg2+ binding to the NTD not only selectively decreases Mg2+-binding affinity ∼sevenfold but also abrogates Mg2+ binding-induced secondary, tertiary, and quaternary structure changes. Disruption of NTD Mg2+ binding strikingly potentiates mitochondrial Mg2+ uptake in WT and Mrs2 knockout cells. Our work exposes a mechanism for human MRS2 autoregulation by negative feedback from the NTD and identifies a novel gain of function mutant with broad applicability to future Mg2+ signaling research.

Green energy-saving robust control for ship course-keeping system based on nonlinear switching feedback

To further save energy and reduce carbon emissions, a simple and robust green energy-saving control algorithm was proposed under the premise that the ship achieved an excellent course-keeping effect. To this end, the controller is designed by employing the third-order closed-loop gain shaping algorithm, and the final control law is obtained via the nonlinear switching feedback technique. The robustness of the system is proved by the Nyquist stability criterion. An evaluation model is carefully established for energy-saving and carbon-reduction of the course-keeping controller. The nonlinear Nomoto and Norrbin models for MV “Yukun” are implemented for simulating and further assessing under normal and heavy sea conditions. Compared with the nonlinear decoration controller, the proposed controller enhances the ship's course-keeping accuracy, shortens the delay time and settling time of the controller, lessens the steering angle and steering frequency of the rudder, increases the robustness of the system, and reduces the comprehensive energy-saving index by 26.1% under normal sea conditions. Meanwhile, good controller performance and green energy-saving effects are more in line with the requirements of navigation practice, which is essential for ships to achieve safe, economical, green, and low-carbon navigation.

Set stabilizability of switched Boolean control networks via Ledley antecedence solution

This paper studies two kinds of set stabilizability issues of switched Boolean control networks (SBCNs) by Ledley antecedence solution, that is, pointwise set stabilizability and set stabilizability under arbitrary switching signals. Firstly, based on the state transition matrix of SBCNs, the mode-dependent truth matrix is defined. Secondly, using the mode-dependent truth matrix in every step, a switching signal and the corresponding Ledley antecedence solutions are determined. Furthermore, a state feedback switching signal and a state feedback control are obtained for the pointwise set stabilizability. Thirdly, with the help of all mode-dependent truth matrices, the Ledley antecedence solutions are derived for a set of Boolean inclusions, which admits a state feedback control for the set stabilizability under arbitrary switching signals. Finally, an example is given to show the effectiveness of the proposed results.

Fuel Economy-Oriented Vehicle Platoon Control Using Economic Model Predictive Control

Vehicle platoon control based on vehicle-to-vehicle (V2V) communication is one of the promising technologies to improve the performance of transportation systems. This paper presents a distributed controller to optimize a vehicle platoon’s fuel consumption by combining the switching feedback control and economic model predictive control (EMPC) methods. The closed-loop dynamics involving switching feedback gains with the constant time headway (CTH) policy are established firstly, and the multiple-predecessor following (MPF) communication topology is considered. In order to obtain the economy optimal feedback gain, we design a local optimal control problem for each vehicle, based on which the average dwell time is defined and the distributed EMPC algorithm is designed. Based on linear matrix inequalities (LMIs) and the Lyapunov theorem, the feedback gain selection method and the lower bound for average dwell time that guarantees asymptotic stability are analyzed rigorously. Then a modified algorithm that can ensure string stability is designed. Numerical simulations show a maximum of 6.84% fuel benefit compared with pure tracking-oriented methods.

A Control Actuation Concept for Self-Oscillating Resonant Converters

This article presents a concept of controller actuation mechanism for self-oscillating resonant converters (SORCs). Simplicity, robustness, and cost-effectiveness are among the main features of this type of converter. Described as a self-oscillating system with an intrinsic positive-type feedback switching network, also known as the self-oscillating command circuit (SOCC), it performs its own gate drive with self-sustained frequency, designed around an equilibrium point. Designers often disregard this converter as an explicit solution for closed-loop applications, especially those that require extra layers of control, due to its inherent inability to operate under pulse frequency modulation without extra circuitry. Thus, in this article, a robust, efficient, and simple way of controlling the SORC through frequency modulation is proposed. The idea consists of varying the self-oscillating frequency through the equivalent magnetizing inductance of the SOCC, using a mechanism called variable current transformer. Thus, through the injection of a small controllable dc current, it is possible to modulate the frequency of resonant converters. This allows the self-oscillating system to follow a reference current signal, operating in closed-loop over a wide range of input voltage and load variation.

Practical Stability Analysis and Switching Controller Synthesis for Discrete-time Switched Affine Systems via Linear Matrix Inequalities

This paper considers the practical asymptotic stabilization of adesired equilibrium point in discrete-time switched affine systems.The main purpose is to design a state feedback switching rule forthe discrete-time switched affine systems whose parameters can beextracted with less computational complexities. In this regard,using switched Lyapunov functions, a new set of sufficientconditions based on matrix inequalities are developed to solve thepractical stabilization problem. For any size of the switched affinesystem, the derived matrix inequalities contain only one bilinearterm as a multiplication of a positive scalar and a positivedefinite matrix. It is shown that the practical stabilizationproblem can be solved via a few convex optimization problems,including Linear Matrix Inequalities (LMIs) through gridding of ascalar variable interval between zero and one. The numericalexperiments on an academic example and a DC-DC buck-boost converter,as well as comparative studies with the existing works, prove thesatisfactory operation of the proposed method in achieving betterperformances and more tractable numerical solutions.

Approximate bang-bang control assisted rapid switching feedback stabilization for stochastic qubit systems

For stochastic qubit systems under measurement feedback, an approximate bang-bang control assisted rapid switching control scheme with fewer switching times between the two subsets of state space is proposed in this paper. An eigenstate for single-qubit systems and any GHZ entangled state for multi-qubit systems are prepared successfully. In our control scheme, the state space is partitioned into two parts: a subset S1 containing the target state and its complementary set S2. On each subset, a Lyapunov function is selected and the corresponding control law is designed, where the control laws in S1 are of approximate bang-bang form and therefore can speed up the control process and the control laws in S2 ensure the strictly monotonic descent of the corresponding Lyapunov function and therefore can reduce the switching times. In particular, for multi-qubit systems with degenerate measured observables, we use two control channels to distinguish the target state from other isospectral eigenstates. By properly constructing the control Hamiltonians and using stochastic Lyapunov stability theory, we prove that the switching control laws in this paper render the system trajectory to switch at most twice on the boundary of S1 and S2 and to converge to the target state contained in S1 rapidly. Numerical simulations verify the effectiveness and rapidity of the proposed rapid control scheme.

Sliding Model-Based Predictive Torque Control of Induction Motor for Electric Vehicle

This article presents a sliding model-based predictive torque control (S-PTC) of an induction motor for the electric vehicle application. In this work, a battery-operated bidirectional converter fed induction machine-driven power train system is considered. In the conventional predictive torque control (C-PTC), only the machine model is used for the prediction of stator flux, current, and electromagnetic torque. Unlike the C-PTC, the presented control scheme offers a nonlinear switching feedback term in the prediction equation to overcome the model uncertainties, disturbances, and variation in motor parameters. The gains of the feedback terms are selected based on the Lyapunov stability criterion. Adaptive full order observer is used for the estimation of speed and rotor flux. This method is implemented and the speed response and torque ripple of the motor are analyzed for various operating modes of the vehicle. The robustness of the control is verified for variation in motor parameters and a comparison is shown to justify the achievement of objectives through S-PTC than with C-PTC. The control algorithm for the developed system is verified experimentally through the laboratory prototype.

A switching feedback control approach for persistence of managed resources

<p style='text-indent:20px;'>An adaptive switching feedback control scheme is proposed for classes of discrete-time, positive difference equations, or systems of equations. In overview, the objective is to choose a control strategy which ensures persistence of the state, consequently avoiding zero which corresponds to absence or extinction. A robust feedback control solution is proposed as the effects of different management actions are assumed to be uncertain. Our motivating application is to the conservation of dynamic resources, such as populations, which are naturally positive quantities and where discrete and distinct courses of management actions, or control strategies, are available. The theory is illustrated with examples from population ecology.</p>

Robust control for uncertain impulsive systems with input constraints and external disturbance

AbstractThis paper is concerned with the problem of robust control for uncertain impulsive systems with input constraints. The parametric uncertainties are assumed to be time‐varying and norm‐bounded. The input constraints under consideration are novel reverse polytopic constraints avoiding a set of specified input values. Via the designed state feedback switching control law, the input constraints can be satisfied. Moreover, by applying the Lyapunov function theory, sufficient conditions for robust stabilization and control are established in terms of linear matrix inequalities. A numerical example is given to demonstrate the effectiveness of the proposed control method.

A Dynamic Event-Triggered Approach to State Estimation for Switched Memristive Neural Networks With Nonhomogeneous Sojourn Probabilities

This paper investigates the state estimation for switched memristive neural networks with nonhomogeneous sojourn probabilities. Essentially different from most current literature, a novel switching law is developed to depict the dynamic behavior of switched memristive neural networks, in which the sojourn probabilities of each subsystem are assumed to be nonhomogeneous, and a higher-level deterministic switching signal is proposed to regulate proper feedback switching information by means of the average dwell time approach. Meanwhile, to alleviate the constraint network bandwidth resource efficiently, a dynamic event-triggered mechanism with a novel threshold parameter is proposed in determining if the current data should be released or not. By resorting to the Lyapunov functional technique and the stochastic analysis strategy, some sufficient conditions are addressed to ensure the stochastic stability of the augmented switched memristive neural networks. In the end, the effectiveness and superiority of the developed results are verified by a numerical example.