Switching Instants Research Articles

Differential Riccati equation‐based adaptive stabilization for switched linear systems

SummaryIn this paper, a novel adaptive control design is proposed to stabilize a class of switched linear systems with parametric uncertainties and disturbances. In particular, a family of differential Riccati equations that holds for the finite switching intervals are established, of which the closed‐form solutions are exploited to develop the Lyapunov function for the closed‐loop system. This Lyapunov function is imposed to be decreasing at and between two arbitrary switching instants by solving a group of matrix inequalities, based on which the adaptive controllers for switched linear system with and without disturbances are proposed, respectively. In the nondisturbed setting, asymptotic stability of the adaptive switched linear system is achieved, while the system is bounded in a mean square sense in the disturbed setting. A numerical example of flight control for F4E fighter aircraft is used to illustrate the proposed adaptive control methodology.

Numerical Methods for Event-Detection State Vector Simulation of Switched-Mode Power Supplies

This article presents a new method for the state vector simulation of switched-mode power supplies using decomposed matrices. With this method, switching instances are updated reliably from previously computed values, providing a highly efficient means for event-detection state vector simulation. The method is demonstrated on a 23rd-order state-space piecewise linear model of a boost converter with and without control feedback, resulting in up to $1000\times $ speedup of the simulation, relative to the same circuit simulated in LTspice or Piecewise Linear Electrical Circuit Simulation for Simulink (PLECS).

Wide-Range ZVS Control Technique for Bidirectional Dual-Bridge Series-Resonant DC–DC Converters

For high-voltage and high-power bidirectional dc–dc converters, soft switching of all active power devices is mandatory to ensure the high efficiency and reliability. This paper describes a control technique for wide-range zero-voltage switching (ZVS) implementation of dual-bridge series-resonant dc–dc converters. The proposed control technique integrates variable-frequency modulation (VFM) and phase-shift modulation (PSM), in which the former effectively achieves the ZVS for both step-down and step-up operation, while the latter is employed to further extend the power transmission capability. The proposed technique is built on the time-domain analysis of the ZVS condition. A closed-form solution is formulated that guarantees the sufficient ZVS commutation current at switching instants, accounting for the presence of switches parasitic and/or snubber capacitances, while maintains the rms tank current at near-to-minimum levels. Furthermore, a compensation strategy for the effect of conduction losses is presented achieving better switching behavior and higher efficiency. Compared with the minimum rms current trajectory modulation, lower switching losses, enhanced efficiency, and mitigated voltage ringings are obtained. Effectiveness of the proposed technique is verified by means of a 800 W experimental prototype. Closed-loop operation with the proposed VFM+PSM controller is also implemented and experimentally tested.

Problem of Stabilizing a Switching System Using a Piecewise-Linear Control System

The problem of stabilizing a mathematical hybrid system with switchings between the operating modes is solved. Each of these modes is associated with nonlinear differential equations that have control parameters. The switching instances (conditions) are control components. A stabilizer must be designed in positional form that allows the trajectory of the entire nonlinear system to reach the target set in the phase space for a (prescribed) finite time. To solve the problem, k]an apparatus of continuous piecewise-linear Lyapunov functions is used along with the corresponding piecewise-linear control functions. A theorem concerning the sufficient conditions for the stabilizability of a hybrid system in the considered class of controls is proved. An algorithm for constructing the Lyapunov functions and the stabilizer is given.

Switching Tube-Based MPC: Characterization of Minimum Dwell-Time for Feasible and Robustly Stable Switching

We study the problem of characterizing mode dependent dwell-times that guarantee safe and stable operation of disturbed switching linear systems in a model predictive control (MPC) framework. We assume the switching instances are not known a priori , but instantly at the moment of switching. We first characterize dwell-times that ensure feasible and stable switching between independently designed robust MPC controllers by means of the well established exponential stability result available in the MPC literature. Then, we employ the concept of multiset invariance to improve on our previous results, and obtain an exponential stability guarantee for the switching closed-loop dynamics. The theoretical findings are illustrated via a numerical example.

Event-triggered [formula omitted] control for network-based switched linear systems with transmission delay

This paper investigates the event-triggered L∞ control for network-based switched linear systems with transmission delay. Necessary samplings of the feedback signal are determined by the improved periodic sampling based event-triggering schemes with extra design parameters, which can further reduce redundant signal transmissions and updates. Moreover, under the state feedback control, a time-delay closed-loop switched system is developed. Particularly, in the developing process an active packet loss technique is given to fully deal with the relationship between the network transmission delay and sampling period. Then by utilizing the piecewise Lyapunov functional method and average dwell time technique, sufficient conditions in terms of linear matrix inequalities (LMIs) are constructed to render the time-delay closed-loop switched system globally uniformly ultimately bounded (GUUB) and having an L∞ performance. In addition, since the event-triggered instants and switching instants both exist in the system and may stagger with each other, their coupling effect on the stability analysis is clarified. Subsequently, the conditions for finding the parameters of state feedback gains and improved event-triggering schemes are presented. An example is provided to show the effectiveness of the proposed method.

Stabilisation for switched positive systems under extended asynchronous switching

This study first addresses an extended asynchronous switching control issue resulting from switching delay and false alarm for a family of switched positive systems. Based on a new set of switching signals superior to the average dwell time switching, the state-feedback controller is designed to guarantee the positivity and global asymptotic stability for the closed-loop system. In addition, the corresponding sufficient condition formulated in terms of linear programming problem is derived. Different from the previous works, the authors' established results further relax the restriction that all subsystems must be stabilisable in the normal-running period with matched controller, and allow the increase of the Lyapunov function in the switching delay period, false alarm period, normal-running period with matched controller and all switching instants. Finally, a numerical example with practical considerations is used to show the effectiveness and potential of the proposed theories.

Application of the Angular Independent Variable and Its Regularizing Transformation in the Problems of Optimizing Low-Thrust Trajectories

The expediency of using the true longitude or the associated angle as an independent variable in the problems of optimizing multi-revolution, low-thrust trajectories of spacecraft is considered. The auxiliary longitude is introduced, which is used further as a new independent variable instead of time. The advantage of using the auxiliary longitude as an independent variable in the problem of optimizing the trajectories with a fixed angular range and optimum transfer time is demonstrated. The problems of optimizing the trajectories of spacecraft with an ideally controlled, limited-power engine and a limited-thrust engine with a constant exhaust velocity are considered. The possibility of improving the convergence of the methods of solving the problems of optimizing the trajectories with a limited-thrust engine is considered. This improvement is achieved by joint utilization of the smoothing approximation of a relay thrust-switching function and the regularizing transformation of an independent variable, which extends the switching function values in the vicinity of thrust switching instants. Based on the results, the method for solving the problems of optimizing multi-revolution transfers is proposed; the numerical examples of its application are presented.

Active Cancellation of Vibration in Switched Reluctance Motor Using Mechanical Impulse Response Method

Vibration and acoustic noise are considered as major factors preventing the widespread use of switched reluctance motor (SRM) drives in industrial and commercial applications. In this paper, a new active vibration cancellation strategy for radial vibration is proposed based on the optimal current switching instants. The mechanical impulse response method has been used to estimate the radial vibration of the stator and an optimization routine was developed to define the optimal instants for phase current switching in such a way that the resulting vibration would cancel the vibration caused by prior switching. Experimental verification was conducted on an 8/6 SRM and the results show significant reduction in the stator radial vibration which in turn contributes to reduction of acoustic noise.

Harmonic Minimization in Three-Phase Hybrid Cascaded Multilevel Inverter Using Modified Particle Swarm Optimization

This paper proposes a modified particle swarm optimization (MPSO) for fast convergence and harmonic minimization in three-phase eleven-level hybrid cascaded multilevel inverter (HC-MLI). Selective harmonic elimination pulsewidth modulation (SHE-PWM) technique implemented through MPSO has been used in the proposed work for synthesizing an eleven-level output voltage using two dc sources, a precharged capacitor, and twelve switches. The switching angles of the three-phase eleven-level HC-MLI has been computed for eliminating specified lower order odd harmonics such as 5th, 7th, 11th, and 13th from the output voltage of the HC-MLI. In the proposed MPSO optimized HC-MLI, capacitor voltage balance is also ensured even at higher modulation indices by utilizing the redundant switching states available at different switching instances of the HC-MLI. The performance of the MPSO optimized three-phase eleven-level HC-MLI has been verified through simulation and experimentation on a 1.5-kW prototype using closed-loop control. The results obtained through MPSO are compared with the results obtained through genetic algorithm (GA) and particle swarm optimization (PSO) in terms of convergence rate and harmonic content. It has been found that MPSO gives improved results in comparison to GA and PSO.

Stability conditions of switched nonlinear systems with unstable subsystems and destabilizing switching behaviors

In this paper, the global uniform exponential stability (GUES) for a class of switched nonlinear systems is discussed in both continuous-time and discrete-time contexts. Different from multiple Lyapunov function and average dwell time in the previous work, a general multiple Lyapunov-like function and a modified admissible edge-dependent average dwell time switching scheme based on a directed graph are implemented in this paper. By further allowing the Lyapunov-like function to increase and decrease during the running time of active subsystems, and permitting the admissible transition edge-dependent weights (ATEDWs) to be greater or less than one, the extended stability results for switched systems in a nonlinear situation are first derived. Given a new amalgamation condition between the increasing ratio and decreasing ratio of the Lyapunov-like function at switching instants, the minimal admissible edge-dependent average dwell time (AEDADT) for admissible switching signals are is obtained. By contrasting with the results available on the subject, we allow that all the switching behaviors of the switching systems at switching instants are destabilizing, and the transition weights of admissible transition edge may be less than one1. More especially, even if some of the subsystems are not stable and all the switching behaviors of are destabilizing, the stability property of the switched system can still be preserved. Finally, two numerical examples are illustrated to show the validity of the proposed results.

Optimal Linear Quadratic Regulator of Switched Systems

This paper considers the optimal control problem of linear switched systems with linear quadratic (LQ) cost or multiple LQ cost. By adopting an embedding transformation, the switching design problem is relaxed and transformed into a traditional optimal control problem. The bang–bang-type solutions of the embedded optimal control problems are obtained for both the positive definite LQ cost case and the multiple LQ cost case, which are the optimal solutions to the original problems. The switching sequence of modes and the switching instants can be calculated by solving a closed-form optimal switching condition. The optimal state feedback control law is determined simultaneously. Finally, numerical results are provided to illustrate the effectiveness of the proposed method.

Exact Solution of ZVS Boundaries and AC-Port Currents in Dual Active Bridge Type DC–DC Converters

This letter presents an approach to develop an exact, unified model of zero voltage switching (ZVS) regions and ac-port currents (peak and RMS) in dual active bridge type dc–dc converters for all its operating modes and modulation strategies. It is executed for a single-phase system, where the method is used to compute closed-form expressions of ac current at switching instants. Then, exact formulae of ZVS regions for all devices, system peak, and RMS currents are derived. Simulation and hardware results for forward and reverse power transfer are reported to validate the proposed approach.

Stability analysis of switched systems on time scales with all modes unstable

In this paper, global uniform asymptotic stability problems of switched systems on time scales with all modes unstable are considered. First, a more general stability criterion is proposed for nonlinear switched systems on time scales, in which the value of Lyapunov function at some switching instants may not necessarily decrease. Second, based on the discretized Lyapunov function technique, a sufficient condition is derived for stability analysis of linear switched systems with all subsystems unstable on a special kind of time scale (the graininess function is constant). It is shown that this approach does not require the system matrix of one subsystem must commute with the one of the other subsystem, which is essential for stability analysis of linear switched systems on non-uniform time domains by the eigenvalue based approach in the existing results. Moreover, the idea of this paper not only provides a unified approach to study continuous switched systems and their discrete counterparts simultaneously, but also is effective to investigate stability problems of other systems on uniform or non-uniform time domains. Two examples are given for illustrating the effectiveness of the proposed results.

New Results on Stability Analysis of Markovian Switching Singular Systems

This paper addresses the stability problem for linear continuous-time Markovian switching singular systems. Considering the inherent state jump behavior at the switching instants, a necessary and sufficient condition of exponential stability in the mean square sense for the Markovian switching singular system is established in terms of linear matrix inequalities by means of a stochastic Lyapunov approach. Based on the obtained stability result, sufficient conditions of exponential stability in the mean square sense for the Markovian switching singular system with uncertain and partly unknown transition probability are presented. Numerical examples are presented to illustrate the effectiveness of the proposed approach.

Guaranteed performance control of switched linear systems: A differential-Riccati-equation-based approach

This paper studies a quadratic performance certificate in terms of an upper bound and a lower bound for switched linear systems over all admissible dwell-time switching signals. The infinite-horizon performance is reformulated into the summation of the finite-horizon performance for each subsystem over switching intervals that can be calculated by solving a family of differential Riccati equations. The time-varying positive definite solutions are exploited to construct a novel piecewise quadratic Lyapunov function for the closed-loop system, which guarantees that the Lyapunov function is decreasing at and between the switching instants. This decreasing property results in consistency between the piecewise quadratic Lyapunov function for switched systems and standard quadratic Lyapunov function for non-switched systems, based on which an upper bound of the quadratic performance is obtained by referring to the techniques for non-switched systems. In addition, a lower bound is established by solving a family of algebraic Riccati equations. The effectiveness of the guaranteed performance control method is illustrated by making use of a numerical example.

Dynamic output feedback control for network‐based switched linear systems with performance dependent event‐triggering strategies

This study investigates the dynamic output feedback L ∞ control for network-based switched linear systems subject to communication delay and quantisation. To reasonably configure the network communication resources according to the dynamic and steady-state characteristics of the system, the performance dependent event-triggering strategies are proposed. Moreover, the quantiser and dynamic output feedback controllers are applied, and the time-delay closed-loop switched system models corresponding to the system dynamic and steady-state processes are developed using a transformation technique. Subsequently, by utilising the average dwell time and piecewise Lyapunov functional techniques, sufficient conditions are derived to render the state of the time-delay closed-loop switched system globally uniformly ultimately bounded with an L ∞ performance level. In particular, the coupling between the switching instants and the data updating instants in the actuator is analysed during the system performance analysis. Furthermore, the design conditions of the event-triggered dynamic output feedback controllers are presented. Finally, numerical simulations verify the effectiveness of the proposed approach.

Event‐triggered stabilisation for continuous‐time switched non‐linear systems under switching constraints

In this work, the authors investigate event-triggered stabilisation problem for continuous-time switched systems, where switching instants and transitions are under given constraints. By designing some event-triggered conditions and a proper switching law, they establish some sufficient stabilisation criteria for the considered systems. The proposed event-triggered scheme is advantageous to reduce the utilisation of communication and computation resources. Further, they study the switching synchronisation problem for two continuous-time switched non-linear systems with different initial values. Finally, an example of Chua's circuit with simulations results are presented to illustrate the validity of the method.

Frequency reconfigurable substrate integrated waveguide (SIW) cavity F-shaped slot antenna

This paper shows a frequency reconfigurable SIW F-slot suitable for some applications. Configurability is accomplished by embeddings PIN diode switches in the 'F' slot. The proposed antenna is equipped for exchanging between working band of 3.172 GHz to 3.606 GHz in four different narrow bands and it underpins the cognitive system for LTE2300, WiMAX and WLAN. For each case reflection coefficient is ascertained, it keeps up less than -10 dB all through the resonating frequency in all instances of diode switching. The electromagnetic energy is kept inside the cavity because of the frame of a metallic vias. In all instances of diodes exchanging, it's uncovered a decent effectiveness of efficiency and gain.

Frequency reconfigurable substrate integrated waveguide (SIW) cavity F-shaped slot antenna

This paper shows a frequency reconfigurable SIW F-slot suitable for some applications. Configurability is accomplished by embeddings PIN diode switches in the 'F' slot. The proposed antenna is equipped for exchanging between working band of 3.172 GHz to 3.606 GHz in four different narrow bands and it underpins the cognitive system for LTE2300, WiMAX and WLAN. For each case reflection coefficient is ascertained, it keeps up less than -10 dB all through the resonating frequency in all instances of diode switching. The electromagnetic energy is kept inside the cavity because of the frame of a metallic vias. In all instances of diodes exchanging, it's uncovered a decent effectiveness of efficiency and gain.