Closed-loop Stability Research Articles

Robust Fixed-Order Controller Design for Uncertain Systems With Generalized Common Lyapunov Strictly Positive Realness Characterization

This article investigates the design of a robust fixed-order controller for single-input–single-output (SISO) polytopic systems with interval uncertainties, with the aim that the closed-loop stability is appropriately ensured and the performance specifications on sensitivity shaping are conformed in a specific finite frequency range. Utilizing the notion of generalized common Lyapunov strictly positive realness (CL-SPRness), the equivalence between strictly positive realness (SPRness) and strictly bounded realness (SBRness) is established; and then, the specifications on robust stability and performance are transformed into the SPRness of newly constructed systems and further characterized in the framework of linear matrix inequality (LMI) conditions. The proposed methodology avoids the tedious yet mandatory evaluations of the specifications on all vertices of the uncertain polytopic system in an explicit form. Instead, solving five LMIs exclusively suffices for ensuring the robust stability and performance regardless of the number of vertices, and thus, the typically heavy computational burden is considerably alleviated. It is also noteworthy that the proposed methodology additionally provides the necessary and sufficient conditions for this robust controller design with the consideration of a prescribed finite frequency range, and therefore, significantly less conservatism is attained in the system performance.

Frequency-Domain Properties of the Hybrid Integrator-Gain System and Its Application as a Nonlinear Lag Filter

This brief investigates frequency-domain properties of the hybrid integrator-gain system (HIGS) by analytically deriving its higher-order sinusoidal input describing functions (HOSIDFs). Furthermore, a novel application of this nonlinear control element is proposed, where it is utilized as a nonlinear lag filter. Hereby, the closed-loop stability can be guaranteed based on a non-parametric plant model—while ensuring robustness against plant uncertainties—by utilizing a circle criterion-like argument. Control design is initially based on a describing function (DF) analysis of the HIGS. This yields magnitude characteristics similar to those of a linear lag filter, while having the freedom to tune the induced phase lag. However, the excitation of higher-order harmonics by the HIGS is, in that case, neglected. Based on the derived HOSIDFs, it is shown that the validity of this assumption depends on the properties of the plant and the controller, as well as the spectral properties of the external inputs. Finally, the potential of the nonlinear lag filter is investigated by means of simulations and experiments on a high-precision industrial motion stage, showing performance improvements compared with a linear lag filter.

Enhancing Output Feedback Robust MPC via Lexicographic Optimization

In this article, a novel approach to hierarchical implementation of output feedback robust model predictive control is proposed for the linear polytopic uncertain model. One optimization problem for minimizing the performance index is followed with the other assessing estimation error set (EES). The two problems are posed in a lexicographic order. Since in the latter problem, the controller parametric matrices are retaken as the degrees of freedom for the optimization, a much less conservative EES is calculated. Therefore, by applying the new approach, the control performance can be greatly improved as compared with the earlier schemes without lexicographic optimization. The proposed approach is proven to be recursively feasible, and the closed-loop stability is specified by the notion of quadratic boundedness. The result is verified through two numerical examples.

Distributed Dynamic Event-Triggered Secure Model Predictive Control of Vehicle Platoon Against DoS Attacks

This paper studies the distributed dynamic event-triggered model predictive control (MPC) of vehicle platoon systems subject to denial-of-service (DoS) attacks and external disturbances. We develop a novel DoS-attack-aware event-triggered mechanism for each vehicle to determine whether the MPC problem should be solved or not at each sampling time instant. If the MPC problem is solved, the constructed vehicular beacon information will be transmitted to its neighbouring vehicles through the vehicular ad-hoc network (VANET). In the DoS-attack-aware event-triggered condition, the dynamic threshold adjusts adaptively according to DoS attack durations, local vehicular data, and beacon information from its neighbours. Then, an exponential-type robustness constraint is introduced in the MPC problem to deal with external disturbances. Subsequently, sufficient conditions are given to guarantee the recursive feasibility of the MPC algorithm and closed-loop platoon system stability. Finally, extensive simulation examples are provided to illustrate the effectiveness of the proposed algorithm in terms of communication efficiency and platoon resilience control performance.

Robust Model Predictive Control Using a Two-Step Triggering Scheme

This article is concerned with event-triggered robust model predictive control for linear discrete-time systems with bounded disturbances. A two-step scheme involving a tentative verification of a triggering condition and a delayed triggering with a waiting horizon is proposed to reduce the average triggering rate and fully utilize the nominal optimal control sequence minimizing a quadratic cost function. The triggering condition and the waiting horizon are synthesized based on a prediction model of the plant and a robust positively invariant set associated with it. Under mild conditions, recursive feasibility and closed-loop robust stability are guaranteed. Two examples are used to show the effectiveness and merits of the proposed approach.

Autler–Townes splitting in the trap-loss fluorescence spectroscopy due to single-step direct Rydberg excitation of cesium cold atomic ensemble

We experimentally investigate trap-loss spectra of the cesium 6S1/2(F = 4) → 71P3/2 Rydberg transition by combining the cesium atomic magneto-optical trap with the narrow-linewidth, continuously tunable 318.6 nm ultraviolet laser. Specifically, the atoms in the magneto-optical trap are excited to the Rydberg state due to the ultraviolet laser single-step Rydberg excitation, which leads to the reduction of atomic fluorescence. Based on the trap-loss spectroscopy technology, the Autler–Townes (AT) splitting due to a strong cooling laser is observed, and the parameter dependence of the AT splitting interval of trap-loss spectroscopy is investigated. The effective temperature of cold atoms is measured by using simplified time-of-flight fluorescence imaging. In addition, closed-loop feedback power stabilization of 318.6 nm ultraviolet laser is carried out. This lays the foundation for further experimental research related to the Rydberg atoms using ultraviolet lasers, which is of great significance for the development of quantum computing and quantum information.

Projection Scheme and Adaptive Control for Symmetric Matrices With Eigenvalue Bounds

A projection scheme to handle eigenvalue bounds for adaptive control with uncertain symmetric matrix parameters is introduced. Conventional parameter projection techniques are generally unable to handle explicit eigenvalue bounds. The continuous projection scheme presented here maintains the closed-loop stability properties for adaptive controllers while simultaneously satisfying <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> available eigenvalue bounds of the uncertain symmetric matrix valued parameters. The projection scheme uses the eigen decomposition of the symmetric matrix parameter to project its eigenvalues to lie within the prescribed bounds. The eigenvalues of the symmetric matrix may be lower bounded or upper bounded or both. A direct adaptation over the eigenvalues and the eigen projections of the symmetric matrix parameter is also derived to help circumvent expensive eigen decomposition calculations. The new projection here shows improved performance in numerical simulations of rigid body attitude tracking control and trajectory tracking of robotic manipulators with unknown inertia parameters.

Direct Search Algorithm for Load Frequency Control of a Time-Delayed Electric Vehicle Aggregator

This article addresses the topic of frequency regulation of a single-area power system connected to an electric vehicle (EV) aggregator over a non-ideal communication network. It is considered that the command control action is received by the EV aggregator with constant delay and the power system includes uncertain parameters. Due to the presence of uncertainties and the delay term, the frequency regulation problem is non-convex and hard to solve. The present approaches in the literature convert the non-convex control design problem into a convex problem with a set of Linear Matrix Inequalities (LMIs), which is conservative and in many cases results infeasibility. In this paper, an innovative iterative algorithm, called direct search, is employed for the time-delayed system to design the unknown parameters of a pre-assumed controller. The controller choice is not limited and various controllers’ structures can be assumed. Without loss of generality, a proportional-integral (PI) controller is designed. The novel direct search algorithm can determine a feasible solution whenever at least one solution lays in the design space. Hence, by selecting a wide design space, we can anticipate that the PI controller guarantees closed-loop stability. Numerical simulations are carried out to demonstrate the performance of the developed controller compared to the state-of-the-art approach.

Isolating Trajectory Tracking From Motion Control: A Model Predictive Control and Robust Control Framework for Unmanned Ground Vehicles

This letter studies the trajectory tracking and motion control problems of unmanned ground vehicles (UGVs). A model predictive control and robust control (MPC-RC) framework for UGVs is proposed to improve tracking accuracy, yaw stability and robustness in a modular fashion without introducing complexity into controller. The trajectory tracking problem and three-dimensional phase trajectory planning with high stability of a vehicle motion can be performed in the model predictive control design simultaneously. Also, combining the advantages of linear matrix inequality, sliding mode control, and back-stepping control law, three robust motion controllers can track the generated three-dimensional phase trajectory steadily so that the UGV motion stability is guaranteed. The robust performance is guaranteed through considering model uncertainties and terra-aerodynamic disturbances in robust controllers. Sufficient conditions for closed-loop stability under the diverse robust factors are provided by the Lyapunov method analytically, which ensures the series system's feasibility. The results of simulations on MATLAB-Carsim platform demonstrate that the proposed controller can significantly enhance tracking accuracy, motion stability, and robustness compared to the existing methods, which guarantees the feasibility and capability of driving in a nonlinear extreme scenario.

Computationally Efficient Stability-Based Nonlinear Model Predictive Control Design for Quadrotor Aerial Vehicles

This article presents the design of a stability-guaranteed nonlinear model predictive controller for quadrotor-type microaerial vehicles to operate robustly on fast trajectories. The basic controller structure operates without having to use terminal conditions in the optimization problem. As a result, the controller is computationally less demanding and provides more stable closed-loop performance than traditional nonlinear predictive control schemes. This article presents a detailed stability analysis without terminal costs or terminal constraints and proves the asymptotic stability and necessary conditions for the recursive feasibility of the system. This article derives the growth-bound sequence that enables obtaining the shortest possible prediction horizon for stability. The proposed analysis provides the necessary conditions to implement the controller while using the shortest stabilizing prediction horizon compared to major traditional predictive control schemes reported in the literature. This particular feature enables the proposed controller to perform fast optimization and, hence, the capability to implement fast trajectories using feedback regularization. In order to demonstrate the validity of this new proposed control scheme, first, several MATLAB simulations are conducted to demonstrate the improved performance of the controller especially when the quadrotor vehicle follows fast trajectories. Real-time lab experiments are also conducted to validate the performance of the proposed scheme for point stabilization (hovering) and trajectory tracking problems. The results show that the proposed scheme can stabilize the system with a relatively short prediction horizon, a fast convergence rate, and a small tracking error.

On the Sliding Mode Control Applied to a DC-DC Buck Converter

This work shows the voltage regulation of a DC–DC buck converter by applying sliding mode control using three different cases of sliding surfaces. The DC–DC buck converter is modeled by ordinary differential equations (ODEs) that are solved by applying numerical methods. The ODEs describe two state variables that are associated to the capacitor voltage and the inductor current. The state variable associated to voltage is regulated by applying two well-known sliding surfaces and a third one that is introduced herein to improve the response of the sliding mode control. The stability of the proposed sliding surface is verified by using a Lyapunov theorem to guarantee closed-loop stability. Finally, simulation results show the improvement of voltage regulation when applying the proposed sliding surface compared to already reported approaches.

Model-based decoupling control for the thermal management system of proton exchange membrane fuel cells

As one of the most promising sustainable energy technologies available today, proton exchange membrane fuel cell (PEMFC) engines are becoming more and more popular in various applications, especially in transportation vehicles. However, the complexity and the severity of the vehicle operating conditions present challenges to control the temperature distribution in single cells and stack, which is an important factor influencing the performance and durability of PEMFC engines. It has been found that regulating the input and output coolant water temperature can improve the temperature distribution. Therefore, the control objective in this paper is regulating the input and output temperature of coolant water at the same time. Firstly, a coupled model of the thermal management system is established based on the physical structure of PEMFC engines. Then, in order to realize the simultaneous control of the inlet and outlet cooling water temperature of the PEMFC stack, a decoupling controller is proposed and its closed-loop stability is proved. Finally, based on the actual PEMFC engine platform, the effectiveness, accuracy and reliability of the proposed decoupling controller are tested. The experimental results show that with the proposed decoupling controller, the inlet and outlet temperatures of the PEMFC stack cooling water can be accurately controlled on-line. The temperature error range is less than 0.2 °C even under the dynamic current load conditions.

Robust Control Based on Observed States Designed by Means of Linear Matrix Inequalities for Grid-Connected Converters

This paper provides a procedure to design robust controllers based on observed states applied to three-phase inverters with LCL filters connected to a grid with uncertain and possibly time-varying impedances, which can arise in renewable energy systems and microgrid applications. Linear matrix inequalities are used to rapidly compute, off-line, based only on the choice of two scalar parameters for pole location, sets of gains for the controller and the observer, and also to provide a theoretical certificate of the closed-loop stability, including a limit for the rate of variations of the grid impedances. The proposed design procedure allows the easy implementation of robust state feedback controllers with a reduced number of sensors, ensuring good performance for different sets of grid impedances. Additionally, larger regions of guaranteed stability are provided by the proposed procedure, when compared with a similar condition from the literature. The control law using the observed states can ensure grid currents with low harmonic content, complying with the IEEE 1547 Standard requirements, with negligible loss of performance concerning the feedback of the measured state variables. Three optimal state feedback controllers from the literature are reproduced here and successfully implemented using the observed state variables based on the proposed procedure. In all cases, the viability of the proposal was confirmed by simulations and experimental results.

On the pole placement of scalar linear delay systems with two delays

AbstractThis paper concerns some spectral properties of the scalar dynamical system defined by a linear delay-differential equation with two positive delays. More precisely, the existing links between the delays and the maximal multiplicity of the characteristic roots are explored, as well as the dominance of such roots compared with the spectrum localization. As a by-product of the analysis, the pole placement issue is revisited with more emphasis on the role of the delays as control parameters in defining a partial pole placement guaranteeing the closed-loop stability with an appropriate decay rate of the corresponding dynamical system.

Integral Backstepping Control Algorithm for a Quadrotor Positioning Flight Task: A Design Issue Discussion

For quadrotor control applications, it is necessary to rely on attitude angle changes to indirectly achieve the position trajectory tracking purpose. Several existing literature studies omit the non-negligible attitude transients in the position controller design for this kind of cascade system. The result leads to the position tracking performance not being as good as expected. In fact, the transient behavior of the attitude tracking response cannot be ignored. Therefore, the closed-loop stability of the attitude loop as well as the position tracking should be considered simultaneously. In this study, the flight controller design of the position and attitude control loops is presented based on an integral backstepping control algorithm. This control algorithm relies on the derivatives of the associated virtual control laws for implementation. Examining existing literature, the derivatives of the virtual control law are realized approximated by numerical differentiations. Nevertheless, in practical scenarios, the numerical differentiations will cause the chattering phenomenon of control signals in the presence of unavoidable measurement noise. The noise-induced control signals may further cause damage to the actuators or even diverge the system response. To address this issue, the analytic form for the derivative of the virtual control law is derived. The time derivative virtual control law is analyzed and split into the disturbance-independent compensable and disturbance-dependent non-compensable terms. By utilizing the compensable term, the control chattering due to the differentiation of the noise can be avoided significantly. The simulation results reveal that the proposed control algorithm has a better position tracking performance than the traditional dual-loop control scheme. Meanwhile, a relatively smooth control signal can be obtained for a realistic control algorithm realization. Simulations are provided to illustrate the position tracking issue of a quadrotor and to demonstrate the effectiveness of the proposed compromised control scheme.

A convex optimization approach to multi-objective design of two-stage compensators for MIMO linear systems

The previous design of two-stage compensators with multi-objectives concerns the closed-loop stability, the low-sensitivity, and the satisfactory time-domain performance. However, the design only considers the single-input single-output system. This paper aims to present the design of two-stage compensators for multi-input multi-output (MIMO) linear systems which contain dynamical interaction between inputs and outputs. When Youla parameterization is applied to the MIMO linear system, the design criteria can be cast as a nonlinear optimization. In addition, the infinite dimension optimization problem is approximated to a finite dimension problem with Ritz approximation. The suitable form of design parameters is proposed to ensure the low sensitivity of the MIMO system. The two-stage compensator design is formulated as convex optimization which is efficiently solved using available solvers. Finally, the two-stage compensators are designed for Wood and Berry’s model of binary distillation column. The numerical results indicate that all design objectives of frequency domain and time domain can be achieved by the two-stage compensators.

A novel hierarchical temperature control method of an electric oven and its experimental evaluation

PurposeOvens are semi-industrial multipurpose equipment that are used to provide a desired temperature for specific chemical processes. Temperature regulation in the presence of different type of disturbances and dealing with nonlinear dynamics with large dead time (up to a few minutes) are some undesirable factors that have to be considered in the controller design procedure of the oven systems. Due to these factors, the classical PID controller tuned using Cohen-Coon or Ziegler–Nichol’s tuning methods often fails to meet satisfactory closed-loop performance.Design/methodology/approachIn this paper, to deal with the limitations on the oven system due to the undesirable factors, a hierarchical automaton-guided form controller has been designed. The proposed controller includes several discrete PI controllers, each of which operates locally in the defined operating regions whose separation idea is specific to this paper. Based on the idea proposed in the separation of regions, the controller’s coefficients tuning rules are extracted prior to any determination. Then, a supervisor controller has assumed the task of switching between local controllers. In the next step, by considering a conceptual model for the oven system and using a candidate Lyapunov function, the stability conditions of closed-loop system are discussed and the necessary conditions for the asymptotic stability are derived. The proposed controller is practically implemented with the help of the Arduino Nano platform.FindingsUsing several experiments, the superiority of the proposed hierarchical controller in terms of performance and energy consumption has been demonstrated.Originality/valueThe proposed hierarchical controller has been implemented practically and an acceptable closed-loop performance has been achieved. To illustrate the efficiency of the proposed method, the closed-loop stability of this method is shown using the Lyapunov theory.

Fuzzy L1 adaptive controller for chaos synchronization of uncertain fractional-order chaotic systems with input nonlinearities

This research work proposes a fuzzy fractional-order [Formula: see text] adaptive controller to deal with projective chaos synchronization problems for a general class of uncertain fractional-order chaotic systems subject to unknown input nonlinearities (dead-zone and sector nonlinearities). The suggested control architecture includes a fractional-order sliding surface, a fuzzy system, and an [Formula: see text] adaptive controller. The latter consists of a predictor, a control law, and its adaptive mechanism. The fuzzy system takes the role of an online estimator for system nonlinear uncertain functions which helps in the handling of the input nonlinearities. A designed low-pass filter is placed within the input channel of the [Formula: see text] adaptive controller to ensure that the control loop is decoupled from the estimation loop, which preserves response robustness along with improving transient performances. Finally, the closed-loop stability is rigorously proved, and the acquired results are demonstrated by two simulation examples as well as a comparative study.

Fault diagnosis and fault-tolerant control design for neutral time delay system

This paper presents a new approach of fault-tolerant control (FTC) for the transmission line as a neutral variable time-delay system. The main goal of this work guarantees faulty neutral variable time delay system stabilization using the state feedback control design based on Lyapunov function and the Linear Matrix Inequality resolution. The use of the FTC method is to achieve actuator and sensor fault compensation. This method is based on two steps. The first one is the synthesis of a nominal control, which remains to maintain the closed-loop system stability. The second step is based on adding a new control law to the nominal one to compensate the fault effect on system behaviour and maintain the desired performance in the closed loop system. Then, a conception of an adaptive observer is used to detect and estimate the fault. Finally, the developed approach is applied for the transmission line. The given results are presented to prove the effectiveness of this approach.

Finite-Time Command Filtered Control for Oxygen-Excess Ratio of Proton Exchange Membrane Fuel Cell Systems with Prescribed Performance

In recent years, proton exchange membrane fuel cell (PEMFC) has received growing attention as a new sustainable energy source because of its high-power density and zero-emission. In the PEMFC system, the air supply control has a significant impact on the efficiency and lifetime of the PEMFC stack. However, external disturbances and output constraints regularly have negative effects on air supply control. This paper aims to investigate a novel system analysis and advanced strategy control for the oxygen-excess ratio of a PEMFC system under the variant load current disturbance. The air-supply dynamic model is established which takes into account the supply manifolds, compressor, and the PEMFC stack. The proposed control method is designed based on finite-time command-filter control (FTCFC) to improve the tracking performance and ensure the finite-time convergence. Moreover, owing to the suggested prescribed performance function, the oxygen-excess ratio output remains in the pre-boundedness. Theoretical analysis exhibits that the closed-loop system stability is guaranteed by the Lyapunov theory. Finally, the simulation and hardware-in-loop (HIL) experiments are carried out on MATLAB environment and a 100 W power PEMFC system to validate the effectiveness of the suggested methodology.