Stability Of Closed-loop System Research Articles

Fault-tolerant model predictive sliding mode control with fixed-time attitude stabilization and vibration suppression of flexible spacecraft

This brief proposes two novel double-loop fault-tolerant controllers to tackle the problems of stabilizing the attitude and nullifying appendages' vibration of flexible spacecraft by integrating the advantages of model predictive control (MPC) and sliding mode control (SMC). The structure of the first method is as follows: First in the external loop, by using terminal sliding mode (TSM), the attitude of the spacecraft is derived to its reference value, and the proper angular velocity of the interior part is generated. Then, by employing the preciseness and constrained attributes of MPC, an optimal fault-tolerant controller is suggested in the internal part. Constrained fault-tolerant MPC tracks the angular velocity to the set value while guaranteeing appendages' passive vibration suppression. In another method, as opposed to the first technique, in the inner loop fault-tolerant finite-time TSM, and in the outer loop MPC are designed. The unified double-layer nonlinear controller schemes guarantee good dynamics and robustness against external torques and actuator faults. The closed-loop system's stability of the controllers is precisely proved using the Lyapunov theorem in the presence of actuator faults and external disturbances and in the absence of the damping matrix to study the advantages of the proposed methods. The performance of the proposed methods has been compared with each other. Moreover, the simulation results substantiate that the proposed method outperforms faster fixed-time sliding model control significantly.

Model predictive tracking control with disturbance compensation for wheeled mobile robots in an environment with obstacles

This paper explores the trajectory tracking control problem for a wheeled mobile robot (WMR) in an environment with obstacles and unknown disturbances. A fixed-time extended state observer is presented, which is utilized to estimate unknown disturbances and improve the convergence speed of estimation errors. By introducing the obstacle avoidance cost, a model predictive controller with disturbance compensation is proposed to guarantee desired tracking performance in the presence of obstacles. The proposed method is analyzed for recursive feasibility and closed-loop system stability subject to unknown disturbances and obstacles. Finally, both simulation and experiment are conducted to express the satisfactory tracking effect of the developed approach.

A New Control for Improving the Power Quality Generated by a Three-Level T-Type Inverter

A new controller based on a fractional-order synergetic controller (FOSC) is proposed for a three-level T-type inverter using a shunt active power filter (SAPF). The SAPF is designed to compensate for the reactive power and eliminate the current harmonics caused by non-linear loads, in cases of distorted or unbalanced source voltages. The proposed FOSC technique with the designed parameters and defined macro-variable is a robust control technique that operates well in both transient and steady-state scenarios, ensuring fast convergence and closed-loop system stability. The FOSC technique utilizes a phase-locked loop (PLL) technique on a self-tuning filter (STF) to enhance the SAPF’s ability to compensate current harmonics and reactive power in all situations involving non-linear loads and source voltage variations according to IEEE Std. 519. The proposed control was implemented and verified using Matlab software, where the obtained results were compared with the results of the conventional control based on proportional-integral (PI) controllers in different operating conditions. The results indicate that the proposed FOSC technique outperformed the traditional control in terms of DC voltage tracking and the minimization of the total harmonic distortion of the current.

T-S Fuzzy Tracking Control Based on H∞ Performance with Output Feedback for Pendulum-Cart System

In some practices, not all state variables are available because of limited or noisy measurements. Thus, via output feedback, an observer is used to estimate the unmeasured states. To apply linear controllers to the pendulum-cart system, the Takagi-Sugeno fuzzy model is utilized by linearizing the system in more than one operating point. The effect of disturbances on tracking performance is reduced to the prescribed attenuation level by H∞ performance. The stability of the whole closed-loop system is investigated using the Lyapunov function. Sufficient conditions are derived in terms of a set of Linear Matrix Inequality (LMI) to obtain the controller and observer gain. Simulation results show that the proposed control method can make the system track the sinusoidal reference signal, maintain stability, and attenuate the effect of disturbances to less than the prescribed attenuation level measured by L2 gain. In the implementation process, an adjustment is needed to move the observer’s pole and speed up the observer’s responses.

Adaptive Two-Degrees-of-Freedom Current Control for Solenoids: Theoretical Investigation and Practical Application

In this article, an adaptive two-degrees-of-freedom current control algorithm for solenoids is presented comprising an adaptive pole placement controller in combination with a regularized least-squares parameter estimation law. An additional adaptive feedforward controller takes advantage of the estimated plant parameters to further enhance the tracking performance. The stability of the overall closed-loop system is rigorously proven. The proposed solution differs from existing approaches by the adaptive feedforward controller and the way the parameter estimation is performed. The control concept is applied with the same controller parametrization to three solenoids from different applications, with substantially differing parameters. The experimental results show high tracking performance and fast parameter convergence even with poor initial estimates and despite the nonlinear dependence of the inductance on the current and position. The experimental results are also compared to two benchmark control design paradigms known from the literature, i.e. a second-order sliding mode controller and a nonlinear model reference adaptive control solution, which are both outperformed by the proposed controller.

Practical prescribed-time tracking control for uncertain strict-feedback systems with guaranteed performance under unknown control directions

In this paper, we consider the practical prescribed-time performance guaranteed tracking control problem for a class of uncertain strict-feedback systems subject to unknown control direction. Due to the existence of unknown nonlinearities and uncertainties, it is challenging to design a controller that can ensure the stability of closed-loop system within a predetermined finite time while maintaining the specified transient performance. The underlying problem becomes further complex as the control directions are unknown. To deal with the above problems, a special translation function as well as Nussbaum type function are introduced in the prescribed performance control (PPC) framework. Finally, a PPC as well as preset finite time tracking control scheme is designed, and its effectiveness is confirmed by both theoretical analysis and numerical simulation.

Non-fragile PD control of linear time-delay positive discrete-time systems

This paper addresses the issue of proportional-derivative (PD) controllers design for positive linear systems in the discrete-time domain, which still remains a challenging problem in positive systems theory. The specific aim is to design a PD controller for a system with constant time delay, which simultaneously ensures closed-loop system stability and preserves positivity. Moreover, additive gain variation of the controller is considered in the synthesis process. Systematic formulation and tractable algorithms are developed to find the PD controller gains for positive stabilization. The performance of such methods is validated by numerical examples.

Novel adaptive law for super-twisting controller: USV tracking control under disturbances

A novel adaptive super-twisting control algorithm, for Unmanned Surface Vehicles (USV) tracking control is presented. The proposed adaptive law is obtained using a Lyapunov approach, to analyze the system closed-loop stability. Furthermore, several conditions are given to guarantee robustness in presence of unknown bounded disturbances/uncertainties, chattering mitigation and the finite-time convergence. This adaptive control strategy has the advantage that the controller gains, which are in terms of a single control parameter, requires adjusting a small number of parameters compared with other adaptive strategies, moreover and its dynamics is smooth, improving the controller performance. To assess the proposed control methodology effectiveness, a trajectory tracking control is designed and implemented on an unmanned surface vehicle under the action of bounded unknown uncertainties and external perturbations. Numerical simulations and experimental results conducted with a vessel prototype demonstrate the performance and advantages under payload variations and external environmental conditions. Finally, a comparative study between the proposed approach with other adaptive super-twisting works has been conducted.

On Sontag’s formula for the sampled-data observer-based stabilization of nonlinear time-delay systems

In this paper, a new methodology for the design of sampled-data dynamic output feedback (DOF) stabilizers for control-affine nonlinear time-delay systems is proposed. In particular, the methodology here developed is based on the Artstein’s theory of control Lyapunov functions and related Sontag’s formula, here extended, for the first time in the literature, to the case of DOF controllers. Firstly, the new notion of Steepest Descent Error Dynamics (SDED) is introduced and used to suitably re-formulate the well-known Sontag’s universal formula for the case of DOF controllers. Then, it is shown that, under suitably fast sampling, a proposed sampled-data DOF controller based on the new provided version of Sontag’s universal formula ensures the semiglobal practical stability of the related sampled-data closed-loop system. Time-varying sampling intervals, as well as the intersampling system behavior, are taken into account. In the theory here developed, the case of delay-free systems is addressed as a special case. Applications are presented for the validation of the proposed theoretical results.

Predictive control for networked high-order fully actuated systems subject to communication delays and external disturbances

This research is concerned with an output tracking problem for networked high-order fully actuated (NHOFA) systems subject to communication delays and external disturbances, where communication delays occur in sensor to network node and network node to actuator. A HOFA system model, as a novel system representation, is applied to establish the dynamics of networked control systems (NCSs). Accordingly, a disturbance observer based HOFA predictive control approach is proposed to address this problem. In the proposed approach, a disturbance observer is utilized to cope with the external disturbances, and then a local HOFA feedback with disturbance compensation is designed to adjust the closed-loop system performances. Further, a Diophantine Equation is applied to establish an incremental HOFA (IHOFA) prediction model to substitute a reduced-order prediction model, such that multi-step ahead predictions are derived to minimize a cost function involving the optimization of tracking performance and the compensation of network-induced communication delays. A necessary and sufficient criterion is given to discuss the stability and tracking performance of closed-loop NHOFA systems, it is simple to use in system analysis and extend in practice. The availability of the proposed approach is demonstrated via simulated and experimental results for tracking control of air-bearing spacecraft (ABS) simulator.

Simple Dynamic Positioning Control Design for Surface Vessels With Input Saturation and External Disturbances

This brief addresses the dynamic positioning (DP) control problem of surface vessels with input saturation and external disturbances, and a simple DP control law is proposed. First, a saturation handling model and a dynamic compensation system are designed to deal with input saturation. Then, an exponentially convergent disturbance observer is constructed to approximate the external disturbances. Moreover, to guarantee the asymptotic stability of the DP closed-loop system and reduce the design complexity of the DP control law, a simple auxiliary control law is designed by combining the hyperbolic tangent function. Notably, combined with LaSalle’s invariance principle, a DP system stability analysis strategy is constructed, which ensures that the DP system can be asymptotically stable, even if the derivative of the scalar function proving the stability of the DP system is semi-negative definite. Finally, the numerical simulation results demonstrate the effectiveness of the proposed DP control law.

Command-Filtered Neuroadaptive Output-Feedback Control for Stochastic Nonlinear Systems With Input Constraint.

In this article, an adaptive neural-network (NN) command-filtered output-feedback control strategy is proposed for a class of stochastic nonlinear systems (SNSs) with the actuator constraint. The problem of "explosion of complexity" existing in the conventional backstepping design procedure for SNSs is successfully resolved based on the command filter technique, and the error compensation mechanism is introduced to remove effectively the influence of filtered error. By using the NNs to identify the unknown nonlinear functions, a neural-network-based state observer is designed to estimate the unmeasurable states of the SNSs. Based on the quartic Lyapunov function, the stability of stochastic closed-loop systems is analyzed. It is proved that all signals of the closed-loop systems are bounded in probability, and the tracking error approaches a small neighborhood of the origin in probability. Finally, the effectiveness of the developed control algorithm in this article is verified by a comparison example.

A Looped Functional Method to Design State Feedback Controllers for Lurie Networked Control Systems

Dear Editor, This letter deals with the stabilization of Lurie networked control systems with network-induced delays (NID). By constructing a two-sided looped Lyapunov functional, a sufficient condition is derived to ensure the absolute stability of the resultant closed-loop system under a state feedback controller. Then, based on this condition, a cone complementary linearisation (CCL) iterative algorithm is presented to design state feedback controller. It is shown via a numerical example that the proposed method can deliver less conservative results as well as fewer iterations if compared with existing ones.

Robust Global stabilization of aerial continuum manipulation systems via hybrid feedback

In this paper, the control problem of aerial continuum manipulation systems (ACMSs) is considered. This study introduces a new platform for ACMSs in which a quadrotor is equipped with a tendon-bent concentric tube continuum robot. The decoupled dynamic modeling of ACMSs is utilized to derive the proposed feedback control law. The control design process is split into two distinct control loops. In the first loop, a terminal synergetic controller is presented to control the continuum robot’s tip to track the desired trajectory. In the second loop, an improved synergetic controller is introduced to control the position and velocity of the quadrotor, which ensures asymptotic stability of the origin of the error dynamic. Moreover, in this loop a hybrid feedback law is designed to operate with the improved synergetic controller, which overcomes topological obstructions and globally stabilizes the attitude of the quadrotor. Furthermore, the stability of the resultant closed-loop system is verified utilizing the Lyapunov stability theorem. The efficiency and advantages of the proposed controller are verified by a comparative analysis in simulations.

Composite anti-unwinding attitude control of spacecraft under actuator saturation and angular velocity limits

Spacecraft attitude control employs quaternion representation to avoid singularity issues and obtain global maneuver stability. However, it has redundancy associated, resulting in dual equilibrium points. The attitude control may confront the unwinding phenomenon due to the presence of the equilibria. In this paper, an anti-unwinding controller for spacecraft stabilization in the presence of external disturbances and inertial uncertainties, angular velocity limit, actuator saturation and faults is presented. Specifically, a modified extended state observer (ESO) is designed to obtain total disturbance estimates of the rigid-body spacecraft. Auxiliary parameters are added in the design to avoid initial high estimates in the proposed ESO design resulting in faster convergence. The proposed disturbance observer is to release the assumption that requires the estimated disturbance to be constant or varying at slow rates. Using the ESO estimates, a particular back-stepping-SMC (ESO-BTSMC) controller is devised to formulate anti-unwinding control law for spacecraft stabilization. Lyapunov stability theory is employed to prove closed-loop stability of system and estimation error convergence. Comparative simulations are performed to demonstrate the performance of the proposed control scheme. It is found that the proposed control scheme gives smooth and precise control performance along with faster transient response. Additionally, it also alleviates the chattering phenomenon.

Smith Predictor Controller Design Using the Direct Synthesis Method for Unstable Second-Order and Time-Delay Systems

Industrial processes often involve a long time delay, which adversely affects the stability of closed-loop control systems. The traditional Smith Predictor (SP) is a model-based controller used in processes with large time delays. The variation of system parameters and load disturbance situations are disadvantages of the traditional SP, and researchers have, therefore, proposed modified SP structures. In this paper, a design method based on the direct synthesis approach on a modified SP structure is discussed. In the design, an I-PD controller structure is used on the set-point tracking side of the SP, and a cascading PD lead–lag controller is used on the disturbance rejection side. In contrast with other studies in the literature, the use of simpler controllers enables the mathematical expressions that arise in the direct synthesis method to be significantly reduced. The proposed method is examined under the disturbance input effects for normal and parameter-changing conditions on system models with unstable second-order plus time-delay processes. The first plant model has two unstable poles, the second has one stable and one unstable pole, and the third has one unstable and one zero pole. When the results obtained using the proposed method were compared with other methods, significant improvements were achieved in terms of set-point tracking, disturbance rejection, and robustness conditions.

Intelligent control of convergence rate of impulsive dynamic systems affected by nonlinear disturbances under stabilizing impulses and its application in Chua’s circuit

This paper investigates the variable convergence rate stability and variable convergence rate stabilization of impulsive dynamic linear systems with stabilizing impulses affected by nonlinear disturbances. The eigenvalues (poles) of the system state are closely related to the convergence or divergence rate of the system. Sufficient conditions for the variable convergence rate stability are obtained by using the generalized pole placement idea and the method of system transformation. By designing a memoryless state feedback controller, sufficient conditions of variable convergence rate stabilization are obtained, ensuring the asymptotic stability of the target closed-loop system and accurately adjusting the system state’s convergence rate. An algorithm for adjusting the speed of system state convergence and its flow chart are designed by referring to the C programming language. Combined with the variable convergence rate stabilization method, the intelligent control of system state convergence speed is realized at the operation level. As a representative example of chaotic systems, Chua’s circuit affected by impulses verifies the effectiveness of the variable convergence rate stabilization method.

Active Compensation-Based Harmonic Reduction Technique to Mitigate Power Quality Impacts of EV Charging Systems

This article presents a novel active compensation-based harmonic reduction (ACHR) technique in order to mitigate the existing third harmonic component in the input current of the power factor corrector (PFC) circuit in electric vehicle (EV) charging systems. Traditional PFC control scheme includes an outer voltage loop to control the output dc voltage and an inner current loop to ensure that the grid current is sinusoidal. The work shows how third and other high-order harmonic components are created, while the signal is transmitting through the voltage control loop, and then, an analytical model is developed to calculate the dominant third harmonic magnitude according to the circuit specifications and control parameters. The ACHR approach takes advantage of multilevel filter design to prevent the presence of high-order odd harmonics in addition to mitigating the existing third harmonic component created by the voltage control loop before it is passed through the current control loop. ACHR is designed optimally, and its performance is analyzed in detail to have a robust and stable closed-loop system while keeping the characteristics of fundamental harmonic. A totem-pole boost PFC proof-of-concept is built to verify the proposed ACHR technique. The results show that the third harmonic magnitude is reduced from 244 mA in conventional control scheme to 130 mA in the proposed ACHR technique. Moreover, total harmonic distortion (THD) in input current is decreased from 4.88% to 4.03%.

On Semi-Global Exponential Stability Under Sampling for Locally Lipschitz Time-Delay Systems

In this article, the stability preservation problem for locally Lipschitz nonlinear time-delay systems, by emulation of continuous-time dynamic output feedback controllers, is studied. Sufficient Lyapunov-like conditions are provided such that, by suitably fast sampling, the Euler emulation of continuous-time dynamic output feedback controllers ensures the semiglobal exponential stability of the related sampled-data closed-loop system. If other emulation schemes than the Euler one are used, practical semiglobal exponential stability is guaranteed, with arbitrarily small final target ball, by suitably fast sampling. The intersampling system behavior, as well as time-varying sampling intervals, is taken into account. In the provided results, the delay-free case is included as a special case. The practical applicability of the provided results is shown through the study of a nonlinear chemical reactor system with recycle and a glucose–insulin system.

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.