Closed-loop Stability Analysis Research Articles

Continuous finite-time terminal sliding mode to solve the tracking problem in a class of mechanical systems

The major contribution of this study is the feedback design of a finite-time convergence sliding mode control to solve the trajectory-tracking problem in a class of mechanical systems. Some advantages are that the controller presents a continuous signal by integration of the high-frequency switching term. Another benefit is the design and implementation of an uncertainty and disturbance estimator (UDE) to robustify the closed-loop system. We use Lyapunov tools to develop the closed-loop stability analysis and to give an expression of the convergence time [Formula: see text] t through this, we can reduce the convergence time by tuning the gains of the controller. We illustrate the performance of the proposed control structure via numerical simulations conducted for a mass-spring-damper system and experiments developed in a pendular system.

Autonomous Obstacle Avoidance and Trajectory Planning for Mobile Robot Based on Dual-Loop Trajectory Tracking Control and Improved Artificial Potential Field Method

In order to better meet the practical application needs of mobile robots, this study innovatively designs an autonomous obstacle avoidance and trajectory planning control strategy with low computational complexity, high cost-effectiveness, and the ability to quickly plan a collision-free smooth trajectory curve. This article constructs the kinematic model of the mobile robot, designs a dual-loop trajectory tracking control strategy for position control law and attitude control law algorithms, and improves the traditional artificial potential field method to achieve a good obstacle avoidance strategy for mobile robots. Based on the dual-loop trajectory tracking control and the improved artificial potential field method, the autonomous obstacle avoidance and trajectory planning scheme of the mobile robot is designed, and closed-loop stability verification and analysis are conducted on the overall control system. And through the detailed simulation and experiments, the advantages of the proposed method in trajectory tracking accuracy and motion stability compared to the existing methods are verified, showing good effectiveness and feasibility and laying a good foundation for the application of mobile robots in practical complex scenes.

A Decentralized Power Management and Sliding Mode Control Strategy for Hybrid AC/DC Microgrids including Renewable Energy Resources

This paper presents a new decentralized robust strategy to improve small and large-signal stability and power-sharing of hybrid AC/DC microgrids and improve its performance for nonlinear and unbalanced loads. In addition to the sliding mode controller for DC/DC converters, for the sake of improving power sharing and regulating active and reactive powers injected by distributed energy resources, and moreover, controlling harmonic and negative-sequence current in the presence of nonlinear and unbalanced loads, two separate controllers for positive sequence power control and negative sequence current control are designed based on the sliding mode control and Lyapunov function theory, respectively. The theoretical concept of the proposed robust control strategy, including mathematical modeling of microgrid components, basic theorems, controller design procedure, and robustness and closed loop stability analysis are outlined. Also, this direct power/current/voltage control scheme is governed by a new hybrid AC/DC hierarchical control scheme that exploits a harmonic virtual impedance loop and voltage compensation scheme. To show the effectiveness of the proposed robust control scheme, offline time-domain simulations are done on a hybrid AC/DC wind/photovoltaic/fuel-cell microgrid with nonlinear and unbalanced loads in MATLAB/Simulink environment, and the results are experimentally verified by OPAL-RT real-time digital simulator.

Assembly-Oriented Finite-Time Coordinated Control of Underactuated Dual Rotary Cranes for Payload Position and Attitude Regulation

With strong load capacity and high maneuverability of payload attitude regulation, dual rotary cranes (DRCs) are widely applied for transportation and assembly tasks in infrastructure construction. For DRCs, to achieve safe and accurate control of the payload position and attitude, it is necessary to enhance the motion synchronization of two cranes, under the premise of controlling more state variables with fewer control inputs based on nonlinear coupling dynamics; moreover, the finite-time convergence of positioning errors is also expected to be guaranteed for high efficiency. To this end, this paper proposes an assembly-oriented finite-time coordinated controller <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">without</i> any linearization to the nonlinear crane dynamics, which realizes accurate and stable regulation of the payload position and attitude through coordinated boom motions. To our knowledge, the proposed controller provides the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">first</i> closed-loop control solution to realize both horizontal and non-horizontal payload hoisting for DRCs based on practical assembly demands. Theoretically, through elaborate design of the synchronization error and coupling errors, the real-time information exchange between the two cranes is realized for the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">first</i> time, which enhances the boom motion synchronization while suppressing payload swings. Furthermore, by introducing continuous terminal sliding mode surfaces with a multi-layer nested structure, the finite-time convergence of the boom positioning errors and the synchronization error is ensured with chattering reduction. Additionally, rigorous closed-loop stability analysis is provided based on Lyapunov techniques and Barbalat’s Lemma. Finally, the effectiveness and robustness of the proposed controller are verified by hardware experimental results. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This paper is motivated by the coordinated motion control problem of dual rotary cranes (DRCs), which aims to achieve safe and accurate control of the payload position and attitude oriented on practical assembly demands. At present, most control methods for DRCs only realize horizontal payload transportation, which not only ignores the requirements of payload attitude regulation in assembly tasks, but also lacks the guarantee for boom motion coordination and the finite-time convergence of state variables. To address these issues, based on the nonlinear crane dynamics <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">without</i> any linearization, this paper proposes an assembly-oriented finite-time coordinated controller for DRCs, which achieves precise and stable regulation of the payload position and attitude through coordinated boom motions, and simultaneously enhances the system rapidity by ensuring the finite-time convergence of boom positioning errors. Furthermore, the detailed controller design and stability analysis process is provided, and the effectiveness of the proposed method is verified by hardware experiments. In the future research, we will try to apply the proposed method to practical operations of DRCs for complex assembly tasks of large heavy objects.

A Concurrent Event-Triggered Approach for Fuzzy Adaptive Control of Nonlinear Strict-Feedback Systems.

If a control input signal constructed by backstepping is used to generate an event-triggered control signal, then not only the real control input is discontinuous, but all the virtual control signals that make up the control signal are also discontinuous and have the same triggering instants with the control input. This fact makes the control design and stability analysis more difficult and complex via backstepping. This article focuses on this problem and works at coming up a new backstepping design procedure of event-triggered fuzzy adaptive control for nonlinear strict feedback systems. A concurrent event-triggered mechanism is proposed to ensure that the real control input and the virtual control signals have the same triggering instants. Then, a systemic backstepping design procedure is developed to construct event-triggered fuzzy adaptive controller. The Lyapunov technique for nonlinear impulsive system is employed to provide the closed-loop stability analysis. It is shown that the derived event-triggered fuzzy adaptive controller ensures that the closed-loop system output well follows the desired tracking trajectory and the other closed-loop signals remain bounded. Eventually, two examples are provided to further verify the applicability and reliability of the presented control scheme.

Closed-loop stability analysis of a linear matrix inequalities based reduced multiple-model control algorithm

Closed-loop stability analysis of a linear matrix inequalities based reduced multiple-model control algorithm

On the robustness of force estimation methods for robot manipulators: An experimental study

Force control of robot manipulators has been extensively studied for the last decades. Whether a direct or an indirect approach is pursued, it is always desirable to know the contact forces/torques, which are usually attained through force sensors. However, there are a variety of reasons for which it may not be desirable to employ them. For instance, they are expensive and not free of noise, and for some applications, they might just be too big to be a practical solution. Following these reasons, there have been many efforts to develop estimation techniques. Some of the main challenges are the need of exact robot models as well as position, velocity, and even acceleration measurements. In this work, a compilation of some of the most employed approaches developed in the last two decades is presented, along with the design of a novel force estimation algorithm. The proposed method is a modification of the well-known Generalized Momentum approach, with the advantages of finite-time convergence and improved performance. A comparative analysis is carried out to elucidate which of the methods delivers a better performance based on two key assumptions presented at the experimental implementation: 1) the robot model is accurate, and 2) the estimated forces/torques should be employed in a control scheme without a previous closed-loop stability analysis. Both assumptions are meant to test the robustness of the different approaches since the former is not realistic, while the latter is not advisable because no separation principle is valid for nonlinear systems. However, from a practical point of view, it is interesting to substitute force measurements with no further analysis. The experimental outcomes show closed-loop stability in all cases.

A novel ESO-based adaptive RISE control for asymptotic position tracking of electro-hydraulic actuator systems

This paper is focused on asymptotic tracking control of electro-hydraulic actuator (EHA) systems subject to matched and mismatched time-varying disturbances. To counteract the matched disturbance, a novel extended state observer (ESO) is proposed to achieve asymptotic convergence of the estimation error, by incorporating the strictly positive real (SPR) Lyapunov design method and a Nussbaum function. To further suppress the mismatched disturbance, an adaptive robust integral of the sign of the error (RISE) controller is formulated in the backstepping framework based on the proposed ESO. Asymptotic tracking performance is theoretically achieved via closed-loop system stability analysis. The efficacy of the proposed control scheme is verified through comparative experiments executed on an EHA test rig. In this study, a priori bounds of the disturbances and their higher-order derivatives are no longer needed, and only one auxiliary error signal is introduced. This approach loosens the restrictions on the disturbances and reduces the design conservativeness, thus making it promising in practice.

Distributed consensus control for voltage tracking and current distribution in DC microgrid

DC microgrids are extensively researched because of advancements in power electronics, penetration of DC loads, and the growing demand for DC power. The DC microgrid is also broached as a multi-agent system (MAS) because of its distributed nature. In this paper, a distributed consensus controller for DC microgrids is proposed that has basically two main objects; the first object is to track the desired reference voltage for the distributed generation units while maintaining the voltage stability at the point of common coupling (PCC), whereas the second object is to distribute current proportionally among distributed loads. Furthermore, a linear distributed model is constructed in which the dynamics of the net current for the distributed generation units are established using the directed graph of power lines. Moreover, local information from neighboring agents is utilized to construct a distributed linear controller, and the consensus control problem is solved for voltage tracking and current distribution of the DC microgrid. Furthermore, the control gains for the proposed controller are optimized using closed-loop stability analysis. Finally, simulation results are illustrated for both open-loop and closed-loop systems, and the effects of the directed power line graph and the undirected communication graph are analyzed. The effects of parameter uncertainties on the performance of the proposed controller are investigated through simulations. The results show that the distributed controller efficiently solves the consensus control problem for the MAS.

Generalized robust MPC with zone-tracking

We propose a robust nonlinear model predictive control design with generalized zone tracking (ZMPC) in this work. The proposed ZMPC has guaranteed convergence into the target zone in the presence of bounded disturbance. The proposed approach achieves this by modifying the actual target zone such that the effect of disturbances is rejected. A control invariant set (CIS) inside the modified target zone is used as the terminal set, which ensures the closed-loop stability of the proposed controller. Closed-loop stability analysis is presented. Simulation studies based on a continuous stirred tank reactor (CSTR) are performed to validate the effectiveness of the proposed ZMPC.

Fixed-time disturbance observer based robust tracking control of wheeled mobile robot with multiple disturbances

In this article, the problem of robust tracking control for wheeled mobile robot (WMR) with skidding, slipping, and parameter uncertainties is addressed. Through designing double sliding mode variables, a fixed time disturbance observer is developed to estimate the multiple disturbances within a fixed time, and the convergence time is regardless of the initial estimation error of the system. Based on the fixed-time disturbance observer (FTDOB) and the novel power reaching law sliding mode technique, a robust tracking controller is synthesized. The proposed control method eliminates the chattering problem existing in the traditional sliding mode control, and can guarantee the high-precision tracking control performance even in the presence of skidding, slipping and parameter uncertainties. The closed-loop system stability analysis is verified by the Lyapunov stability theory. Meanwhile, simulation comparative results are carried out to illustrate the effectiveness of the proposed control method.

Distributed Control Algorithm for DC Microgrid Using Higher-Order Multi-Agent System

During the last decade, DC microgrids have been extensively researched due to their simple structure compared to AC microgrids and increased penetration of DC loads in modern power networks. The DC microgrids consist of three main components, that is, distributed generation units (DGU), distributed non-linear load, and interconnected power lines. The main control tasks in DC microgrids are voltage stability at the point of common coupling (PCC) and current sharing among distributed loads. This paper proposes a distributed control algorithm using the higher-order multi-agent system for DC microgrids. The proposed control algorithm uses communication links between distributed multi-agents to acquire information about the neighbors’ agents and perform the desired control actions to achieve voltage balance and current sharing among distributed DC loads and DGUs. In this research work, non-linear ZIP loads and dynamical RLC lines are considered to construct the model. The dynamical model of the power lines and DGU are used to construct the control objective for each distributed DGU that is improved using the multi-agent system-based distributed current control. The closed-loop stability analysis is performed at the equilibrium points, and control gains are derived. Finally, simulations are performed using MATLAB/Simulink environment to verify the performance of the proposed control method.

A dynamical convolutional neural network–based adaptive observer for information-poor systems

The objective of this paper is to propose a novel self-learning observer for effectively estimating unmeasured states of a dynamical information-poor system. By inspiring the success of convolutional neural network (CNN) in image and voice recognition applications, the dynamical convolutional neural network (DCNN) architecture (which is nonlinear-in-parameter unlike traditional basis functions–based neural network or fuzzy logic architectures) is proposed for approximating the unknown system dynamics, uncertainties, and disturbances. Instead of using an output observation error filtering method, complex weight-updating mechanism, strictly positive real (SPR) assumption, offline-tuning mechanisms, static approximation of gradients in back-propagation algorithm, or any other strong or strict requirement, the simple yet effective and novel rules for tuning DCNN weights and kernels are derived. Furthermore, the problems such as parameters over-tuning and unnecessary consumption of large amounts of computational power commonly found in traditional neuro-adaptive and fuzzy-adaptive controllers/observers are addressed and their solution is incorporated in the design of the observer. Thus, the proposed DCNN-based adaptive observer is energy-efficient. A quadratic function based on the convolution operator is also proposed which is utilized to provide the closed-loop stability analysis using Lyapunov’s approach. An example is simulated to demonstrate the performance of the proposed observer.

Quaternion Constrained Structured Adaptive Attitude Control

In this paper, a novel, attitude-constrained, structured adaptive control strategy is proposed for a spacecraft in the presence of parametric uncertainties. A set of cone angles are defined as a way to quantify the relative orientation error between two reference frames. While tracking the desired attitude, the corresponding cone angles are driven to zero while being constrained to lie within a maximum value. Using an error transformation, the restriction on the cone angles is converted into quaternion constraints that are subsequently used in barrier Lyapunov function (BLF) based controller synthesis. Attitude error constraints are satisfied by ensuring the boundedness of BLFs in the closed-loop Lyapunov stability analysis. Eventually, an adaptive control law is synthesized that drives the spacecraft to the desired attitude with the help of approximate and nominal spacecraft dynamics. While doing so, a function approximation strategy is used to obtain a stable weight update rule to estimate the disturbance term. Finally, the effectiveness of the proposed adaptive control law is demonstrated via numerical simulations.

Stabilization of a chaotic oscillator via a class of integral controllers under input saturation

This work presents the straightforward design of an integral controller with an anti-windup structure to prevent undesirable behavior when actuator saturation is considered, and the proposed controller improves the performance of the closed-loop dynamics of a class of nonlinear oscillators. The proposed integral controller has an adaptive control gain, which includes the absolute value of the named control error to turn off the integral action when it is saturated. Closed-loop stability analysis is performed under the Lyapunov theory framework, where it can be concluded that the system behaves in an asymptotically stable way. The proposed methodology is successfully applied to a Rikitake-type oscillator, considering a single input-single output (SISO) structure for regulation and tracking trajectory purposes. For comparison, an equivalent fixed gain integral controller is also implemented to analyze the corresponding anti-windup properties of the proposed control structure. Numerical experiments are conducted, showing the superior performance of the proposed controller.

Robust output-feedback orbital stabilization for underactuated mechanical systems via high-order sliding modes

The manuscript deals with the robust orbital stabilization for a class of disturbed Euler–Lagrange systems with one degree of underactuation. The proposed strategy relies on the virtual holonomic constraints approach, using incomplete state measurements. First, a high-order sliding-mode extended observer estimates the state and the disturbances affecting the input channel. Then, proposing a new set of coordinates, the so-called virtual holonomic constraints, a robust output partial-feedback linearization approach takes the system into a double integrator with a particular zero dynamics. Thus, considering the general integral of motion of the zero dynamics, the orbital stabilization is reduced to stabilize a linear time-varying system. The resulting control law is a continuous signal. Therefore, the robustness to disturbances is addressed without the tarnishing effects of chattering. The closed-loop stability analysis is done using the Lyapunov theory. The feasibility of the method is illustrated experimentally in a cart-pendulum system.

Saturating PI Control of Stable Nonlinear Systems Using Singular Perturbations

This article presents an antiwindup propor- tional-integral (PI) controller, using a saturating integrator, for a single-input and single-output (SISO) stable nonlinear plant, whose steady-state input–output map is increasing. We prove that, under reasonable assumptions, there exists an upper bound on the controller gain such that for any constant reference input, the corresponding equilibrium point of the closed-loop system is exponentially stable, with a “large” region of attraction. When the state of the closed-loop system converges to this equilibrium point, then the tracking error tends to zero. The closed-loop stability analysis employs Lyapunov methods in the framework of the singular perturbations theory. Finally, we show that if the plant satisfies the asymptotic gain property, then the closed-loop system is globally asymptotically stable for any sufficiently small controller gain. The effectiveness of the proposed PI controller is proved by showing how it performs as part of the control algorithm of a synchronverter (a special type of dc to ac power converter).

Disturbance Observer and Tube-based Model Reference Adaptive Control for Active Suspension Systems with Non-ideal Actuators

Active suspension systems undertake a vital role in ensuring passengers’ ride comfort and vehicle vibration attenuation. This work proposes a tube-based model reference adaptive control (TMRAC) that identifies a correctional control component at each time instant for performance amplification of active suspension systems with non-ideal actuators. The TMRAC is augmented by a disturbance observer (DO) to compensate for the effects of dead-zone and hysteresis. Closed-loop stability analysis of the developed method is also investigated in the sense of Lyapunov theory. The developed control scheme's feasibility with regard to suspension safety, road handling, and ride comfort is assessed through simulations by using a class C road profile. Comparison results with DO-based conventional MRAC are also conducted. The obtained results demonstrate that the proposed DO-based control strategy provides a superior ride comfort quality and better road disturbance mitigation with less control effort than the conventional method.

Adaptive sliding mode controller based consensus protocol for swarm of UAVs

PurposeThe requirement of robust cooperative control is essential to achieve consensus between unmanned aerial vehicles (UAVs) operating in swarm formation. Often the performance of these swarm formations is affected by wind gust disturbances. This study proposes an effective robust consensus protocol, which will ensure the UAVs in swam formation to collectively meet the desired objective in real-time scenario.Design/methodology/approachIn this work, the swarm of UAVs are modeled as multiagent systems by using the concepts of algebraic graph theory. To address the challenges of a complex and dynamic environment, an adaptive sliding mode control (SMC)-based consensus protocol is proposed. The closed loop stability analysis is established through Lyapunov theory.FindingsThe efficacy of the discussed robust consensus controller is analyzed through numerical simulations. Further, the quantitative analysis using Monte-Carlo simulations validates performance of the proposed robust consensus protocol. The presented consensus protocol can be easily implementable as robust flight controller for swarm of UAVs. Also, as the consensus theory is based on the algebraic graph theory, the proposed design is scalable for a large number of UAVs in swarm formation.Originality/valueThe proposed adaptive SMC achieves robust consensus of longitudinal dynamics states between all the UAVs by mitigating the effects of wind gust disturbances. Also, the adaptive SMC offers chattering-free control efforts.

Parameter-Variation-Tolerant Robust Current Sensorless Control of a Single-Phase Boost PFC

With the objective to eliminate the input current sensor in a totem-pole boost power factor corrector (PFC) for its low-cost design, a novel discretized sampling-based robust control scheme is proposed in this work. The proposed control methodology proves to be beneficial due to its ease of implementation and its ability to support high-frequency operation, while being able to eliminate one sensor and, thus, enhancing reliability and cost-effectiveness. In addition, detailed closed-loop stability analysis is carried out for the controller in discrete domain to ascertain brisk dynamic operation when subjected to sudden load fluctuations. To establish the robustness of the proposed control scheme, a detailed sensitivity analysis of the closed-loop performance metrics with respect to undesired changes and inherent uncertainty in system parameters is presented in this article. A comparison with the state-of-the-art (SOA) methods is provided, and conclusive results in terms of better dynamic performance are also established. To verify and elaborate on the specifics of the proposed scheme, a detailed simulation study is conducted, and the results show 25% reduction in response time as compared to SOA approaches. A 500-W boost PFC prototype is developed and tested with the proposed control scheme to evaluate and benchmark the system steady-state and dynamic performance. A total harmonic distortion of 1.68% is obtained at the rated load with a resultant power factor of 0.998 (lag), which proves the effectiveness and superiority of the proposed control scheme.