Smooth Control Law Research Articles

Neural network adaptive control for turbo‐generator of power systems with prescribed performance and unknown asymmetric actuator dead zone

AbstractThis paper investigates a neural network adaptive controller design method for turbo‐generator of power systems with external disturbance, unknown system dynamic, prescribed performance, and unknown actuator dead zone. First, the unknown system dynamic is estimated and overcome through a neural network. Using the implicit function theorem, the unknown asymmetric dead‐zone behavior of the actuator is overcome by another static neural network. Second, the external disturbance and the reconstruction error of neural networks are handled by a robust term updated online. Moreover, there is no requirement to pre‐know or off‐line estimate the reconstruction error of neural networks and the upper bound of the system external disturbance. Third, based on Lyapunov theory, the smooth control law is proposed. In the meantime, the uniform ultimate boundedness of the networks weights is strictly proved. Furthermore, the system state error satisfies the prescribed transient performance and can converge to a small neighborhood around zero. Finally, a numerical simulation shows the effectiveness of the proposed method.

Adaptive barrier function‐based fractional‐order chattering‐free finite‐time control for uncertain chaotic systems

This study proposes the adaptive continuous barrier function as the fractional‐order control system using the terminal sliding mode control technique with chattering‐free property to stabilize chaotic systems that have unknown uncertainties. The important reason for using the fractional‐order controller is its greater flexibility than the integer‐order controller. Using adaptive approach and Lyapunov's stability theory, an adaptive continuous barrier fractional‐order chattering‐free finite‐time controller for a category of chaotic systems with the unknown uncertainties and external disturbances is presented. The suggested controller can stabilize the chaotic system excellently with a continuous and smooth control law even without knowing the boundaries and in the presence of unknown disturbances due to the model uncertainties. According to MATLAB simulation results, the high efficiency of the suggested control technique to control the chaotic systems in the attendance of unknown perturbations is obviously confirmed.

Reaching global leaderless consensus in directed networks via smooth and bounded control

AbstractThis short communication revisits the leaderless consensus problem in directed networks. The network topology is described by a general directed graph which is only needed to contain at least a directed spanning tree, and is not necessarily strongly connected. A bounded and smooth control law using the hyperbolic tangent function is developed as the consensus protocol. Explicit stability analysis based on Lyapunov's second method and the concept of condensation graph is given. The proposed approach transforms the leaderless consensus problem into two subproblems: reaching leader‐following consensus under a graph containing a directed spanning tree with the leader being the root node and reaching leaderless consensus under a strongly connected graph. Remarkably, a perturbed system is formulated as the bridge between these two subproblems which are solved by Lyapunov's second method. The global leaderless consensus is achieved based on the stability of the perturbed system. Finally, two numerical examples are presented to illustrate the effectiveness of the proposed approach.

Design of Asynchronous Motor Controller Based on Controlled Lagrangians Method

Asynchronous motor system has the characteristics of high order, strong coupling, and nonlinearity. From the dynamical model, it is the underactuated mechanical system, which means that the dimension of its input space is fewer than the degree of freedom. Following this perspective, the energy based nonlinear control technology-CL (controlled Lagrangians) method is used to solve the control problem in this paper. Based on the expected controlled energy and its derivative with respect to time, controlled Lagrangians and generalized force are constructed, and they produce the controlled equations. In order to ensure the complete matching between the controlled equation and the original equation, the gyroscopic forces containing the first-order term of velocity are innovatively introduced into the generalized force, and the matching conditions are obtained. By solving the matching conditions composed of some partial differential equations, the nonlinear smooth feedback control law can realize the global asymptotic stabilization of not only velocity but also position. Finally, the controlled energy is selected as the Lyapunov function, and the stability is proved according to the LaSalle invariant theorem. The effectiveness of the designed control law is demonstrated in the results of the simulation.

Stabilization control of quadrotor helicopter through matching solution by controlled Lagrangian method

AbstractThis paper implements the controlled Lagrangian method on nonlinear quadrotor system with two degrees of underactuation. A Lagrangian system based on virtual angles is developed for the quadrotor. Based on the model, the matching conditions presented by nonlinear partial differential equations are explicitly solved for the nonlinear quadrotor system without decoupling or division. Besides, it is demonstrated that a constant controlled kinetic matrix could be utilized for energy shaping and simplify the matching conditions since gyroscopic force terms are omitted. Smooth state feedback control laws guaranteeing asymptotic stability of quadrotor system are obtained. Stability analysis and range of the control parameters are deduced based on the reshaped closed‐loop energy. Simulation for a quadrotor helicopter shows the feasibility and efficiency of the theoretical results.

Energy shaping control for systems with underactuation degrees two by controlled Lagrangian method

AbstractThis article investigates underactuated systems' energy shaping control by controlled Lagrangian (CL) method. The existence of CL based control depends on a set of matching conditions, which are usually in terms of partial differential equations (PDEs). In this work, the matching conditions are derived and simplified for underactuation‐degrees‐two systems. Moreover, the solvability conditions are provided for a class of systems satisfying Assumptions 1 and 2, based on which the controlled energy could be explicitly solved. By the proposed matching solution method, the desired equilibrium can be effectively assigned. The proposed matching controller is implemented for a strongly coupled single rigid body system with six degrees of freedom for the first time. Smooth state feedback control laws guaranteeing asymptotic stability of the system are presented. The range of the control parameters could be obtained based on the positive definiteness of reshaped closed‐loop energy. Simulations for comparison with relate work show the effectiveness of the theoretical results.

Angular velocity stabilization of underactuated rigid satellites based on energy shaping

Angular velocity stabilization problem for underactuated rigid satellites with only two independent control inputs is investigated, and a novel stabilization control strategy based on energy shaping is presented in this paper. Firstly, a desired closed-loop system with a specific structure is constructed for the control objective. The matching condition and controller structure are determined by equating the underactuated satellite system with the desired system. Moreover, a feasible sufficient condition satisfying the matching condition is derived. By solving the sufficient condition according to three different structures of the satellite inertia tensor matrix, three nonlinear smooth stabilization control laws are obtained, and global asymptotic stability of the related closed-loop system is rigorously proved. Simulation results show effectiveness of the proposed control method.

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Angular velocity stabilization problem for underactuated rigid satellites with only two independent control inputs is investigated, and a novel stabilization control strategy based on energy shaping is presented in this paper. Firstly, a desired closed-loop system with a specific structure is constructed for the control objective. The matching condition and controller structure are determined by equating the underactuated satellite system with the desired system. Moreover, a feasible sufficient condition satisfying the matching condition is derived. By solving the sufficient condition according to three different structures of the satellite inertia tensor matrix, three nonlinear smooth stabilization control laws are obtained, and global asymptotic stability of the related closed-loop system is rigorously proved. Simulation results show effectiveness of the proposed control method.

Insights on the catalyst fertilizer global market to 2026 - featuring Chempack, Clariant International and Johnson Matthey among others

Angular velocity stabilization problem for underactuated rigid satellites with only two independent control inputs is investigated, and a novel stabilization control strategy based on energy shaping is presented in this paper. Firstly, a desired closed-loop system with a specific structure is constructed for the control objective. The matching condition and controller structure are determined by equating the underactuated satellite system with the desired system. Moreover, a feasible sufficient condition satisfying the matching condition is derived. By solving the sufficient condition according to three different structures of the satellite inertia tensor matrix, three nonlinear smooth stabilization control laws are obtained, and global asymptotic stability of the related closed-loop system is rigorously proved. Simulation results show effectiveness of the proposed control method.

Big West Oil lets contract for unit revamp at Utah refinery; Includes HF-to-ISOALKY alkylation unit conversion

Angular velocity stabilization problem for underactuated rigid satellites with only two independent control inputs is investigated, and a novel stabilization control strategy based on energy shaping is presented in this paper. Firstly, a desired closed-loop system with a specific structure is constructed for the control objective. The matching condition and controller structure are determined by equating the underactuated satellite system with the desired system. Moreover, a feasible sufficient condition satisfying the matching condition is derived. By solving the sufficient condition according to three different structures of the satellite inertia tensor matrix, three nonlinear smooth stabilization control laws are obtained, and global asymptotic stability of the related closed-loop system is rigorously proved. Simulation results show effectiveness of the proposed control method.

PPG, Oriental Silicas Corporation enter into strategic agreement

Angular velocity stabilization problem for underactuated rigid satellites with only two independent control inputs is investigated, and a novel stabilization control strategy based on energy shaping is presented in this paper. Firstly, a desired closed-loop system with a specific structure is constructed for the control objective. The matching condition and controller structure are determined by equating the underactuated satellite system with the desired system. Moreover, a feasible sufficient condition satisfying the matching condition is derived. By solving the sufficient condition according to three different structures of the satellite inertia tensor matrix, three nonlinear smooth stabilization control laws are obtained, and global asymptotic stability of the related closed-loop system is rigorously proved. Simulation results show effectiveness of the proposed control method.

Albemarle reports 3Q 2021 sales growth of 11% and increases guidance: Key figures and catalysts

Angular velocity stabilization problem for underactuated rigid satellites with only two independent control inputs is investigated, and a novel stabilization control strategy based on energy shaping is presented in this paper. Firstly, a desired closed-loop system with a specific structure is constructed for the control objective. The matching condition and controller structure are determined by equating the underactuated satellite system with the desired system. Moreover, a feasible sufficient condition satisfying the matching condition is derived. By solving the sufficient condition according to three different structures of the satellite inertia tensor matrix, three nonlinear smooth stabilization control laws are obtained, and global asymptotic stability of the related closed-loop system is rigorously proved. Simulation results show effectiveness of the proposed control method.

SD touts startup of Fujian Gulei's new EO/EG project in Zhangzhou

Angular velocity stabilization problem for underactuated rigid satellites with only two independent control inputs is investigated, and a novel stabilization control strategy based on energy shaping is presented in this paper. Firstly, a desired closed-loop system with a specific structure is constructed for the control objective. The matching condition and controller structure are determined by equating the underactuated satellite system with the desired system. Moreover, a feasible sufficient condition satisfying the matching condition is derived. By solving the sufficient condition according to three different structures of the satellite inertia tensor matrix, three nonlinear smooth stabilization control laws are obtained, and global asymptotic stability of the related closed-loop system is rigorously proved. Simulation results show effectiveness of the proposed control method.

Fixed Frequency Slide Mode Controller Cascaded with Proportional Resonant Controller and Droop Controller a New Approach for an Effective 3-Phase Microgrid under Islanded Operation

Inverter-based distributed generation (DG) units in microgrid (MG) call for robust and precise control methods that attain high performance under both normal and unbalanced conditions. Efficient control scheme needs to be investigated for the proper operation of a microgrid in both grid-tied and islanding condition. Using the excellent performance of slide mode controller(SMC) for nonlinear loads and the ability of proportional resonant(PR) controller to precisely track reference sinusoidal signal, a cascaded SMC and PR controller has been proposed for stable operation of microgrid. The phenomenon of chattering a drawback in SMC is eliminated by using fixed frequency switching of the inverter circuit using smooth control law in a narrow boundary layer. For effective sharing of the loads among different DER’s during isolation mode of operation a droop controller is proposed. The proposed controller showed excellent results for linear and nonlinear loading. To analyze the performance of droop controller, proposed for parallel operation of two DG units, simulations are performed under linear and distorted load conditions. Results obtained shows that proposed cascaded controller and droop controller improves the output by the reduction of the total harmonic distortion (THD), high degree of robustness, fast response time, and efficient power sharing among DG units.

On event‐triggered nonsmooth attitude tracking controller for a rigid spacecraft

AbstractThis article focuses on the problem of finite‐time attitude tracking control for a rigid spacecraft with event‐triggered inputs. The existing event‐based attitude control methods are developed from the smooth control law and can only provide at best Lipschitzian exponentially convergent. Because the nonsmooth control law shows a faster convergent rate and better control performance, a new event‐triggered nonsmooth attitude tracking controller is proposed through the emulation method of a continuous‐time finite‐time attitude controller. With the aid of Lyapunov theory and finite‐time stability lemma, the stability analysis of the closed‐loop system is given and the event‐triggered control system is Zeno‐free. Like the case of a continuous‐time nonsmooth attitude controller, it is proved that the event‐triggered nonsmooth attitude controller maintains a better disturbance rejection ability. Finally, some simulation results are given to verify the theoretical results.

Dynamic multi-objective matrix control for a class of switched systems

This article focuses on the tracking and stabilizing issues of a class of discrete switched systems. These systems are characterized by unknown switching sequences, a non-minimum phase, and time-varying or dead modes. In particular, for those governed by an indeterminate switching signal, it is very complicated to synthesize a control law able to systematically approach general reference-tracking difficulties. Taking into account the difficulty to express the dynamic of this class of systems, the present paper presents a new Dynamic matrix control method based on the multi-objective optimization and the truncated impulse response model. The formulation of the optimization problem aims to approach the general step-tracking issues under persistent and indeterminate mode changes and to overcome the stability problem along with retaining as many desirable features of the standard dynamic matrix control (DMC) method as possible. In addition, the formulated optimization problem integrates estimator variables able to manipulate the optimization procedure in favor of the active mode with an appropriate adjustment. It also provides a progressive and smooth multi-objective control law even in the presence of problems whether in subsystems or switching sequences. Finally, simulation examples and comparison tests are conducted to illustrate the potentiality and effectiveness of the developed method.

Global Sampled-Data Regulation of a Class of Fully Actuated Invariant Systems on Simply Connected Nilpotent Matrix Lie Groups

In this article, we examine a regulator problem for a class of fully actuated continuous-time invariant systems on Lie groups, using a discrete-time controller with constant sampling period. We present a smooth discrete-time control law that achieves global regulation on simply connected nilpotent Lie groups. We first solve the problem when both the plant state and exosystem state are available for feedback, then in the case where the plant state and plant output are available for feedback. The class of plant outputs considered includes, for example, the quantity to be regulated. This class of outputs allows us to use the classical Luenberger observer to estimate the exosystem states. In the full-information case, the regulation quantity on the Lie algebra is shown to decay exponentially to zero, which implies that it tends asymptotically to the identity on the Lie group.

Majorant-Based Control Methodology for Mechatronic and Transportation Processes

This paper provides a unified approach via majorant systems, which allows one to easily design a family of robust, smooth and effective control laws of proportional - <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$h$ </tex-math></inline-formula> order integral - <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> order derivative <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(PI_{h} D_{k})$ </tex-math></inline-formula> -type for broad classes of uncertain nonlinear multi-input multi-output (MIMO) systems, including mechatronic and transportation processes with ideal or real actuators, subject to bounded disturbances and measurement errors. The proposed control laws are simple to design and implement and are used, acting on a single design parameter, to track a sufficiently smooth but generic reference signal, yielding a tracking error norm less than a prescribed value, with a good transient phase and feasible control signals, despite the presence of disturbances, parametric and structural uncertainties, measurement errors, and in case of real actuators and amplifiers. Moreover, some guidelines to easily design the proposed controllers are given. Finally, the stated unified methodology and various performance comparisons are illustrated and validated in two case studies.

Design of global smooth implicit control Lyapunov function for multiple-integrator system with input constraint

In this study, we propose a new method to design a smooth implicit control Lyapunov function and a smooth control law for a multi-integrator system with an input constraint. The proposed controller is almost linear near the origin, and it tends to a homogeneous controller of the previous implicit Lyapunov function methods as the state goes to infinity. The proposed method can be used for the backstepping method with a restricted virtual input, which is a nonlinear function of the state, and the desired virtual input is designed as a bounded function. Furthermore, we apply our method to the control of a magnetic levitation system, and a simulation result presents the advantage of the proposed method.

Chattering-free model free adaptive sliding mode control for gas collection process with data dropout

Stable pressure control of coke oven gas collectors is difficult due to the problems of nonlinearity, couplings, time-variation, disturbances and data-dropout. This paper proposes a novel chattering-free model free adaptive sliding mode control scheme for the gas collection process of coke ovens. Unlike the conventional data-driven sliding mode control approaches, the proposed controller is based on the data-dropout compensation scheme and predictive control strategy, whereby a novel data-driven sliding surface estimator and a new data-driven sliding mode prediction model are developed to facilitate the controller design. On one hand, the effect of data dropout could be attenuated by applying the proposed estimator. On the other hand, a chattering-free smooth control law with strong robustness to couplings, time-variation and disturbances is obtained owing to the application of the predictive control strategy and the sliding mode control technique. In addition, the convergence of the proposed algorithm could be guaranteed theoretically. Finally, experimental results soundly confirm the efficacy and superiority of the developed approach.