Cyclic Constraint Analysis for Attitude Synchronization of Networked Spacecraft Agents

2013 ◽  
Vol 135 (6) ◽  
Author(s):  
Hanlei Wang ◽  
Yongchun Xie
Keyword(s):  
Multiple Equilibria ◽  
Closed Loop ◽  
Euler Parameters ◽  
Networked System ◽  
Synchronization Errors ◽  
Synchronization Problem ◽  
Constraint Analysis ◽  
The Stability ◽  
Error Orientation ◽  
Attitude Synchronization

In this paper, we investigate the attitude synchronization problem for multiple networked spacecraft, and the spacecraft agents are assumed to interact on an undirected and connected graph. We adopt a physically motivated PD-like attitude consensus scheme which takes Euler parameters or quaternions of the error orientation matrix between the spacecraft agents as the attitude deviation, resulting in nonlinear attitude coupling among the networked spacecraft agents and additionally multiple equilibria of the closed-loop networked system. The stability of the closed-loop networked system is shown by the Lyapunov stability analysis. To show the convergence of the attitude synchronization errors, we develop a new tool called cyclic constraint analysis. With this synthesis tool, we show that attitude synchronization is achieved without relying on any assumptions of the spacecraft orientations. Simulation study is presented to shed some light on the obtained results.

A simulation apparatus for the experimental study of batch reactor control methods

1986 ◽  
Vol 51 (6) ◽  
pp. 1259-1267
Author(s):  
Josef Horák ◽  
Petr Beránek
Keyword(s):  
Experimental Study ◽  
Closed Loop ◽  
Dynamic Properties ◽  
Batch Reactor ◽  
Exothermic Reaction ◽  
Electric Heating ◽  
Batch Reactors ◽  
Exchange Area ◽  
The Stability ◽  
Methods Of Control

A simulation apparatus for the experimental study of the methods of control of batch reactors is devised. In this apparatus, the production of heat by an exothermic reaction is replaced by electric heating controlled by a computer in a closed loop; the reactor is cooled with an external cooler whose dynamic properties can be varied while keeping the heat exchange area constant. The effect of the cooler geometry on its dynamic properties is investigated and the effect of the cooler inertia on the stability and safety of the on-off temperature control in the unstable pseudostationary state is examined.

Adaptive attitude-tracking control of spacecraft considering on-orbit refuelling

2020 ◽  
pp. 014233122097313
Author(s):  
Yiqi Xu
Keyword(s):  
Tracking Control ◽  
Closed Loop ◽  
Closed Loop System ◽  
Tracking Errors ◽  
Attitude Tracking ◽  
Control Scheme ◽  
Inertia Model ◽  
And Performance ◽  
Attitude Tracking Control ◽  
The Stability

This paper studies the attitude-tracking control problem of spacecraft considering on-orbit refuelling. A time-varying inertia model is developed for spacecraft on-orbit refuelling, which actually includes two processes: fuel in the transfer pipe and fuel in the tank. Based upon the inertia model, an adaptive attitude-tracking controller is derived to guarantee the stability of the resulted closed-loop system, as well as asymptotic convergence of the attitude-tracking errors, despite performing refuelling operations. Finally, numerical simulations illustrate the effectiveness and performance of the proposed control scheme.

Stability of slender inverted flags and rods in uniform steady flow

2016 ◽  
Vol 809 ◽  
pp. 873-894 ◽  
Author(s):  
John E. Sader ◽  
Cecilia Huertas-Cerdeira ◽  
Morteza Gharib
Keyword(s):  
Multiple Equilibria ◽  
Complex Dynamics ◽  
Flow Direction ◽  
Flow Speed ◽  
Uniform Flow ◽  
Biological Phenomena ◽  
Cantilever Length ◽  
The Stability ◽  
Elastic Sheets ◽  
Clamped Edge

Cantilevered elastic sheets and rods immersed in a steady uniform flow are known to undergo instabilities that give rise to complex dynamics, including limit cycle behaviour and chaotic motion. Recent work has examined their stability in an inverted configuration where the flow impinges on the free end of the cantilever with its clamped edge downstream: this is commonly referred to as an ‘inverted flag’. Theory has thus far accurately captured the stability of wide inverted flags only, i.e. where the dimension of the clamped edge exceeds the cantilever length; the latter is aligned in the flow direction. Here, we theoretically examine the stability of slender inverted flags and rods under steady uniform flow. In contrast to wide inverted flags, we show that slender inverted flags are never globally unstable. Instead, they exhibit bifurcation from a state that is globally stable to multiple equilibria of varying stability, as flow speed increases. This theory is compared with new and existing measurements on slender inverted flags and rods, where excellent agreement is observed. The findings of this study have significant implications to investigations of biological phenomena such as the motion of leaves and hairs, which can naturally exhibit a slender geometry with an inverted configuration.

LPV Based Sliding Mode Control for Limit Protection of Aircraft Engines

2018 ◽  
Author(s):  
Shubo Yang ◽  
Xi Wang
Keyword(s):  
Closed Loop ◽  
Sliding Mode ◽  
Aircraft Engine ◽  
Gain Scheduling ◽  
Engine Control ◽  
Aircraft Engines ◽  
Sliding Surface ◽  
Closed Loop System ◽  
Limit Protection ◽  
The Stability

Limit protection, which frequently exists as an auxiliary part in control systems, is not the primary motive of control but is a necessary guarantee of safety. As in the case of aircraft engine control, the main objective is to provide the desired thrust based on the position of the throttle; nevertheless, limit protection is indispensable to keep the engine operating within limits. There are plenty of candidates that can be applied to design the regulators for limit protection. PID control with gain-scheduling technique has been used for decades in the aerospace industry. This classic approach suggests linearizing the original nonlinear model at different power-level points, developing PID controllers correspondingly, and then scheduling the linear time-invariant (LTI) controllers according to system states. Sliding mode control (SMC) is well-known with mature theories and numerous successful applications. With the one-sided convergence property, SMC is especially suitable for limit protection tasks. In the case of aircraft engine control, SMC regulators have been developed to supplant traditional linear regulators, where SMC can strictly keep relevant outputs within their limits and improve the control performance. In aircraft engine control field, we all know that the plant is a nonlinear system. However, the present design of the sliding controller is carried out with linear models, which severely restricts the valid scope of the controller. Even if the gain scheduling technique is adopted, the stability of the whole systems cannot be theoretically proved. Research of linear parameter varying (LPV) system throws light on a class of nonlinear control problems. In present works, we propose a controller design method based on the LPV model to solve the engines control problem and achieve considerable effectiveness. In this paper, we discuss the design of a sliding controller for limit protection task of aircraft engines, the plant of which is described as an LPV system instead of LTI models. We define the sliding surface as tracking errors and, with the aid of vertex property, present the stability analysis of the closed-loop system on the sliding surface. An SMC law is designed to guarantee that the closed-loop system is globally attracted to the sliding surface. Hot day (ISA+30° C) takeoff simulations based on a reliable turbofan model are presented, which test the proposed method for temperature protection and verify its stability and effectiveness.

scholarly journals Nonlinear feedback controller for the synchronization of (chaotic) systems with known parameters

2020 ◽  
Vol 23 (02) ◽  
pp. 124-135
Author(s):  
Muhammad Haris ◽  
Muhammad Shafiq ◽  
Adyda Ibrahim ◽  
Masnita Misiran
Keyword(s):  
Closed Loop ◽  
Lyapunov Stability Theory ◽  
Feedback Controller ◽  
Control Signal ◽  
Stability And Convergence ◽  
Nonlinear Feedback ◽  
Nonlinear Part ◽  
Synchronization Errors ◽  
Novel Structure ◽  
Linear And Nonlinear

This paper proposes, designs, and analyses a novel nonlinear feedback controller that realizes fast, and oscillation free convergence of the synchronization error to the equilibrium point. Oscillation free convergence lowers the failure chances of a closed-loop system due to the reduced chattering phenomenon in the actuator motion, which is a consequence of low energy sm ooth control signal. The proposed controller has a novel structure. This controller does not cancel nonlinear terms of the plant in the closed-loop; this attribute improves the robustness of the loop. The controller consists of linear and nonlinear parts; each part executes a specific task. The linear term in the controller keeps the closed-loop stable, while the nonlinear part of the controller facilitates the fast convergence of the error signal to the vicinity of the origin. Then the linear controller synthesizes a smooth control signal that moves the error signals to zero without oscillations. The nonlinear term of the controller does not contribute to this synthesis. The collaborative combination of linear and nonlinear controllers that drive the synchronization errors to zero is innovative. The paper establishes proof of global stability and convergence behavior by describing a detailed analysis based on the Lyapunov stability theory. Computer simulation results of two numerical examples verify the performance of the proposed controller approach. The paper also provides a comparative study with state-of-the-art controllers.

On the Oscillatory Instability of Closed-Loop Thermosyphons

1985 ◽  
Vol 107 (4) ◽  
pp. 826-832 ◽  
Author(s):  
K. Chen
Keyword(s):  
Turbulent Flows ◽  
Closed Loop ◽  
Numerical Solutions ◽  
Angular Frequency ◽  
Oscillatory Instability ◽  
Neutral Stability ◽  
Horizontal Segment ◽  
Aspect Ratios ◽  
The Stability ◽  
Laminar And Turbulent Flows

The stability of natural convection flows in single-phase closed-loop thermosyphons is investigated. The thermosyphons considered in the present analysis are fluid-filled tubes bent into rectangular shapes. The fluid is heated over the lower horizontal segment and cooled over the upper horizontal segment. Analytical and numerical solutions are presented for a range of loop aspect ratios and radii for both laminar and turbulent flows. It is found that the steady-state results for thermosyphons with different aspect ratios and radii can be expressed in terms of a single dimensionless parameter. When this parameter is less than a critical value, the flow is always stable. Above this critical point, oscillatory instability exists for a narrow range of a friction parameter. The calculated neutral stability conditions show that the flow is least stable when the aspect ratio of the loop approaches unity. The frequency of the convection-induced oscillation is slightly higher than the angular frequency of a fluid particle traveling along the loop.

Stability of a Class of Piezoelectric State-Switching Methods

2000 ◽  
Author(s):  
Andrew J. Kurdila ◽  
William W. Clark ◽  
Weijian Wang ◽  
Dwayne E. McDaniel
Keyword(s):  
Lyapunov Functions ◽  
Closed Loop ◽  
Control Strategies ◽  
Short Circuit ◽  
Open Circuit ◽  
Hybrid Dynamical Systems ◽  
Multiple Lyapunov Functions ◽  
Control Laws ◽  
State Switching ◽  
The Stability

Abstract Experimental and anecdotal evidences have shown that state-switched control strategies for piezoelectric actuators can be advantageous. However, most discussions of the stability of these systems has relied on heuristic, or physically motivated, arguments. In this paper, we show that recent open-circuit/short-circuit state-switching control laws can be viewed as hybrid dynamical systems of Witsenhausen type. Within this framework, the closed-loop stability of OC/SC switching is rigorously established using the method of multiple Lyapunov functions.

scholarly journals A stable proportional–proportional integral tracking controller with self-organizing fuzzy-tuned gains for parallel robots

2019 ◽  
Vol 16 (1) ◽  
pp. 172988141881995
Author(s):  
Francisco G Salas ◽  
Jorge Orrante-Sakanassi ◽  
Raymundo Juarez-del-Toro ◽  
Ricardo P Parada
Keyword(s):  
Stability Analysis ◽  
Performance Index ◽  
Closed Loop ◽  
Tracking Error ◽  
Parallel Robots ◽  
Control Loop ◽  
Closed Loop System ◽  
Proportional Integral ◽  
The Stability ◽  
Self Organizing

Parallel robots are nowadays used in many high-precision tasks. The dynamics of parallel robots is naturally more complex than the dynamics of serial robots, due to their kinematic structure composed by closed chains. In addition, their current high-precision applications demand the innovation of more effective and robust motion controllers. This has motivated researchers to propose novel and more robust controllers that can perform the motion control tasks of these manipulators. In this article, a two-loop proportional–proportional integral controller for trajectory tracking control of parallel robots is proposed. In the proposed scheme, the gains of the proportional integral control loop are constant, while the gains of the proportional control loop are online tuned by a novel self-organizing fuzzy algorithm. This algorithm generates a performance index of the overall controller based on the past and the current tracking error. Such a performance index is then used to modify some parameters of fuzzy membership functions, which are part of a fuzzy inference engine. This fuzzy engine receives, in turn, the tracking error as input and produces an increment (positive or negative) to the current gain. The stability analysis of the closed-loop system of the proposed controller applied to the model of a parallel manipulator is carried on, which results in the uniform ultimate boundedness of the solutions of the closed-loop system. Moreover, the stability analysis developed for proportional–proportional integral variable gains schemes is valid not only when using a self-organizing fuzzy algorithm for gain-tuning but also with other gain-tuning algorithms, only providing that the produced gains meet the criterion for boundedness of the solutions. Furthermore, the superior performance of the proposed controller is validated by numerical simulations of its application to the model of a planar three-degree-of-freedom parallel robot. The results of numerical simulations of a proportional integral derivative controller and a fuzzy-tuned proportional derivative controller applied to the model of the robot are also obtained for comparison purposes.

Stability analysis in machining process by using adaptive closed-loop feedback control system in turning process

2020 ◽  
pp. 107754632095261
Author(s):  
Kashfull Orra ◽  
Sounak K Choudhury
Keyword(s):  
Control System ◽  
Feedback Control ◽  
Closed Loop ◽  
Machining Process ◽  
Feedback Control System ◽  
Turning Process ◽  
Tool Vibration ◽  
Loop Feedback ◽  
Closed Loop Feedback ◽  
The Stability

The study presents model-based mechanism of nonlinear cutting tool vibration in turning process and the strategy of improving cutting process stability by suppressing machine tool vibration. The approach used is based on the closed-loop feedback control system with the help of electro–magneto–rheological damper. A machine tool vibration signal generated by an accelerometer is fed back to the coil of a damper after suitable amplification. The damper, attached under the tool holder, generates counter forces to suppress the vibration after being excited by the signal in terms of current. The study also discusses the use of transfer function approach for the development of a mathematical model and adaptively controlling the process dynamics of the turning process. The purpose of developing such mechanism is to stabilize the machining process with respect to the dynamic uncut chip thickness responsible for the type-II regenerative effect. The state-space model used in this study successfully checked the adequacy of the model through controllability and observability matrices. The eigenvalue and eigenvector have confirmed the stability of the system more accurately. The characteristic of the stability lobe chart is discussed for the present model-based mechanism.

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