Coupled Dynamics and Integrated Control for Position and Attitude Motions of Spacecraft:A Survey

Inspired by the integrated guidance and control design for endo-atmospheric aircraft,the integrated position and attitude control of spacecraft has attracted increasing attention and gradually induced a wide variety of study results in last over two decades,fully incorporating control requirements and actuator characteristics of space missions.This paper presents a novel and comprehensive survey to the coupled position and attitude motions of spacecraft from the perspective of dynamics and control.To this end,a systematic analysis is firstly conducted in details to show the position and attitude mutual couplings of spacecraft.Particularly,in terms of the time discrepancy between spacecraft position and attitude motions,space missions can be categorized into two types:space proximity operation and space orbital maneuver.Based on this classification,the studies on the coupled dynamic modeling and the integrated control design for position and attitude motions of spacecraft are sequentially summarized and analyzed.On the one hand,various coupled position and dynamic formulations of spacecraft based on various mathematical tools are reviewed and compared from five aspects,including mission applicability,modeling simplicity,physical clearance,information matching and expansibility.On the other hand,the development of the integrated position and attitude control of spacecraft is analyzed for two space missions,and especially,five distinctive development trends are captured for space operation missions.Finally,insightful prospects on future development of the integrated position and attitude control technology of spacecraft are proposed,pointing out current primary technical issues and possible feasible solutions.

Adaptive Dynamic Surface Control for Integrated Missile Guidance and Autopilot

Integrated guidance and control for homing missiles utilizing adaptive dynamic surface control approach is considered based on the three channels independence design idea. A time-varying integrated guidance and control model with unmatched uncertainties is first formulated for the pitch channel, and an adaptive dynamic surface control algorithm is further developed to deal with these unmatched uncertainties. It is proved that the proposed feedback controller can ensure not only the accuracy of target interception, but also the stability of the missile dynamics. Then, the same control approach is further applied to the control design of the yaw and roll channels. The 6-degree-of-freedom （6-DOF） nonlinear missile simulation results demonstrate the feasibility and advantage of the proposed integrated guidance and control design scheme.

Global stabilizing controller design for linear time-varying systems and its application on BTT missiles

A parametric method for the gain-scheduled controller design of a linear time-varying system is given. According to the proposed scheduling method, the performance between adjacent characteristic points is preserved by the invariant eigenvalues and the gradually varying eigenvectors. A sufficient stability criterion is given by constructing a series of Lyapunov functions based on the selected discrete characteristic points. An important contribution is that it provides a simple and feasible approach for the design of gain-scheduled controllers for linear time-varying systems, which can guarantee both the global stability and the desired closed-loop performance of the resulted system. The method is applied to the design of a BTT missile autopilot and the simulation results show that the method is superior to the traditional one in sense of either global stability or system performance.

Dynamic modelling and PFL-based trajectory tracking control for underactuated cable-driven truss-like manipulator

In recent years,an innovative underactuated robot was developed,named as underactuated cable-driven trusslike manipulator(UCTM),to be suitable in aerospace applications.However,there has been strong consensus that the stabilization of planar underactuated manipulators without gravity is a great challenge since the system includes a second order nonholonomic constraint and most classical control methods are not suitable for this kind of system.Furthermore,the complexity of the truss-like structure results in tremendous difficulty of computational complicacy and high nonlinearity during dynamic modelling in addition to controller design.It is paramount to solve these difficulties for UCTM's future applications.To solve the above difficulties,this paper presents a dynamic modelling method for UCTM and a trajectory tracking control method based on partial feedback linearization(PFL)that fulfills the control goal of moving UCTM from its original position to a desired position by tracking a given trajectory of the joint angles.To achieve this,a model equivalent method is proposed to make UCTM equivalent with a three-link manipulator in the sense of dynamic behavior.Then the Lagrangian equation combined with complex vector method is proposed in the dynamic modelling process of UCTM,which simplifies the derivation procedure.Based on the established dynamic model,a coordinate transformation method is proposed to transform the control force matrix into the conventional form of an underactuated system,so that the control force can be separated from the unactuated term.The PFL method in combination with the LQR control method is then proposed to realize the targets that the joint angles can track given desired trajectory.Simulation experiments are conducted to verify the correctness and effectiveness of the proposed methods.

Disturbance Observer-Based Predictive Tracking Control of Uncertain HOFA Cyber-Physical Systems

Dear Editor,In this letter,an output tracking control problem of uncertain cyber-physical systems(CPSs)is considered in the perspective of high-order fully actuated(HOFA)system theory,where a lumped disturbance is used to denote the total uncertainties containing parameters perturbations and external disturbances.

Stabilization Controller of An Extended Chained Nonholonomic System With Disturbance:An FAS Approach

This study examines the stabilization issue of extended chained nonholonomic systems(ECNSs)with external disturbance.Unlike the existing approaches,we transform the considered system into a fully actuated system(FAS)model,simplifying the stabilizing controller design.We implement a separate controller design and propose exponential stabilization controller and finite-time stabilization controller under finite-time disturbance observer(FTDO)for the two system inputs.In addition,we discuss the specifics of global stabilization control design.Our approach demonstrates that two system states exponentially or asymptotically converge to zero under the provided switching stabilization control strategy,while all other system states converge to zero within a finite time.

Model-based predictive controller design for a class of nonlinear networked systems with communication delays and data loss

This paper discusses the model-based predictive controller design of networked nonlinear systems with communica- tion delay and data loss. Based on the analysis of the closed-loop networked predictive control systems, the model-based networked predictive control strategy can compensate for communication delay and data loss in an active way. The designed model-based predictive controller can also guarantee the stability of the closed-loop networked system. The simulation re- suits demonstrate the feasibility and efficacy of the proposed model-based predictive controller design scheme.

Tracking control for air-breathing hypersonic cruise vehicle based on tangent linearization approach

This paper is focused on developing a tracking controller for a hypersonic cruise vehicle using tangent linearization approach.The design of flight control systems for air-breathing hypersonic vehicles is a highly challenging task due to the unique characteristics of the vehicle dynamics.Motivated by recent results on tangent linearization control,the tracking control problem for the hypersonic cruise vehicle is reduced to that of a feedback stabilizing controller design for a linear time-varying system which can be accomplished by a standard design method of frozen-time control.Through a proper model transformation,it can be proven that the tracking error of the designed closed-loop system decays exponentially.Simulation studies are conducted for trimmed cruise conditions of 110000 ft and Mach 15 where the responses of the vehicle to step changes in altitude and velocity are evaluated.The effectiveness of the controller is demonstrated by simulation results.

Robust Output Feedback Control for a Class of Nonlinear Systems with Input Unmodeled Dynamics

The robust global stabilization problem of a class of uncertain nonlinear systems with input unmodeled dynamics is considered using output feedback, where the uncertain nonlinear terms satisfy a far more relaxed condition than the existing triangulartype condition. Under the assumption that the input unmodeled dynamics is minimum-phase and of relative degree zero, a dynamic output compensator is explicitly constructed based on the nonseparation principle. An example illustrates the usefulness of the proposed method.

Finite-time coordination control for formation flying spacecraft

This paper investigates a distributed coordination control scheme using an adaptive terminal sliding mode for formation flying spacecraft with coupled attitude and translational dynamics. In order to overcome the singularity of the traditional fast terminal sliding manifold, a novel fast terminal sliding manifold is given. And then, based on the adaptive control method, a continuous robust coordinated controller is designed to compensate external disturbances and to alleviate the chattering phenomenon. The theoretical analysis shows that the coordinated controller can guarantee the finite-time stability of the overall closed-loop system through local information exchange, and numerical simulations also demonstrate its effectiveness.

Robust model-reference control for descriptor linear systems subject to parameter uncertainties

Robust model-reference control for descriptor linear systems with structural parameter uncertainties is investigated. A sufficient condition for existing a model-reference zero-error asymptotic tracking controller is given. It is shown that the robust model reference control problem can be decomposed into two subproblems： a robust state feedback stabilization problem for descriptor systems subject to parameter uncertainties and a robust compensation problem. The latter aims to find three coefficient matrices which satisfy four matrix equations and simultaneously minimize the effect of the uncertainties to the tracking error. Based on a complete parametric solution to a class of generalized Sylvester matrix equations, the robust compensation problem is converted into a minimization problem with quadratic cost and linear constraints. A numerical example shows the effect of the proposed approach.

H-infinity measurement-feedback control for discrete-time systems with a single measurement delay

H-infinity control problem for linear discrete-time systems with instantaneous and delayed measurements is studied. A necessary and sufficient condition for the existence of the H-infinity controller is derived by applying reorganized innovation analysis approach in Krein space. The measurement-feedback controller is designed by performing two Riccati equations. The presented approach does not require the state augmentation.

Fractional order nonsingular terminal sliding mode control for flexible spacecraft attitude tracking

This paper investigates a fractional terminal sliding mode control for flexible spacecraft attitude tracking in the presence of inertia uncertainties and external disturbances. The controller is based on the fractional calculus and nonsingular terminal sliding mode control technique,and it guarantees the convergence of attitude tracking error in finite time rather than in the asymptotic sense. With respect to the controller,a fractional order sliding surface is given,the corresponding control scheme is proposed based on Lyapunov stability theory to guarantee the sliding condition,and the finite time stability of the whole close loop system is also proven. Finally,numerical simulations are presented to illustrate the performance of the proposed scheme.

An identity concerning controllability observability and coprimeness of linear systems and its applications

It is shown in this paper that any state space realization （A, b, c） of a given transfer function T（s） =β（s）/α（s）with α（s）monic and dim（A）=deg（α（s））,satisfies the identity β（A）=Qe（A,b）Sα Qo（A,c）where Qc （A,b）and Qo（A, c） are the controllability matrix and observability matrix of the matrix triple （A, b, c）, respectively, and S,~ is a nonsingular symmetric matrix. Such an identity gives a deep relationship between the state space description and the transfer function description of single-input single-output （SISO） linear systems. As a direct conclusion, we arrive at the well-known result that a realization of any transfer function is minimal if and only if the numerator and the denominator of the transfer function is coprime. Such a result is also extended to the SISO descriptor linear system case. As an applications, a complete solution to the commuting matrix equation AX --- XA is proposed and the minimal realization of multi-input multi-output （MIMO） linear system is considered.

Robust passive control for discrete-time T-S fuzzy systems with delays

This article deals with the robust stability analysis and passivity of uncertain discrete-time Takagi- Sugeno （T-S） fuzzy systems with time delays. The T-S fuzzy model with parametric uncertainties can approximate nonlinear uncertain systems at any precision. A sufficient condition on the existence of robust passive controller is established based on the Lyapunov stability theory. With the help of linear matrix inequality （LMI） method, robust passive controllers are designed so that the closed-loop system is robust stable and strictly passive. Furthermore, a convex optimization problem with LMI constraints is formulated to design robust passive controllers with the maximum dissipation rate. A numerical example illustrates the validity of the proposed method.

Stability analysis and controller design of T-S fuzzy systems with time-delay under imperfect premise matching

The issue of the stability and controller design of Takagi-Sugeno（T-S） fuzzy control systems with time-delay is investigated under imperfect premise matching when the T-S fuzzy time-delay model and fuzzy controller do not share the same membership functions.A new stability criterion which contains the information of membership functions is derived.The new stability criterion is less conservative,and enhances the design flexibility.Two numerical examples are presented to illustrate the conservativeness and effectiveness of the proposed method.

Robust reliable H_∞ control for a class of uncertain time-delay systems

This paper deals with the problem of robust reliable H∞ control for a class of uncertain nonlinear systems with time-varying delays and actuator failures. The uncertainties in the system are norm-bounded and time-varying. Based on Lyapunov methods, a sufficient condition on quadratic stabilization independent of delay is obtained. With the help of LMIs (linear matrix inequalities) approaches, a linear state feedback controller is designed to quadratically stabilize the given systems with a H∞ performance constraint of disturbance attenuation for all admissible uncertainties and all actuator failures occurred within the prespecified subset. A numerical example is given to demonstrate the effect of the proposed design approach.

On invariant ellipsoids for discrete-time systems by saturated optimal controls

Analytical approximation of the maximal invariant ellipsoid for discrete-time linear systems with saturated optimal control is established, which is less conservative than existing computationally un-intensive results. Simultaneously, necessary and sufficient conditions for such approximation being equal to the real maximal invariant ellipsoid is presented. All results are given analytically and can easily be implemented in practice. An illustrative example is given to show the effectiveness of the proposed approach.

Nonlinear dynamic model and control of three-axis stabilized liquid-filled spacecraft attitude system

The fuel slosh in the storage tanks affects the attitude dynamics of the liquid-filled spacecraft during orbit transferring. To describe the interactions between the fuel slosh dynamics and the spacecraft attitude dynamics, a novel nonlinear dynamic model for three-axis liquid-filled spacecraft is presented, and in this paper, the multi-body dynamics method is utilized. In this model, the fuel slosh is represented by the motions of an equivalent sphere pendulum, and the fuel slosh is underactuated. The proposed dynamics model meets the demand of attitude controller design of liquid-filled spacecraft. Then, a nonlinear proportional-plus-derivative (PD) type controller is designed for the proposed model based on the Lyapunov direct approach. This controller can suppress the fuel slosh and stabilize the attitude of the liquid-filled spacecraft. Numerical simulations are presented to verify the effectiveness of the proposed nonlinear dynamic model and the designed underactuated controller when compared with the conventional control scheme.

Robust Near-Hovering Flight Controller for Model-Scale Helicopters Via Parametric Approach

This paper aims to provide a parametric design for robust flight controller of the model-scale helicopter. The main contributions lie in two aspects. Firstly,under near-hovering condition,a procedure is presented for simplification of the highly nonlinear and under-actuated model of the model-scale helicopter. This nonlinear system is linearized around the trim values of the chosen flight mode,followed by decomposing this high-order linear model into three lower-order subsystems according to the coupling properties among channels.After decomposition,the three subsystems are obtained which include the coupling subsystem between the roll( pitch) motion and the lateral( longitudinal) motion,the subsystem of the yaw motion and the subsystem of the vertical motion. Secondly,by using eigenstructure assignment,the problem of flight controller design can be converted into solving two optimization problems and the linear robust controllers of these subsystems are designed through solving these optimization problems. Besides, this paper contrasts and analyzed the performances of the LQR controller and the parametric controller. The results demonstrate the effectiveness and the robustness against the parametric perturbations of the parametric controller.