Satellite Attitude Control Problem Research Articles

Satellite attitude control using optimal adaptive and fuzzy controllers

In this paper, a comparison between optimal adaptive and fuzzy control methods is performed for the problem of satellite attitude control. The optimal adaptive controller is designed based on Markov parameters, which can be utilized to follow a given control command. The fuzzy controller is shown to achieve faster response than the optimal adaptive controller. Moreover, the problem of satellite attitude control using the adaptive controller with on–off thrusters is studied. Simulation results affirm that the adaptive control method with on–off thrusters is robust against the variations in the inertia matrix and that the optimal adaptive control method is robust against constant disturbances.

The Adaptive Dynamic Programming Toolbox.

The paper develops the adaptive dynamic programming toolbox (ADPT), which is a MATLAB-based software package and computationally solves optimal control problems for continuous-time control-affine systems. The ADPT produces approximate optimal feedback controls by employing the adaptive dynamic programming technique and solving the Hamilton–Jacobi–Bellman equation approximately. A novel implementation method is derived to optimize the memory consumption by the ADPT throughout its execution. The ADPT supports two working modes: model-based mode and model-free mode. In the former mode, the ADPT computes optimal feedback controls provided the system dynamics. In the latter mode, optimal feedback controls are generated from the measurements of system trajectories, without the requirement of knowledge of the system model. Multiple setting options are provided in the ADPT, such that various customized circumstances can be accommodated. Compared to other popular software toolboxes for optimal control, the ADPT features computational precision and time efficiency, which is illustrated with its applications to a highly non-linear satellite attitude control problem.

A fractional-order sliding mode control for nominal and underactuated satellite attitude controls

Sliding mode control (SMC) is widely used in many existing nonlinear control solutions due to its capability against external disturbances and uncertainties, while the fractional order control (FOC) is employed as it can further enhance the control performance due to its robustness. This paper attempts to implement a fractional-order sliding mode control (FOSMC) for a small satellite with reaction wheels (RWs). In this work, a conventional SMC was initially designed to cope with the uncertainties of satellite attitude dynamics. In order to improve the attitude control performance, the FOSMC was designed accordingly and the classical chattering problem was alleviated by using the hyperbolic tangent function. This current work is the maiden work on FOSMC especially for small satellites using RWs. The FOSMC was also tested for a satellite with only two functional RWs, in which the control allocation technique is proposed to solve the underactuated satellite attitude control problem. Since the angular momentum of the reaction wheel will become saturated over time, it will be managed using the momentum unloading technique with the unique fuzzy proportional-integral (FPI) control. All control algorithms were numerically treated and analysed. The results show that the FOSMC is effective in achieving the overall desired attitude control performance for nominal and underactuated satellites.

Robust adaptive magnetic control of satellites with uncertain parameters

Recently developed results for direct adaptive control design in the context of uncertain systems in descriptor form are discussed and applied to a satellite attitude control problem. Thanks to descriptor model handling the methodology allows to address with convexity arguments uncertainties on the inertia matrix. The design of the adaptive law is done with semi-definite programming tools (LMI solvers) and is applicable with the sole knowledge of a controller stabilizing the nominal system (no passivity assumptions). The tackled satellite model is linear (assuming small pointing errors), full 3D rotations are considered (axes are coupled), and mixed reaction wheel and magnetotorquer actuation is adopted. Compared to the provided initial LTI control law, adaptive control increases robustness margins by a factor 262%.

On stability and stabilization of periodic discrete-time systems with an application to satellite attitude control

An alternative stability analysis theorem for nonlinear periodic discrete-time systems is presented. The developed theorem offers a trade-off between conservatism and complexity of the corresponding stability test. In addition, it yields a tractable stabilizing controller synthesis method for linear periodic discrete-time systems subject to polytopic state and input constraints. It is proven that in this setting, the proposed synthesis method is strictly less conservative than available tractable synthesis methods. The application of the derived method to the satellite attitude control problem results in a large region of attraction.

Attitude Control of Chaotic Satellite with Unknown Input and uncertainties based on Sliding Control

attitude control of missiles, spacecraft and satellites is essential; in order to remain them fixed in space to perform their missions accurately. The attitude equation of a satellite is a six- dimensional nonlinear system which includes some types of nonlinear behavior such as periodic trajectory, chaotic dynamics. In this paper, a sliding mode control design method for stabilization of the attitude chaotic satellites with unknown inputs and uncertainties. Using Lyapunov theory, the stability control system is proven. Simulation results show that the proposed controller can be chaotic satellite attitude in the presence of unknown inputs and uncertainties will converge to the unstable equilibrium points. In this section, the satellite system and the chaotic dynamics are studied. In (16) the problem of satellite attitude control with redundant thrusters, and in (17) satellite attitude control with an uneven inertia distribution has been investigated. However, given that the satellite attitude motion under external disturbances becomes chaotic mode, the control satellite system will be very complex. So, be very careful satellite control system is designed. In (13) and (14) satellite attitude control of chaotic behavior has been investigated. The orientation of the satellite at a given point can be locally described in terms of three angles

Satellite Attitude Control Using Analytical Solutions to Approximations of the Hamilton-Jacobi Equation

The solution to the Hamilton-Jacobi equation associated with the nonlinear ℋ∞ control problem is approximated using a Taylor series expansion. A recently developed analytical solution method is used for the second-, third-, and fourth-order terms. The proposed controller synthesis method is applied to the problem of satellite attitude control with attitude parameterization accomplished using the modified Rodrigues parameters and their associated shadow set. This leads to kinematical relations that are polynomial in the modified Rodrigues parameters and the angular velocity components. The proposed control method is compared with existing methods from the literature through numerical simulations. Disturbance rejection properties are compared by including the gravity-gradient and geomagnetic disturbance torques. Controller robustness is also compared by including unmodeled first- and second-order actuator dynamics, as well as actuation time delays in the simulation model. Moreover, the gap metric distance induced by the unmodeled actuator dynamics is calculated for the linearized system. The results indicated that a linear controller performs almost as well as those obtained using higher-order solutions for the Hamilton-Jacobi equation and the controller dynamics.

Decentralized Robust Adaptive Control for Attitude Synchronization Under Directed Communication Topology

T HE need to maintain accurate relative orientation between spacecraft is critical in many satellite formation missions. For instance, in interferometry application, the relative orientation between spacecraft in a formation is required to be maintained precisely during formation maneuvers. In interspacecraft laser communication operation, the participating spacecraft are also required to maintain accurate relative attitude throughout the communication process. This control problem, commonly referred to as attitude synchronization in the literature, has attracted much research attention. Various solutions have been proposed and these can be broadly classified according to the advocated techniques: leader– follower [1–4], virtual structure [5,6], behavior-based [7–11], and graph-theoretical approach [12–15]. In particular, the graph-theoretical approach has been actively studied for cooperative control of multi-agent system using limited local interaction [16,17] and was adopted for attitude synchronization problem in [12–15]. In the above-cited decentralized attitude synchronization results, except [14,15], it is assumed that the interspacecraft communication links are undirected (i.e. bidirectional). However, in practice, the interspacecraft communication topology may be restricted to be directed, such as in unidirectional satellite laser communication system. The control problem of attitude synchronization under directed communication topology is more challenging as compared with the case with undirected communication topology. This issue was studied in [14] but the proposed control law requires derivative of the angular velocity, which may introduce additional noise into the system. Furthermore, the attitude-tracking performance analysis in [14] is applicable only to the casewhere the directed graph can be simplified to a graph with only one node. This constraint on communication topology is relaxed in [15], which uses modified Rodriguez parameters and Euler– Lagrange system to describe the satellite attitude dynamics. However,modifiedRodriguez parameters contain singularity and are thus not suitable for the development of globally stabilizing control algorithms. This Note proposes a decentralized adaptive sliding-mode control lawwhich regulates attitude and angular velocity errors of individual spacecraft with respect to reference commands and minimizes relative attitude and angular velocity errors between spacecraft. Thus, the proposed control law ensures that each spacecraft attains desired time-varying attitude and angular velocity while maintaining attitude synchronization with other spacecraft in the formation even in the presence of model uncertainties and external disturbances. Moreover, the design is applicable to general communication topology and is not restricted to ring topology or undirected communication topology. In the following section, unit quaternion representation will be introduced into the satellite attitude control problem and algebraic graph theory will be applied to describe general directed communication topology.

Efficient offline model predictive control of constrained nonlinear periodic systems

We propose an offline model predictive control approach for nonlinear periodically time-varying systems subject to state and input constraints. Under the assumption that the nonlinear system can be approximated using a periodic linear differential inclusion, we offline calculate a set of ellipsoids and associated feedback matrices by the solution of a semi-definite program. Online, the smallest ellipsoid containing the current state is determined, and the corresponding control law is applied to the system. The approach relaxes the conditions of existing approaches applicable to the considered system class. The effectiveness of the proposed controller is demonstrated by its application to a magnetic satellite attitude control problem.

An almost disturbance decoupling solution of the attitude control problem

PurposeThe purpose of this paper is to derive a robust nonlinear attitude control law intended for practical application.Design/methodology/approachThe method of input/output feedback linearization is utilized for having a linear model and a recently developed almost disturbance decoupling (ADD) approach is adopted for designing a robust satellite attitude control (SAC) system. The kinematics of the satellite is modeled by modified Rodriguez parameters because of their continuous invertibility. The design is simulated on the model of a realistic satellite project (BILSAT‐I), which is developed by the Turkish Scientific and Technological Research Council.FindingsThe torque requirement of the operation does not exceed the maximum limit provided by the actuator. The square error levels are staying under the boundary of final global attractor, which is one of the important proofs for the successful operation of the generated ADD control law.Originality/valueThe ADD concept is investigated on SAC problem. By that way, simple control structures with known disturbance attenuation capability can be designed.

Parameter robust control design using bimatrix co-evolution algorithms

The parameter robust controller design problem is often expressed as a game between the controller and uncertain parameters. The game is expressed as a constrained minimax problem if design requirements are treated as the constraints, but the saddle-point solution of the constrained minimax problem is difficult to obtain by using conventional methods. This paper proposes a new method of designing parameter robust controllers by introducing a bimatrix co-evolution algorithm which solves the constrained minimax problem. The proposed algorithm approximates the problem as a bimatrix game between two groups having independent fitness measures and finds the saddle-point solution through successive bimatrix games. The resulting controller guarantees robustness against bounded parameter uncertainties and satisfies the design requirements. The performance of the proposed algorithm is verified by its application to a satellite attitude control problem.

The control of higher dimensional chaos: comparative results for the chaotic satellite attitude control problem

Using simulations this paper reports the success and failure of three experiments each using a different technique to control the same higher dimensional chaotic system. The three techniques are: a simple delayed feedback control method originally suggested by Pyragas, the Otani–Jones technique, and a higher dimensional variation of the OGY method. The three methods are applied to a six-dimensional system which describes the attitude dynamics of a satellite (rigid body) subjected to deterministic external perturbations which induce chaotic motion when no control is effected. The attitude of the satellite is controlled by three orthogonal pairs of thrusters aligned with the principal axes and the system can be described by a modified set of Euler equations. The three control methods are compared in terms of the prior calculations required, the real-time computational requirements, and the effectiveness of the method in stabilizing the system. The results show that the method of Pyragas compares very favourably with the other two techniques, requiring no prior calculation and having a very low real-time computational overhead. Pyragas’ method also provides the most satisfactory control solution. The problems in presenting a theoretical justification of Pyragas’ method are briefly discussed and the connection between the method and a recent technique for the location of unstable fixed points in chaotic systems is highlighted.

Genetic programming for prediction and control

The relatively ‘new’ field of genetic programming has received a lot of attention during the last few years. This is because of its potential for generating functions which are able to solve specific problems. This paper begins with an extensive overview of the field, highlighting its power and limitations and providing practical tips and techniques for the successful application of genetic programming in general domains. Following this, emphasis is placed on the application of genetic programming to prediction and control. These two domains are of extreme importance in many disciplines. Results are presented for an oral cancer prediction task and a satellite attitude control problem. Finally, the paper discusses how the convergence of genetic programming can be significantly speeded up through bulk synchronous model parallelisation.

Satellite attitude control via sliding mode with perturbation estimation

The conventional sliding-mode control (SMC) technique requires that the perturbation upperbounds are known a priori to achieve a robust control process. This requirement creates some difficulties, at the least causing the controller to be over-conservative. A recently introduced sliding mode control with perturbation estimation (SMCPE) philosophy removes this condition and replaces it with a continuous perturbation estimation process. It is shown that, for precise state measurements and high-speed control-loop closures, SMCPE manifests much smaller tracking errors than those of SMC. So far nonlinear systems in canonical form have been studied, and in the present paper the domain of application of SMCPE is extended to a more general class. For this extension, an I/O linearisation technique is utilised first, and then the SMCPE steps are followed for an output tracking control. Simulation results prove the strength of the technique for a satellite attitude control problem.

An interactive algorithm for optimal control of a system with multiple criteria

An interactive approach is proposed for the optimization of deterministic systems with multiple criteria. This approach does not require an explicit knowledge of the decision maker's utility function, but it is assumed that the decision maker can provide local information about this function at each interation The use of this interactive approach is then illustrated by applying it to the satellite attitude control problem and results are presented

On the use of optimization theory for practical control system design

The approach to control system design discussed in this paper has as its purpose the more effective utilization of optimal control theory for the development and the evaluation of practical system designs. Rather than specifying initially a single performance index (or an arbitrary scalar function of several indices), the performance bounds relating the various competing performance requirements of the system are first evaluated using optimization techniques, so that the ultimate trade offs achievable between these requirements are well understood. These performance bounds then form the basis not only for a more meaningful specification of optimum system performance, but also for the evaluation of sub-optimal designs which are developed from approximations of the optimal control strategies, from previous designs, and from the experience and insight of the designer. The specific example of the satellite attitude control problem is used to illustrate this design approach. Performance bounds between control fuel expenditure and control time are obtained over a range of initial conditions. Using this information and the knowledge of the form of the minimum-fuel control law, a simple feedback control design is developed which is superior to either the well-known minimum-time or the minimum-fuel solutions, both from the point of view of achieving on-the-bound performance which represents the best compromise between these competing performance requirements and from the point of view of practical implementation. The final portion of the paper describes the computer-aided design program which has been undertaken to extend this design approach to more complex control problems.