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Genetic-Based Fuzzy Logic Controller for Satellites Stabilized by Reaction Wheels and Gravity Gradient. Hanafy M. Omar Aerospace Department King Fahd University of Petroleum and Minerals Saudi Arabia. Outline. Introduction and Objective Satellite Dynamics Controller Design
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Genetic-Based Fuzzy Logic Controller for Satellites Stabilized by Reaction Wheels and Gravity Gradient Hanafy M. Omar Aerospace Department King Fahd University of Petroleum and Minerals Saudi Arabia
Outline • Introduction and Objective • Satellite Dynamics • Controller Design • Formulation of the Optimization Problem • Genetic Algorithms Code • Simulation Results • Conclusion • Future Work
Introduction • The satellite carries on board different equipment for remote sensing and telemetry which needs to be precisely pointed to the earth. • The satellite may receive an impulsive torque from any particles moving in the space which results in deviation of the satellite from its attitude. • This deviation will result in a poor imaging and communications with the ground stations. • An attitude control must used to return the satellite back to its orientation
Introduction • Most of the current satellite attitude control systems use reaction because they give high pointing accuracy. • Unfortunately, these wheels are internal torquers and they don not change the total momentum of the satellite; they only transfer the momentum from the satellite to the wheels. • Therefore, they are needed to be desaturated by an external torquer.
Introduction • In this work, we chose the gravity gradient as the external torquer which is produced from the gravitational field of the earth. • This torque decreases as the altitude increases, and increases with the increase of the moment of inertial of the satellite. • Hence, to increase the effectiveness of the gravity gradient, a boom with long length is usually used
Motivation • The fuzzy logic control (FLC) is a rule-based controller that is known of its robustness and , suitability for handling linear and non-linear models. • The core of FLC is the rules, which determine the relation between the inputs and the output, usually the FLC rules are obtained by mapping the performance of a skillful operator. The generated rules from this method is not available in satellite operations. • Engineering experience or self organizing FLC can be used for generating the rules but it is not necessarily to be optimum. • The same problem is encountered also in the determination of the distribution of membership functions.
Objective • In this paper, a systematic technique is proposed to design an optimal FLC for controlling the attitude of a satellite stabilized by reaction wheels in the presence of the gravity gradient. • The FLC rules and the distribution of the membership functions parameters are determined by solving an optimization problem using the Genetic Algorithms (GA) technique.
Satellite Dynamics The normalized equations of motion of the satellite with a reaction wheel in the presence of the gravity gradient can be written as
Equations Of MotionPitch where is the normalized liberation period is the ratio of moment of inertia of the wheel w.r.t. the satellite moment of inertia
Equations Of MotionRoll/Yaw where is the normalized orbital speed of the satellite
Controller Design • Choose the number and distribution of membership functions (MF's) for the inputs and the output variables. Constraints Or
Controller Design • Choosing the scaling factors Since the ranges of the membership functions are normalized, scaling factors are used to transform these normalized ranges to the physical operating ranges • Generating the Fuzzy rules and the distribution of the membership functions of the fuzzy inputs an the fuzzy output by solving an optimization problem using Genetic Algorithms (GA)
Formulation of the Optimization Problem • Let The optimization problem can be formulated as Subjected to
Penalty Function The augmented optimization function will be
Genetic Algorithms • Genetic algorithms (GA) are stochastic search algorithms based on the mechanics of natural selection and survival-of-the-fittest. • GAs operate on a population of potential solutions applying the principle of survival of the fittest to produce better and better approximations to a solution. • At each generation, a new set of approximations is created by the process of selecting individuals according to their level of fitness in the problem domain then apply some operations on them that borrowed from natural genetics (i.e. Crossover and Mutation).
Advantages of GA • GA optimize a performance index based on input/output relationships only. • Therefore, derivative information is not needed in the execution of the algorithm and hence many pitfalls that gradient search methods suffer can be overcome especially for dynamic systems.
Structure of the GA individual The encoding system for the FLC output
Genetic Algorithm The values used for the GA parameters are: • Population size: 50 (randomly generated) • Crossover rate: 0.7 • Mutation Rate: 0.01
Initial Conditions • If a single initial condition is used to determine the objective function, GA can produce a controller that works well around this operating condition while it may fail elsewhere. • To be able to find a controller with a satisfactory performance which operates over the entire range of the input spaces, we choose multiple initial condition which are a combination of (max, qmax, 0) • In this case, the total value of the objective function is the sum of the objective functions from all the initial conditions
Stability Analysis • To make sure that the designed controller is stable over the whole operating conditions, another large set of initial conditions, which is different from that one used in the training process, is tested. • It is found that the designed controller was able to damp all the disturbances • Therefore, the satellite system is stable with the designed controller in a broad range of operating conditions.
Objective and Penalty Functionsfor Roll/Yaw Motion Objective Function Penalty Function
Simulation Results The following data are used for in the simulations Satellite Dynamics Pitch Motion Roll/Yaw Motion
Conclusion • A GA code was developed to design an optimal FLC, which includes the generation of the controller rules and the distribution of its membership functions. • Without any prior knowledge of the rules or the distribution of membership function, the developed code was able to generate a fuzzy controller with a satisfactory performance. • With the use of multiple initial conditions in determining the objective function, the designed controller ha an acceptable performance in a broad range of the satellite operating conditions.
Suggestions and Future Work • GA requires heavy computations to able to get the large number of the FLC parameters. The micro-genetic algorithm may be a good candidate to overcome this problem. • Another difficulty in the optimization is the choice of the optimization function and its parameters, which still depends on the engineering experience. This difficulty may be resolved using the multi-objectives technique.
