Adaptive Predictive Functional Control of X-Y Pedestal for LEO Satellite Tracking Using Laguerre Functions

In this paper, Predictive Functional Control (PFC) is used for X-Y pedestal control for LEO satellite tracking. According to the nonlinear characteristics of the X-Y pedestal and pedestal model variation caused by its operating point change, the use of system identification algorithm, which is based on special types of orthonormal functions known as Laguerre functions, is presented. This algorithm is combined with PFC to obtain a novel adaptive control algorithm entitled Adaptive Predictive Functional Control (APFC). In this combination, Laguerre functions are utilized for system identification, while the PFC is the control law. An interesting feature of the proposed algorithm is its desirable performance against the interference effect of channel X and channel Y. The proposed APFC algorithm is compared with Proportional Integral Derivative (PID) controller using simulation results. The results confirm that the proposed controller improves the performance in terms of the pedestal model variations; that is, the controller is capable of adapting to the model changes desirably.

Fractional Generalizations of Rodrigues-Type Formulas for Laguerre Functions in Function Spaces

Generalized Laguerre polynomials, Ln(α), verify the well-known Rodrigues’ formula. Using Weyl and Riemann–Liouville fractional calculi, we present several fractional generalizations of Rodrigues’ formula for generalized Laguerre functions and polynomials. As a consequence, we give a new addition formula and an integral representation for these polynomials. Finally, we introduce a new family of fractional Lebesgue spaces and show that some of these special functions belong to them.

Controller Design Using Laguerre Functions

<div> <div> <div> <p>This paper presents a technique for designing controllers for rational plants using Laguerre functions. The inputs to the process are the a) the plant transfer function P(s), b) the target transfer function T(s) and c) the desired order of the controller. Future work will extend this process so it is applicable to 1) irrational continuous time plants and 2) to irrational discrete time plants. </p> </div> </div> </div>

Controller Design Using Laguerre Functions

<div> <div> <div> <p>This paper presents a technique for designing controllers for rational plants using Laguerre functions. The inputs to the process are the a) the plant transfer function P(s), b) the target transfer function T(s) and c) the desired order of the controller. Future work will extend this process so it is applicable to 1) irrational continuous time plants and 2) to irrational discrete time plants. </p> </div> </div> </div>