Numerical recipes: the art of scientific computing
Numerical recipes: the art of scientific computing
Stochastic optimal control: theory and application
Stochastic optimal control: theory and application
Nonlinear systems analysis (2nd ed.)
Nonlinear systems analysis (2nd ed.)
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This paper provides a core of APL algorithms for control system development and demonstrates their use by solving a typical control problem. In doing so it outlines useful numerical techniques for simulating dynamic systems and for solving some of the central equations of control theory.Although some sections of the paper are addressed to APL2 users, the majority of the paper applies to APL. Moreover, by doing a little extra work to handle complex numbers and by installing a “callable” compiled eigenvalue-eigenvector routine, all of the material presented can be adapted to any APL system.While APL is a comfortable environment for control system development, APL2 contains two especially useful enhancements: 1) complex numbers included in a natural way, and 2) the function EIGEN.APL2's facility with complex numbers permits the direct and clear coding of frequency domain methods such as root locus, bode plots, and the generation of transfer functions. APL2's facility with complex numbers also makes it possible to include a native eigenvalue-eigenvector utility function, EIGEN. This function generates the eigenvalues and eigenvectors of general square matrices, which can then be used for root locus studies, for transforming system equations to canonical forms, and for efficiently solving the Riccati and Lyapunov equations.Non-EIGEN-based functions are also provided so that all APL users will find enough tools to model, simulate, analyze, and develop regulators, observers, and filters for linear dynamic systems.