Sampling Rate Optimization and Execution Time Analysis for Two-Degrees-of-Freedom Control Systems

Abstract

The current journal paper proposes an end-to-end analysis for the numerical implementation of a two-degrees-of-freedom (2DOF) control structure, starting from the sampling rate selection mechanism via a quasi-optimal manner, along with the estimation of the worst-case execution time (WCET) for the specified controller. For the sampling rate selection, the classical Shannon–Nyquist sampling theorem is replaced by an optimization problem that encompasses the trade-off between the fidelity of the controllers’ representation, along with the fidelity of the resulting closed-loop systems, and the implementation difficulty of the controllers. Additionally, the WCET analysis can be seen as a verification step before automatic code generation, a computational model being provided. The proposed computational model encompasses infinite-impulse response (IIR) and finite-impulse response (FIR) filter models for the controller implementation, along with additional relevant phenomena being discussed, such as saturation, signal scaling and anti-windup techniques. All proposed results will be illustrated on a DC motor benchmark control problem.

Sampling rate selection for multi‐loop cascade control systems in an optimal manner

“…However, in order to compute the integral terms from  , in a similar manner with the single-loop case, a set Ω = {𝜔 = 𝜔 1 < 𝜔 2 < ⋯ < 𝜔 N − 𝜔 𝜀 = 𝜔} can be considered, while the similarity performance index being approximated as in (27). Moreover, a sufficiently large value 𝛼 ∞ is mandatory as in (28) such that the stability functional manages to keep the role of determining the feasibility subdomain of , leading to the following approximation of the original performance index:…”

“…This work is an extension of the conference paper from [27], with the results reiterated for a worst-case execution time analysis in [28], and it has the following improvements and modifications for the current paper:…”

“…This work is an extension of the conference paper from [27], with the results reiterated for a worst‐case execution time analysis in [28], and it has the following improvements and modifications for the current paper: (a)the optimization problem is posed in a multi‐rate context, with the direct applicability in MIMO cascade control structures, while in our previous work only the single loop control structure has been considered for the single‐input and single‐output (SISO) case only; (b)the proposed functionals are extended to the multi‐input and multi‐output case by quantifying the magnitude using the singular values of the system; (c)a mixed‐integer artificial bee colony algorithm is designed and implemented for solving the described non‐convex optimization problems instead of using a simple linesearch algorithm; (d)a comparison is performed to the well‐established approaches for sampling rate selection based on a number of variations on the Shannon‐Nyquist theorem, along with variations on the closed‐loop bandwidth approach; (e)a two‐dimensional representation of the global functional is portrayed, with intuitive means of distinguishing clusters of solutions, which reveals the non‐convex nature of the resulting optimization problem and marks the differences towards available approaches. …”