Abstract
This paper proposes an extension to the established loop-shaping method, where the loop-shaping method is modeled mathematically and solved as a mathematical optimization program. In this process, a novel cost function is proposed and employed as the objective of optimization in the controller tuning problem. This cost function evaluates different characteristics of the system in the frequency domain, such as the stability margins and the operability bandwidth. These characteristics reflect the quality of load disturbance rejection, set-point tracking, and operability bandwidth of the control system. Consequently, the proposed technique circumvents running a time-domain simulation completely. More importantly, the proposed technique can be used with any controller structure. The generic cost function can be customized to fit any control objective and application. This is conducted in the second half of this paper, with the aim of obtaining a system with near-optimum time-domain performance with respect to the integral of time times absolute error (ITAE) criterion. At the same time, the control system obtained with the customized cost function has better operability bandwidth than that of a system optimized in the time-domain for the ITAE criterion. The proposed optimization model is analyzed for two plant models: first order and second order plus dead-time (FOPDT), (SOPDT), respectively.
Highlights
This paper follows the timeline of the development of an analytical tool for optimization of controllers in the frequency domain
The mathematical model is used in an optimization program
The analysis starts with systems having first order and second order plus dead-time (FOPDT) plant models
Summary
CONTROLLER DESIGN TECHNIQUES Time-integral criteria were proposed as performance indicators for controller tuning in the 1970’s by [1]. One of these criteria is the integral of time and absolute error (ITAE). Control systems whose time-integral can be evaluated mathematically are very few. These performance indicators require a time-domain simulation which is computationally intensive and not time-efficient. Simulation times for complex systems increase drastically. Evaluation of a system’s frequency response is much more efficient, does not guarantee the fulfillment of important time-domain criteria. Other performance indicators exist, such as: controller effort, system sensitivity, and disturbance rejection [2], [3]
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