An integrated best–worst decomposition approach of nonlinear systems using gap metric and stability margin

Abstract

This article uses gap metric method to design a multi-model controller for nonlinear systems. In order to decompose the nonlinear system into a reduced nominal local models bank as much as possible, and assure the closed-loop robust stability and performance, the decomposition and designing of local controllers are integrated. To this end, robust stability, performance, and gap metric are incorporated to build a binary distance matrix that supports defining the driving and dependence powers for each local model. Then a best–worst analysis is employed considering the driving and dependence powers to find out the nominal local models. The proposed approach screens the value of all local models to choose each nominal local model. As a result, the global multi-model controller has a simple structure and avoids the computational complexity issues. To evaluate the effectiveness of the proposed method, two highly nonlinear systems, pH neutralization and continuous stirred tank reactor process, are simulated.

Robust multi‐model controllers design without impulse in switching times for non‐linear vibrations suppression of sandwich plate

“…The closed-loop response of highly non-linear pH neutralization reactor process FIGURE 13 The manner of error signal of highly non-linear pH neutralization reactor process FIGURE 14 Step response to the nominal model with uncertainty without robust tuning and phase margin compared to the nominal tuning and, thus, a better performance.…”

“…Two important issues in using multi‐model controllers are the system close loop stability and its robust performance. The concepts of gap metric and sensitivity function are criteria for guaranteed stability and robust performance of non‐linear system [12, 13]. The desired performance is achieved by the sensitivity function in the local models [14].…”

Unsupervised optimal model bank for multiple model control systems: Genetic-based automatic clustering approach

“…The representative models should be able to describe the behavior of the system in their associated entire subspace. The MMC approach offers many advantages, including the ability to describe and control complex systems [ 5 ], the ability to be used in a wide range of industrial or switched systems [ 6 ], and the ability to use different classical control methods in its scheme [ 7 ]. However, it should be noted that all the mentioned advantages will be achieved only when the behavior of a complex system could be well described by the considered model bank [ 8 ].…”

Linear controller design approach for nonlinear systems by integrating gap metric and stability margin

“…Therefore, before any attempts at the use of a nonlinear controller, it is often beneficial to verify the adequacy of classical linear control techniques, especially since they have proved to be sufficient for the control of various nonlinear systems. [1][2][3][4] Consequently, there is a need to check the restrictions of linear control performance and quantify the nonlinearity level of a process to determine whether linear control could be sufficient or nonlinear control would be indispensable.…”