Robust Control for Pseudo-Linear Systems
Date Issued
2015
Date
2015
Author(s)
Juang, Bin-Yih
Abstract
This dissertation proposes a robust control scheme for pseudo-linear systems with perturbed terms. The pseudo-linear systems are nonlinear systems, which are also fully feedback linearizable systems. The concept of the scheme utilizes a linear robust controller combine with a feedback linearization controller such that the closed-loop perturbed nonlinear system possess an excellent robust stability (RS) properities. In chapter 3, we elucidate a robust pole-assignment (RPA) scheme for an)interval polynomial based on positive interval Routh-table (PIRT) using a binomial coefficients feedback gain (BCFG). The robust scheme transforms the problem of RPA into the problem of solving a family of stability condition polynomials (SCP) that have positive function values. The condition for the existence of a solution, the greatest lower bound value, GLBV, is that all entries of the Routh-table of binomial coefficients (RTBC) are positive. Importantly, in this chapter, we provide an advanced general formula for the generated entries of the RTBC, confirming that all entries of RTBC are positive. An illustrative example reveals the effectiveness of the scheme. In chapter 4, we elucidate a RPA scheme for an interval polynomial that is based on the Kharitonov theorem, and uses a BCFG. The robust scheme transforms the problem of RPA into the problem of solving four families of SCP that have positive function values. The existence of a solution, GLBV, requires that all entries of the RTBC are positive. Two general formulas, which both exhibit positive property, have been proven to be mutually equivalent. This robust scheme ensures not only that the four Kharitonov polynomials are all stable, but also that their linear combinations are stable; it also guarantees the interval polynomial robust stability. An illustrative example demonstrates the effectiveness of the scheme. In chapter 5, we elucidate a robust(control for nonlinear systems that is subject to some uncertainties, using approximate feedback linearization (AFL) and a RPA controller. A close form solution of AFL is obtained; it transforms the nonlinear system into an equivalent Taylor-linearized form. A formula for transformation, quasi-similarity transformations, between the exact feedback linearization (EFL) form and the AFL is presented. The perturbed Brunovsky-linearized form is utilized to design a RPA controller. The robust controller, which combines the RPA controller, the transformation formula and the AFL controller, is applied to a perturbed nonlinear system such that the closed-loop perturbed nonlinear system exhibits RPA properties. An illustrative example reveals the robust scheme is not influenced under the limited parameter uncertainties and the equilibrium point variants with great effectiveness. Moreover, these simulation results also indicate that the robust scheme for pseudo-linear systems has larger operation region than that of the traditional robust scheme for linear systems. In chapter 6, we elucidate a robust control for nonlinear systems, which is subject to some uncertainties, using exact feedback linearization with H_∞ robust controller. A transfer formula, quasi-similarity transformations, from the AFL to the EFL is presented. Through the transfer formula, the H_∞ robust controller combining the EFL controller is applied to the perturbed nonlinear system such that the closed-loop perturbed nonlinear system has the H_∞ robust properties. An illustrative example reveals the robust scheme is not affected under the limited parameter uncertainties and the equilibrium point variants with great validity. Moreover, these simulation results also imply that the robust scheme for pseudo-linear systems has larger operation region than that of the traditional robust scheme for linear systems.
Subjects
robust pole assignment
interval polynomial
Routh-table of binomial coefficients
positive interval Routh-table
the Kharitonov theorem
Nonlinear systems
approximate feedback linearization
quasi-similarity transformations
exact feedback linearization
H_∞ robust controller.
Type
thesis
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