On the Design of Robust Four Degree of Freedom Controllers for Linear Discrete-Time Systems

• Published in: IEEE access 2023-01, Vol.11, p.1-1
• Main Authors: Murad, Ghassan, Mattar, Ebrahim
• Format: Article
• Language: English
• Subjects: <italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">H <sup xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">2 and <italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">H <sup xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">∞ control and diagnostics; Actuator failure; Actuators; Controllers; Degrees of freedom; Design engineering; Diagnostic systems; Discrete time systems; Distillation; Fault detection; four degree-of-freedom controller; H² and H∞ control and diagnostics; integrated controls and diagnostics design; Integrated design; model-matching; normalized coprime factors; Optimization; Perturbation; Regulators; Robust control; Robust design; Robust stability; robust stability and robust performance; Uncertainty
• ISSN: 2169-3536; 2169-3536
• DOI: 10.1109/ACCESS.2023.3307569

The aim of this paper is to consider an alternative robust design method of integrated controls and diagnostics by making use of the so-called four degree-of-freedom (4-DOF) controller. This controller has 2-inputs and 2-outputs whereby the additional controller output is viewed as a diagnostic output which detects sensor and actuator failures. The 4-DOF controller is a simple case of the standard regulator framework; therefore, the design of integrated controls and diagnostics can thus be done in the framework of H 2 and H ∞ whereby the latter gives the advantage of synthesizing the 4-DOF controller in a single step approach. Unlike previous methods, explicit state-space formulae are derived (in discrete-time) for a 4-DOF controller. For the H ∞ case it stabilizes an augmented plant with respect to unstructured additive coprime factor perturbations whilst simultaneously providing robust control and diagnostic performance when uncertain plants are used. Moreover, the 4-DOF H ∞ controller derived (albeit, of adequate complexity that can be further reduced using model/controller reduction techniques) is applied to a distillation system example to illustrate the effectiveness of the proposed unified framework.