Robust Control Applied to Multiple-Input Multiple-Output Nonlinear Systems
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Robust Control Applied to Multiple-Input Multiple-Output Nonlinear Systems Samaherni Dias · Kurios Queiroz · Aldayr Araujo
Received: 20 December 2013 / Revised: 6 August 2014 / Accepted: 23 August 2014 © Brazilian Society for Automatics–SBA 2014
Abstract Many of practical systems (for example: robotic systems, power systems and electronic circuits) are multipleinput multiple-output nonlinear systems and some of them have coupling between inputs and outputs. Besides all that, these systems can suffer with parametric uncertainties and external disturbances. Any control techniques applied to these systems are complex. This work presents a control structure, based on the union between a modified version of the variable structure model reference adaptive control and a left-inverse decoupling technique, to transform a multipleinput multiple output nonlinear system into a set of singleinput single-output linear systems. In that case each input affects only one output and with a desired closed-loop performance. The proposed structure transforms the variable structure model reference adaptive control, which is usually applied to single-input single-output linear systems, into a controller to be applied to a class of multiple-input multipleoutput nonlinear systems. It is important to note that proposed structure, using only input/output measurements, presents fast transient performance, reduces the output “chattering” and it is robust to parametric uncertainties and disturbances. All these features are verified by simulation results of an electronic circuit that exhibits chaotic behavior (Chua’s circuit).
S. Dias (B) · K. Queiroz · A. Araujo Laboratory of Automation, Control and Instrumentation (LACI), Department of Electrical Engineering, Federal University of Rio Grande do Norte, Natal, RN, Brazil e-mail: [email protected]; [email protected] K. Queiroz e-mail: [email protected] A. Araujo e-mail: [email protected]
Keywords Robust control · Model reference adaptive control · Variable structure control · Decoupled subsystems · Chattering
1 Introduction Nowadays, there has been an increasing interest in applying control techniques for industrial processes. However, many of these processes are multiple-input multiple-output (MIMO) nonlinear systems and some of them have coupling between inputs and outputs. Besides all that, these systems can suffer with parametric uncertainties and external disturbances. Any control techniques applied to these systems are complex. This work, in simplified form, proposes to control a MIMO nonlinear system using a decoupling technique associated with an adaptive control law. Some works in this area can be highlighted for their contributions, such as Hirschorn (1979), in which Hirschorn proved the sufficient condition of the leftinverse existence for a class of nonlinear systems (minimum phase system). In Singh (1981), the algorithm of constructing inverse system proposed by Hirschorn was modified and gave a new invertibility condition for a class of systems, which do not satisfy Hirschorn’
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