Abstract
The design and tuning of a simple feedback strategy with delay to stabilize a class of underactuated mechanical systems with dead time are presented. A linear time-invariant (LTI) model with time delay of fourth order and a Proportional Retarded (PR) controller are considered. The PR controller is shown as an appealing alternative to the application of observer-based controllers. This paper gives a step forward to obtain a better understanding of the effect of output delays and related phenomena in mechatronic systems, making it possible to design resilient control laws under the presence of uncertain time delays in measurements and obtain an acceptable performance without using a derivative action. The Furuta pendulum is a standard two-degrees-of-freedom benchmark example from the class of underactuated mechanical systems. The configuration under study includes an inherent output delay due to wireless communication used to transmit measurements of the pendulum’s angular position. Our approach offers a constructive design and a procedure based on a combination of root loci and Mikhailov methods for the analysis of stability. Experiments over a laboratory platform are reported and a comparison with a standard linear state feedback control law shows the advantages of the proposed scheme.
Highlights
Underactuated mechatronic systems have been a subject of intensive research during the past three decades, where partial feedback linearization, normal forms, and energybased methods have offered successful results as well as breakthrough paradigms [1,2,3,4,5,6,7,8,9]
Quantization errors of encoders, and errors of the wireless communication make the design of a robust control law difficult
The design and stability analysis of a Proportional Retarded (PR) action-based controller for stabilization of the Furuta pendulum under the presence of time delays in measurements is introduced in this work
Summary
Underactuated mechatronic systems have been a subject of intensive research during the past three decades, where partial feedback linearization, normal forms, and energybased methods have offered successful results as well as breakthrough paradigms [1,2,3,4,5,6,7,8,9]. When the sensor signals are transmitted through a wireless network, the time-delay phenomena are unavoidable, representing an important as well as an open challenge [11,12,13]. It is of relevance to understand the effect of time delays in measurements as well as the potential of such delays as a second degree of freedom for control design (see [16, 17]). For this aim, a PR controller design will be presented together with the Mikhailov stability approach.
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