Abstract
We consider tracking control for multibody systems which are modeled using holonomic and non-holonomic constraints. Furthermore, the systems may be underactuated and contain kinematic loops and are thus described by a set of differential-algebraic equations that cannot be reformulated as ordinary differential equations in general. We propose a control strategy which combines a feedforward controller based on the servo-constraints approach with a feedback controller based on a recent funnel control design. As an important tool for both approaches, we present a new procedure to derive the internal dynamics of a multibody system. Furthermore, we present a feasible set of coordinates for the internal dynamics avoiding the effort involved with the computation of the Byrnes–Isidori form. The control design is demonstrated by a simulation for a nonlinear non-minimum phase multi-input, multi-output robotic manipulator with kinematic loop.
Highlights
In the present paper, we propose a combined feedforward and feedback tracking control strategy for underactuated non-minimum phase multibody systems
E) We demonstrate that the combination of the feedforward and feedback control strategies is able to achieve tracking with prescribed performance for a nonlinear, non-minimum phase robotic manipulator with kinematic loop—the controller performance of the combination is favorable compared to the individual controllers (Sect. 6)
We illustrate our findings by a robotic manipulator which is described by a differential-algebraic equations (DAEs) that cannot be reformulated as an ordinary differential equation (ODE) and, at the same time, has unstable internal dynamics
Summary
We propose a combined feedforward and feedback tracking control strategy for underactuated non-minimum phase multibody systems. Since the funnel controller presented in [39] is not feasible for nonminimum phase systems, we use an extension recently developed in [9] An important tool both in feedforward and feedback control design is the Byrnes–Isidori form, which allows a decoupling of the internal dynamics of the system. D) We present a new funnel control design for nonlinear non-minimum phase systems which only have a vector relative degree E) We demonstrate that the combination of the feedforward and feedback control strategies is able to achieve tracking with prescribed performance for a nonlinear, non-minimum phase robotic manipulator with kinematic loop (described by a DAE that cannot be reformulated as an ODE)—the controller. Performance of the combination is favorable compared to the individual controllers (Sect. 6)
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