On the construction of static stabilizers and static output trackers for dynamically linearizable systems, related results and applications

Rodríguez, H.; Astolfi, Alessandro; Ortega, Roméo

doi:10.1080/00207170600849766

Cited by 22 publications

(18 citation statements)

References 14 publications

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“…Proof of (30): We note first the following chain of implications: (32) where we have replaced the expression of obtained in the fourth implication into the second one to get the last equation. Integrating the last equation in (32) we get the first algebraic equations that constrain the residual dynamics (33) where is a constant vector, with . 9 Computing the gradient of from (25) we get where we have used the fact that to get -a constant vector.…”

Section: Main Stabilization Resultsmentioning

confidence: 99%

Interconnection and damping assignment passivity-based control of mechanical systems with underactuation degree one

Acosta

Ortega

Astolfi

et al. 2005

IEEE Trans. Automat. Contr.

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271

104

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Abstract-Interconnection and damping assignment passivity-based control is a new controller design methodology developed for (asymptotic) stabilization of nonlinear systems that does not rely on, sometimes unnatural and technique-driven, linearization or decoupling procedures but instead endows the closed-loop system with a Hamiltonian structure with a desired energy function-that qualifies as Lyapunov function for the desired equilibrium. The assignable energy functions are characterized by a set of partial differential equations that must be solved to determine the control law. We prove in this paper that for a class of mechanical systems with underactuation degree one the partial differential equations can be explicitly solved. Furthermore, we introduce a suitable parametrization of assignable energy functions that provides the designer with a handle to address transient performance and robustness issues. Finally, we develop a speed estimator that allows the implementation of position-feedback controllers. The new result is applied to obtain an (almost) globally stabilizing scheme for the vertical takeoff and landing aircraft with strong input coupling, and a controller for the pendulum in a cart that can swing-up the pendulum from any position in the upper half plane and stop the cart at any desired location. In both cases we obtain very simple and intuitive position-feedback solutions.

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Section: Main Stabilization Resultsmentioning

confidence: 99%

Interconnection and damping assignment passivity-based control of mechanical systems with underactuation degree one

Acosta

Ortega

Astolfi

et al. 2005

IEEE Trans. Automat. Contr.

Self Cite

271

104

View full text Add to dashboard Cite

show abstract

“…Following [11], we could use a dynamic extension to get a decoupling matrix of the full range. However, a different approach based on [16] is now proposed. For doing this, one defines T MR as…”

Section: Control Strategymentioning

confidence: 99%

“…Let us consider the reduced model (16). This system is a differentially flat system in accordance to [11] and the flat outputs are given by…”

Section: Control Strategymentioning

confidence: 99%

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A static feedback stabilizer for the longitudinal dynamics of a small scale helicopter including the rotor dynamics with stabilizer bar

Benitez-Morales

Rodriguez-Cortes

Castro‐Linares

2013

2013 International Conference on Unmanned Aircraft Systems (ICUAS)

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In this paper we propose a solution to the trajectory tracking problem for a small scale helicopters longitudinal dynamics. The controller results from a control design technique that constructs static feedback stabilizers for dynamically feedback linearizable nonlinear systems. The flatness characteristics of the helicopter's longitudinal dynamics are used to construct the desired trajectory showing that the main rotor thrust is never equal zero. Numerical simulations show the performance of the controller even in the case that the main rotor and stabilizer bar dynamics are included.

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“…This method aims to transform the original nonlinear system into an exact linear equivalent model via a state feedback and a coordinates transformation [2,[7][8][9]. The theoretical formalism of inputstate feedback linearization is now well-known.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear state feedback design for continuous polynomial systems

Jemai

Jerbi

Abdelkrim

2011

Int. J. Control Autom. Syst.

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The objective of this paper is to simplify the complexity of practical implementation of the input-state feedback linearization technique for the control of input-affine systems. A polynomial approach which makes use of the Taylor series expansion and the Kronecker product is developed. Our work aims to address the problem of synthesizing a polynomial control via a nonlinear analytical coordinates transformation. To check the effectiveness of the investigated approach, we consider the control problem of a series DC motor. A comparative study with the input-state feedback linearization control is developed.

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On the construction of static stabilizers and static output trackers for dynamically linearizable systems, related results and applications

Cited by 22 publications

References 14 publications

Interconnection and damping assignment passivity-based control of mechanical systems with underactuation degree one

Interconnection and damping assignment passivity-based control of mechanical systems with underactuation degree one

A static feedback stabilizer for the longitudinal dynamics of a small scale helicopter including the rotor dynamics with stabilizer bar

Nonlinear state feedback design for continuous polynomial systems

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