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A model of PVTOL aircraft with two delayed inputs is considered. The origin of this system is globally asymptotically and
locally exponentially stabilized by bounded control laws. The explicit expressions of the control laws applied are determined
through recent extensions of the forwarding approach to systems with a delay in the input. In a second...
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Citations
... los recientes avances de sensores inteligentes y sistemas de visión, suelen requerir un tiempo de procesamiento considerablemente alto, por lo que hay una creciente necesidad de herramientas que permitan analizar y controlar sistemas sin despreciar los retardos. En particular, cuando el retardo se puede asociar a la entrada del sistema, una forma de evitar la inestabilidad es incluyendo un observador-predictor al lazo cerrado para compensar el retardo (Francisco, R., Mazenc, F. y Mondié, S., 2007). Los predictores son reconstructores basados en observadores, cuya finalidad es obtener un estimado del estado a partir de la entrada y la salida del sistema. ...
This article introduces an observer-predictor that estimates the position of a quadrotor with input delay. The predictor whose aim is to compensate the delay, is tuned using multiplicity-induced dominance of the roots of the linearized prediction error. The stability of the prediction error is analyzed using a Lyapunov-Krasovskii functional. Simulation results of the quadrotor in closed-loop with a control law feed with the predicted states are presented.
... In delay differential equation, the time derivatives at the current time depend on the solution and possibly its derivatives at previous time. Time-delays appear in many engineering systems like water quality process [29], aircraft control [9] chemical control systems [28] and laser models [8] and references therein. Recently, the stabilization issue of time-delay switched system has been investigated based on Lyapunov Krasovskii functionals and LMI approach. ...
... Currently there is no an extensive work that focuses on the problem of time-delay generated by both the processing of information and the communication through networks. Some of the relevant works that have focused on this are briefly described next: in [1] a reconstructor for feed forward systems was designed based on nested saturations and it is applied to a VTOL (vertical take off landing); in [2] Lozano et al designed a discrete predictor based controller to stabilize the orientation of a quad rotor in presence of input time-delay; in [3] a discrete predictor-observer based on Kalman filter was developed by Sanz to deal with the delay generated by the inertial sensors; Ordaz et al [4] proposed a controller to compensate the delay generated by GPS or a camera system, this control was also implemented in real-time experiments. ...
... Although the list of works on PVTOL aircraft control we have given is not even remotely exhaustive, to the best of our knowledge all the results available in the literature, except for Francisco et al. (2007), assume that there is no delay in the inputs. Nonetheless, such a delay, due to sensors and information processing, is often present in practice. ...
The paper deals with exact steering predictor-based multirate control of nonlinear dynamics with a non-zero drift term and delayed inputs which admit under feedback a finiteorder sampled-data equivalent model. Simulation results concerning the adopted control strategy are presented.
... , [20], motors [34], [50], multi-agent systems [1], [18], [40], autonomous ground vehicles [39], unmanned aerial vehicles [23] and planar vertical take-off and landing aircrafts [21], [48], and the human musculoskeletal system in applications such as neuromuscular electrical stimulation [32], [38], [51], to name only a few. Motivated by the negative effects of input delays on the stability and performance of such control systems, in this article we present control designs that achieve delay compensation. ...
We develop a predictor-feedback control design for multi-input nonlinear
systems with distinct input delays, of arbitrary length, in each individual
input channel. Due to the fact that different input signals reach the plant at
different time instants, the key design challenge, which we resolve, is the
construction of the predictors of the plant's state over distinct prediction
horizons such that the corresponding input delays are compensated. Global
asymptotic stability of the closed-loop system is established by utilizing
arguments based on Lyapunov functionals or estimates on solutions. We
specialize our methodology to linear systems for which the predictor-feedback
control laws are available explicitly and for which global exponential
stability is achievable. A detailed example is provided dealing with the
stabilization of the nonholonomic unicycle, subject to two different input
delays affecting the speed and turning rate, for the illustration of our
methodology.
... The authors of [5] considered the tracking problem by using flat outputs and linearising the system. In [6] the authors focused on designing a control law with delay in the inputs. Model-free control has also been used in [7]. ...
This paper deals with the nonlinear control of the planar vertical takeoff and landing aircraft (PVTOL) using a simple, fast and nonlinear discrete time control approach. The proposed control approach uses an approximate numerical one-step time discretization of the nonlinear plant model behavior obtained from offline simulations. Using that discretization, a control minimizing the distance between the plant output and a reference linear system is computed, leading the system to adopt its dynamical behavior. Since the prediction horizon is limited to one time-step, the execution time of the algorithm can be completely bounded. It can thus easily be implemented and used to control fast electromechanical systems. Experimental results obtained from some simulations show the performance and robustness of the proposed controller.
... Although the work in [24]- [27] provides fundamental contributions to the input delay problem in feedforward systems, the applicability of these methods to general uncertain mechanical systems (e.g., modeled by Euler-Lagrange dynamics) is not clear. An attempt at designing a transformation to convert an Euler-Lagrange system into a feedforward system in [28] required exact model knowledge; thus, the technique is not applicable when the system parameters are unknown or the dynamics are uncertain, which implies that methods developed for feedforward systems with input delays may not be applicable to uncertain Euler-Lagrange dynamics. ...
This paper examines saturated control of a general class of uncertain nonlinear Euler-Lagrange systems with time-delayed actuation and additive bounded disturbances. The bound on the control is known a priori and can be adjusted by changing the feedback gains. A Lyapunov-based stability analysis utilizing Lyapunov-Krasovskii functionals is provided to prove uniformly ultimately bounded tracking despite uncertainties in the dynamics.
... In [37] and [38], approaches are provided to construct Lyapunov-Krasovskii (LK) functionals for stabilizing input delayed nonlinear system in feedback form and nonlinear cascade systems, where the delay can enter the system through the input or the states. The work in [39]- [41] provide fundamental contributions to the input delay problem in feedforward systems, but its applicability to general uncertain mechanical systems modeled by Euler-Lagrange dynamics (e.g., a musculoskeletal dynamics driven by NMES ) is not clear. A method to transform a cart-pendulum system (a typical example of Euler-Lagrange system) to a feedforward system and subsequently to design a tracking controller was provided in [42]. ...
Electromechanical delay (EMD) is a biological artifact that arises due to a time lag between electrical excitation and tension development in a muscle. EMD is known to cause degraded performance and instability during neuromuscular electrical stimulation (NMES). Compensating for such input delay is complicated by the unknown nonlinear muscle force-length and muscle force-velocity relationships. This paper provides control development and a mathematical stability analysis of a NMES controller with a predictive term that actively accounts for EMD. The results are obtained through the development of a novel predictor-type method to address the delay in the voltage input to the muscle. Lyapunov-Krasovskii functionals are used within a Lyapunov-based stability analysis to prove semi-global uniformly ultimately bounded tracking. Experiments on able-bodied volunteers illustrate the performance and robustness of the developed controller during a leg extension trajectory following task.
... In Mazenc and Bliman (2006), an approach is provided to construct Lyapunov-Krasovskii (LK) functionals for the input delayed nonlinear system in feedback form. In Francisco, Mazenc, and Mondié (2007), bounded state feedback and output-based controllers are developed to stabilize the origin of the dynamic system describing a PVTOL aircraft with delay in the input. The developed control laws are extensions of approach developed for the feedforward system with delays in the input (Mazenc et al., 2003b,a). ...
... The developed control laws are extensions of approach developed for the feedforward system with delays in the input (Mazenc et al., 2003b,a). Although the work in Francisco et al. (2007) and Mazenc et al. (2003b,a) provide fundamental contributions to the input delay problem in feedforward systems, its applicability to general uncertain mechanical systems modeled by Euler-Lagrange dynamics is not clear. The dynamic model considered in Francisco et al. (2007) is a simplified model of equations where dependency on parameters (e.g., mass of the system, lengths, etc.) does not exist. ...
... Although the work in Francisco et al. (2007) and Mazenc et al. (2003b,a) provide fundamental contributions to the input delay problem in feedforward systems, its applicability to general uncertain mechanical systems modeled by Euler-Lagrange dynamics is not clear. The dynamic model considered in Francisco et al. (2007) is a simplified model of equations where dependency on parameters (e.g., mass of the system, lengths, etc.) does not exist. Development was provided in Mazenc and Bowong (2003) to design a tracking controller for a cart-pendulum system (a typical example of Euler-Lagrange system). ...
Controlling a nonlinear system with actuator delay is a challenging problem because of the need to develop some form of prediction of the nonlinear dynamics. Developing a predictor-based controller for an uncertain system is especially challenging. In this paper, tracking controllers are developed for an Euler–Lagrange system with time-delayed actuation, parametric uncertainty, and additive bounded disturbances. The developed controllers represent the first input delayed controllers developed for uncertain nonlinear systems that use a predictor to compensate for the delay. The results are obtained through the development of a novel predictor-like method to address the time delay in the control input. Lyapunov–Krasovskii functionals are used within a Lyapunov-based stability analysis to prove semi-globally uniformly ultimately bounded tracking. Experimental results illustrate the performance and robustness of the developed control methods.
... See also [3] for output tracking along a circle. Later work [8] by Francisco et al. used forwarding results [20] for feedforward systems to design distributed delay nested saturation feedbacks that give global asymptotic stability. Another portion of the PVTOL aircraft literature covers path following. ...
We study a class of feedback tracking problems for the planar vertical takeoff and landing (PVTOL) aircraft dynamics, which is a benchmark model in aerospace engineering. After a survey of the literature on the model, we construct new feedback stabilizers for the PVTOL tracking dynamics. The novelty of our contribution is in the boundedness of our feedback controllers and their applicability to cases where the velocity measurements may not be available, coupled with the uniform global asymptotic stability and uniform local exponential stability of the closed loop tracking dynamics, the generality of our class of trackable reference trajectories, and the input-to-state stable performance of the closed loop tracking dynamics with respect to actuator errors. Our proofs are based on a new bounded backstepping result. We illustrate our work in a tracking problem along a circle.
