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This article presents a new control strategy for the well‐known problem of the planar vertical take‐off and landing. The total thrust is computed using a nonlinear feedback compensation so that the altitude reaches the desired altitude. The horizontal position x is then controlled by choosing the orientation angle θ as a smooth saturation function of x and x˙. A proof of convergence is presented using a Lyapunov approach. The proposed control strategy is successfully tested in numerical simulations. [ABSTRACT FROM AUTHOR]

This paper provides a redesigned version of the Standard High Gain Observer (SHGO) to cope with the peaking phenomenon occurring during the transient periods as well as the sensitivity to high frequency measurement noise. The observer design is performed for a class of uniformly observable systems with noise free as well as noisy output measurements and the resulting observer is referred to as Non Peaking Filtered High Gain Observer (NPFHGO). The NPFHGO shares the same structure as its underlying SHGO and differs only by its corrective term which is still parameterized by a unique positive scalar up to an appropriate expression involving nested saturations. Of a fundamental interest, the power of the scalar parameter does not exceed one unlike in the case of the SHGO where this power grows from 1 to the system dimension. Moreover, it is shown that the equations of the NPFHGO become identical to those of the SHGO after a transient time horizon that can made arbitrarily small for sufficiently high values of the design parameter. A particular emphasis is put on the case of systems with noisy output measurements. It is shown how a multiple integrator of the corrupted outputs can be cascaded with the original system leading to an augmented system included in the class of systems for which the NPFHGO has been designed. The performance and main properties of the NPFHGO are highlighted and compared to those of its underlying SHGO through simulation results involving a single link robot arm system. [ABSTRACT FROM AUTHOR]

The quadrotor unmanned aerial vehicles (UAV) are rich system with attractive and challenging properties such as nonlinearities and underactuated dynamics, which motivates researchers to design advanced and robust control algorithms. In this paper, we contribute to a further improved design of quadrotor UAV. The quadrotor dynamics and kinematics equations are briefly presented. Then, an improved integral sliding mode controller (ISMC) has been proposed and applied within an inner loop to stabilize and track the quadrotor attitude at the desired values. The aim is to enhance the performance of the ISMC controller by eliminating the chattering problem, meanwhile maintaining the trajectory tracking in a robust fashion. In our design, the switching function (sign(s)), causing the chattering, is replaced by the approximated functions (tan h, error, saturation, quasi-sliding mode method) in the ISMC control law. PD controller is applied as an outer loop controller to enable the quadrotor to track the desired position. The performance of the proposed ISMC controller is studied with regard to the chattering attenuation and trajectory tracking robustness and tested by simulation MATLAB/SIMULINK. Finally, a comparison with the switching function (sign(s)) is performed to alleviate the superior performance of the proposed design. [ABSTRACT FROM AUTHOR]

This study provides a new parameterisation for a special class of nested‐saturation controllers, in which some multiplying coefficients appear before saturation functions. In an existing saturation scheme for the chain of integrators, the saturation levels and the multiplying coefficients are separately assigned in two stages, namely determined in the reduction analysis of saturated terms and the stability analysis of a reduced system. In the new parameterisation, it is in the saturation reduction analysis that the mentioned parameters are already determined. Such a convenient parameterisation is also applied to the uncertain multiple integrators and some mechanical systems. [ABSTRACT FROM AUTHOR]

A quasi-static scheme based on pore space spatial statistics is presented to simulate pore-scale two-phase capillary-dominant displacement processes. The algorithm is coupled with computational fluid dynamics in order to evaluate saturation functions. Wettability heterogeneity in partial and fractional/mixed-wet media is implemented using a contact angle map. The simulation process is pixel-wised and performed directly on binary images. Bypassing and snap-off are tackled as non-wetting phase trapping mechanisms. Post-processing results include residual saturations, effective permeability and capillary pressure curves for drainage and imbibition scenarios. The primary advantages of the proposed workflow are eliminating pore space skeletisation/ discretization, superior time efficiency and minimal numerical drawbacks when compared to other direct or network-based simulation techniques. [ABSTRACT FROM AUTHOR]

In this paper, the trajectory tracking control of an autonomous underwater vehicle (AUVs) in six-degrees-of-freedom (6-DOFs) is addressed. It is assumed that the system parameters are unknown and the vehicle is underactuated. An adaptive controller is proposed, based on Lyapunov׳s direct method and the back-stepping technique, which interestingly guarantees robustness against parameter uncertainties. The desired trajectory can be any sufficiently smooth bounded curve parameterized by time even if consist of straight line. In contrast with the majority of research in this field, the likelihood of actuators׳ saturation is considered and another adaptive controller is designed to overcome this problem, in which control signals are bounded using saturation functions. The nonlinear adaptive control scheme yields asymptotic convergence of the vehicle to the reference trajectory, in the presence of parametric uncertainties. The stability of the presented control laws is proved in the sense of Lyapunov theory and Barbalat׳s lemma. Efficiency of presented controller using saturation functions is verified through comparing numerical simulations of both controllers. [ABSTRACT FROM AUTHOR]

An output‐feedback proportional–integral‐derivative‐type control scheme for the global position stabilisation of robot manipulators with bounded inputs is proposed. It guarantees the global regulation objective avoiding input saturation by releasing the feedback not only from the exact knowledge of the system structure and parameter values, but also from velocity measurements. With respect to previous approaches of the kind, the proposed scheme remains simple while increasing design/performance‐adjustment flexibility. For instance, it does not impose the use of a specific sigmoidal function to achieve the required boundedness but involves a generalised type of saturation functions. More importantly, it is characterised by a very simple control‐gain tuning criterion, the simplest hitherto obtained in the considered analytical context. Experimental tests on a 2‐degree‐of‐freedom direct‐drive manipulator corroborate the efficiency of the developed scheme. [ABSTRACT FROM AUTHOR]

Boundary feedback control design is studied for 1D hyperbolic systems with an in-domain disturbance and a boundary feedback controller under the effect of actuator saturation. Nonlinear semigroup theory is used to prove well-posedness of mild solution pairs to the closed-loop system. Sufficient conditions in the form of dissipation functional inequalities are derived to establish global stability for the closed-loop system and L 2 -stability in presence of in-domain disturbances. The control design problem is then recast as an optimization problem over linear matrix inequality constraints. Numerical results are shown to validate the effectiveness of the proposed control design. [ABSTRACT FROM AUTHOR]

The authors are concerned in this study by bounded control of single input non‐linear under‐actuated mechanical systems. The authors focus the exposition on a feedback‐based stabilisation‐bounded control action shaped by saturation functions, and the proposed approach was illustrated via the design and the experimental evaluation of a simple stabilising controller for the cart–pendulum system, a well‐known control benchmark. The proposed simple control strategy is built around a lumped linear continuous time‐invariant description of the concerned under‐actuated non‐linear system. Namely, a model consisted of a cascade non‐linear dynamical system constituted by a chain of four integrators affected by a high‐order smooth non‐linear perturbation. Assuming initialisation of the under‐actuated system to the upper‐half plane, the proposed feedback‐based regulation design procedure involves the simultaneous combination of two control actions: one bounded linear and one bounded quasi‐linear. Control boundedness is provided in both involved control actions by specifically designed saturation functions. The first bounded control action brings the non‐actuated coordinate near to the upright position and keep it inside of a well characterised small vicinity, whereas the second bounded control action asymptotically brings the whole state of the dynamical system to the origin. The necessary closed‐loop stability analysis uses standard linear stability arguments as well as the traditional well‐known Lyapunov method and the LaSalle's invariance principle. The proposed control law ensures global stability of the closed‐loop system in the upper‐half plane. [ABSTRACT FROM AUTHOR]

Abstract: A method is presented to systematically transform a general inequality-constrained optimal control problem (OCP) into a new equality-constrained OCP by means of saturation functions. The transformed OCP can be treated more conveniently within the standard calculus of variations compared to the original constrained OCP. In detail, state constraints are substituted by saturation functions and successively constructed dynamical subsystems, which constitute a (dynamical) system extension. The dimension of the subsystems corresponds to the relative degree (or order) of the respective state constraints. These dynamical subsystems are linked to the original dynamics via algebraic coupling equations. The approach results in a new equality-constrained OCP with extended state and input vectors. An additional regularization term is used in the cost to regularize the new OCP with respect to the new inputs. The regularization term has to be successively reduced to approach the original constrained solution. The new OCP can be solved in a convenient manner, since the stationarity conditions are easily determined and exploited. An important aspect of the saturation function formulation is that the constraints cannot be violated during the numerical solution. The approach is illustrated for an extended version of the well-known Goddard problem with thrust and dynamic pressure constraints and using a collocation method for its numerical solution. [Copyright &y& Elsevier]

Abstract-The joint position regulation problem for robot manipulators under a standard saturated proportional-integral differential (PID) compensator is studied in this brief. The main result states the existence of PID control gains yielding semiglobal asymptotic stability if the control torque bounds are larger than gravitational torques Energy shaping plus damping injection methods, as well as singular perturbation analysis, are used to establish stability conditions to achieve regulation at any desired position. Some experiments are carried out to illustrate the stability results. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we focus on the validation of the nonlinear control structure, proposed in [Marconi L, Naldi R. Robust nonlinear full degree of freedom control of an helicopter. Automatica 2007;43:1909–20], for tracking arbitrary and even aggressive trajectories for small scale helicopters. We show how a systematic tuning procedure, which takes directly into account the aggressiveness of the references and the range of uncertainties of the model parameters, is able to succeed in enforcing the desired references signals. Simulations on a realistic dynamical model of small scale helicopters show the effectiveness of the proposed control strategy in presence of severe uncertainties. The paper is deliberately thought to be complementary to [Marconi L, Naldi R., 2007] to which the interested reader is referred for technical results and proofs of the tested control algorithm. [Copyright &y& Elsevier]

Abstract: We consider the problem of controlling the vertical, lateral, longitudinal and yaw attitude motion of a helicopter along desired arbitrary trajectories with only restrictions on the time derivatives imposed by the functional controllability of the system. To this purpose we design a nonlinear controller, obtained by suitably combining feedforward control actions and high-gain and nested saturation feedback laws, which succeeds in enforcing the desired trajectories robustly with respect to uncertainties characterizing the physical and aerodynamical parameters of the helicopter. Experimental results are also given to show the effectiveness of the method to accomplish aggressive maneuvers. [Copyright &y& Elsevier]

This paper proposes a natural saturating extension of the proportional-derivative (PD) with desired gravity compensation (PDdgc) control law for the global regulation of robot manipulators with bounded inputs. Compared with other algorithms previously proposed under the same analytical framework, it proves to be advantageous in several senses. First, it involves a single saturation function at each joint. Second, it does not need to discriminate the terms that shall be bounded, since these are simply all of them included within the only saturation involved at every joint. Experimental results show the effectiveness of the proposed scheme. As far as the authors are aware, no such type of natural saturating extension (i.e., involving only one saturation function at each joint, where all the terms of the controller are embedded) to the bounded input case had been previously proposed for the PDdgc scheme. Furthermore, it is shown how the proposed approach may be conceived within the framework of the energy shaping plus damping injection methodology. [ABSTRACT FROM AUTHOR]

This brief proposes two alternative approaches for the global regulation of robot manipulators with input saturations. They prove to be simple extensions of the PD-with-gravity-compensation (PDgc) control law to the bounded-input case. Moreover, they turn out to be in a better position to approach (within the restricted range of the control variables) a PDgc control signal than other algorithms previously proposed under the same analytical framework. Closed-loop performance improvements are, therefore, obtained through their implementation. This is corroborated through experimental results. [ABSTRACT FROM AUTHOR]