A Multiple Shooting Method for Numerical Computation of Open and Closed Loop Controls in Nonlinear Systems

Bock, H.G.; Krämer-Eis, Peter

doi:10.1016/s1474-6670(17)61005-x

Cited by 8 publications

(11 citation statements)

References 1 publication

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“…Here, the unknown parameters found upon solution of the above nonlinear problem are the external disturbance together with the initial state of the system at the beginning of the estimation horizon (i.e., the initial condition). The functional in (38c) is the same system as in (37), and terminal constraints on some of the states might be also considered (e.g., the flap deflection is known at the sampling time). Now, the functional subject to minimisation aims to penalise the errorˆ = − between a measured output from the actual system and the estimated output produced by the internal model, which is chosen to be a linear function of the vector state, = L ( ).…”

Section: Nonlinear Estimator and Controllermentioning

confidence: 99%

Proof of Concept for a Hardware-in-the-Loop Nonlinear Control Framework for Very Flexible Aircraft

Artola

Goizueta

Wynn

et al. 2021

AIAA Scitech 2021 Forum

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Nonlinear Moving Horizon Estimation (MHE) and Model Predictive Control (MPC) strategies for very flexible aircraft are presented. They are underpinned by a nonlinear reduced-order model built upon the structure's natural modes of vibration. This internal model aims for a minimal realisation of the aircraft which retains sufficient information to enable efficient real-time estimation and control. It is based on a modal intrinsic description of geometrically-nonlinear beams and a linearised unsteady vortex lattice aerodynamic model. Numerical evidence has shown that models of this form are able to capture the main nonlinear geometrical couplings at a very low computational cost. This opens the door to MHE and MPC strategies, which are naturally more computationally demanding than other linear conventional strategies, but are more versatile and able to provide control in the usually neglected nonlinear regime. The proposed control framework is tested on models built in an in-house open-source nonlinear aeroelasticity simulation and analysis package, to emulate the controller performance on a realistic plant model. Very satisfactory results are obtained in a flutter suppression problem involving a very flexible clamped wing, where the nonlinearity of the problem is leveraged by the internal model to achieve stabilisation, and a payload drop control of a very flexible HALE aircraft.

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Section: Nonlinear Estimator and Controllermentioning

confidence: 99%

Proof of Concept for a Hardware-in-the-Loop Nonlinear Control Framework for Very Flexible Aircraft

Artola

Goizueta

Wynn

et al. 2021

AIAA Scitech 2021 Forum

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“…A consequence of using the modal solution, which is global in space, to locally evaluate the time evolution equations for rotations (6) and displacements (10) is that errors are introduced which accumulate over the time-integration and result in the individually evaluated points in the structure drifting apart [17]. Periodic regularisations in the rotation and displacement fields are performed to keep these errors within some tolerable margin, updating them by integrating equations (5) and (9) in space [17].…”

Section: B Modal Reductionmentioning

confidence: 99%

“…In a multiple shooting scheme the time horizon t f in which the simulation and optimisation are performed is split into several independent time intervals, with independent initial conditions q m 0 = q m (t m−1 ), Ξ m 0 = Ξ m (t m−1 ) for each interval. These are added to the set of optimisation parameters with additional state continuity constraints [5]. Superscript m denotes that the variables belong to the m th interval, with t m−1 ≤ t ≤ t m .…”

Section: Optimal Problem Solution a Multiple Shootingmentioning

confidence: 99%

“…A challenge of implementing NMPC, however, is the computational cost associated with solving its underlying optimisation problems. To address this problem, and to enable efficient online computation of control inputs for systems with fast dynamics, the real-time iteration scheme has been proposed [4], based on the multiple shooting algorithm of [5]. To date, application of NMPC strategies to the control of very flexible structures has yet to be fully exploited, mainly due to the high dimensionality of the systems involved.…”

Section: Introductionmentioning

confidence: 99%

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A Nonlinear Modal-Based Framework for Low Computational Cost Optimal Control of 3D Very Flexible Structures

Artola

Wynn

Palacios

2019

2019 18th European Control Conference (ECC)

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A nonlinear modal-based reduced-order model, equipped with an efficient adjoint-sensitivity analysis, is presented as a low computational cost framework for optimal control of very flexible structures, with particular focus on efficiently computing finite rotations. Multiple shooting is shown to improve convergence of a highly nonlinear problem when compared to the single shooting case, with optimisation further accelerated via parallelisation, which suggests the presented approach may be employed for real-time control of very flexible structures.

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“…This was developed in Ref. 27 and it was demonstrated to be very effectiveness on minimum energy subway operation in Ref. 28.…”

Section: Feedback Controlmentioning

confidence: 99%

Issues in the implementation of time-optimal robot path planning

Longman

Steinbach

et al. 1997

35th Aerospace Sciences Meeting and Exhibit

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We have developed direct numerical methods of solving optimal control problems that are sufficiently fast that it is becoming reasonable to use them to perform time optimal path planning. An overview of the nature of time optimal robot motions has been developed for elbow, polar, and SCARA robots, and it has been shown that for some maneuvers a very large savings in time is possible. This offers the opportunity to increase productivity on assembly lines by making the robots more efficient in executing their point-to-point motions. This paper takes one step toward converting these time optimal results into ones that can be used in routine robot operation. Methods are developed that allow one to make the existing robot feedback controllers produce the optimal torque histories needed for time optimal operation. It is shown that this is easiest accomplished by back-computing the commands to give the robot links from the desired torque histories. (Author) AbstractThe authors and co-workers have developed direct numerical methods of solving optimal control problems that are sufficiently fast that it is becoming reasonable to use them to perform time optimal path planning. In a series of publication, a good overview of the nature of time optimal robot motions has been developed for elbow, polar, and SCARA robots, and it was shown that for some maneuvers a very large savings in time is possible. This offers the opportunity to increase productivity on assembly lines by making the robots more efficient in executing their point-to-point motions. This paper takes one step toward converting these time optimal results into ones that can be used in routine robot operation. Methods are developed that allow one to make the existing robot feedback controllers produce the optimal torque histories needed for time optimal operation. It is shown that this is easiest accomplished by back computing the commands to give the robot links from the desired torque histories.

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A Multiple Shooting Method for Numerical Computation of Open and Closed Loop Controls in Nonlinear Systems

Cited by 8 publications

References 1 publication

Proof of Concept for a Hardware-in-the-Loop Nonlinear Control Framework for Very Flexible Aircraft

Proof of Concept for a Hardware-in-the-Loop Nonlinear Control Framework for Very Flexible Aircraft

A Nonlinear Modal-Based Framework for Low Computational Cost Optimal Control of 3D Very Flexible Structures

Issues in the implementation of time-optimal robot path planning

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