Direct numerical solution of optimal control problems

Rath, Gerhard; Harker, Matthew

doi:10.1109/meco.2016.7525768

Cited by 5 publications

(5 citation statements)

References 5 publications

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“…It can be seen from these diagrams that the proposed procedure brings the load to the end position without leaving oscillations after the end time. The time delays of the spools with a value of 30 ms were not included in the design of the optimal control, since the numerical solvers used could not [24] will make this possible. The additional delay is the reason, why the valves do not close immediately at the end time.…”

Section: Comparison With Start/stop Motion Controlmentioning

confidence: 99%

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Optimal Control for Hydraulic System with Separate Meter-In and Separate Meter-Out

Rath¹,

Zaev²

2017

Linköping Electronic Conference Proceedings

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Individual meter-in and meter-out proportional control of hydraulic cylinders allow more flexible strategies how to handle a payload while optimising certain aspects of the motion. An optimal control approach based on the Hamiltonian is used to plan a motion path for a separate meter-in and separate meter-out system. One goal is to avoid oscillations at the end of the motion in the sense of active vibration damping. With the mathematical model presented, it is possible to include the cylinder pressures into the optimisation goals. Not only the the final values for position and speed of the load can be acquired, but also desired values for the pressures at the end of the motion. Maintaining a minimum pressure level is important in order to avoid cavitation and to keep the stiffness of the system. The course of the pressures follows from the design of the motion and will reach the desired values in an open loop control. In order to estimate the computing effort, the algorithm was tested on three platforms. One of those is an ARM-based hardware that represents the computing power of modern embedded systems, to demonstrate that an implementation on such system is possible. Several motion experiments were carried out in simulation to study the behaviour and to discuss application issues.

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Section: Comparison With Start/stop Motion Controlmentioning

confidence: 99%

“…Reverse motion with too low initial pressures done to work on a solving method that always meets the final conditions exactly[24].…”

mentioning

confidence: 99%

Optimal Control for Hydraulic System with Separate Meter-In and Separate Meter-Out

Rath¹,

Zaev²

2017

Linköping Electronic Conference Proceedings

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“…The number of state variables is represented by p, the number of inputs is q, and n is the number of samples in time from 0 to t f . With an appropriate numerical approximation to a differentiating matrix [5], [6], (7) can be written as,…”

Section: Direct Global Solution Approach a Discretizationmentioning

confidence: 99%

“…An alternative approach to find a global solution after discretization of a system was used to find a curve whose differentials are known by inclinometer measurements [5], [6]. In [7] such method was used for a process in time, solving the canonical system for an optimization problem. It had the advantage to solve the BVP without the need of the matrix exponential, an operation, which may cause problems [8].…”

Section: Introductionmentioning

confidence: 99%

Global least squares solution for LTI system response

Rath

Harker

2017

2017 International Conference on Applied Electronics (AE)

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Linear time invariant (LTI) systems are the most important method to describe dynamic systems for the purpose of modeling, simulation and design of controllers. Dynamic systems are a process developing over time, hence the solution is an initial value problem (IVP). Solvers for ordinary differential equations (ODE) are commonly used for evaluation. A new idea is to solve such systems directly after discretization based on an least-squares problem with equality constraints (LSE). The approach is demonstrated on a simple system with four state variables and a rank-deficient system matrix. A comparison with standard ODE solution shows the correctness of the solution, advantages are discussed.

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“…The method is demonstrated on the following problems: Solving the vibrating string problem with Robin boundary conditions; solving two forms of singular Bessel equations; and computing the modes of an overconstrained vibrating beam, as well as fitting these mode shapes to real-world data of a cantilever beam subject to a load. Some applications of the proposed method include the solution of variational problems, such as optimal control [13], a discrete Rayleigh-Ritz method [5,14], the control of distributed parameter systems [15,16], or the design of beams with desired mode shapes [17]. Code for the proposed method is available freely on the MATLAB file-exchange at: http://www.mathworks.com/matlabcentral/fileexchange/authors/321598…”

mentioning

confidence: 99%

Approximation of Physical Measurement Data by Discrete Orthogonal Eigenfunctions of Linear Differential Operators

Harker

O’Leary

2017

Transactions of the Canadian Society for Mechanical Engineering

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We present a new method for computing the eigenfunctions of a linear differential operator such that they satisfy a discrete orthogonality constraint, and can thereby be used to efficiently approximate physical measurement data. Classic eigenfunctions, such as those of Sturm-Liouville problems, are typically used for approximating continuous functions, but are cumbersome for approximating discrete data. We take a matrix-based variational approach to compute eigenfunctions based on physical problems which can be used in the same manner as the DCT or DFT. The approach uses sparse matrix methods, so it can be used to compute a small number of eigenfunctions. The method is verified on common eigenvalue problems, and the approximation of real-world measurement data of a bending beam by means of its computed mode-shapes.

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Direct numerical solution of optimal control problems

Cited by 5 publications

References 5 publications

Optimal Control for Hydraulic System with Separate Meter-In and Separate Meter-Out

Optimal Control for Hydraulic System with Separate Meter-In and Separate Meter-Out

Global least squares solution for LTI system response

Approximation of Physical Measurement Data by Discrete Orthogonal Eigenfunctions of Linear Differential Operators

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