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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...
Hydraulic equipment suffered a great change during the last years advancing from hydro-mechanical devices to digitally controlled electro-hydraulic systems. There are also changes in hydraulic schemes permitting increased number of control variables (e.g. separate metering systems — SMISMO). Available control strategies which require high computing performances, like optimal control, must be examined...
An optimal control problem based on the Hamiltonian approach involves the solution of the so-called canonical equations. The example application for a hydraulic positioning system with servo valves leads to a stiff system that had no solution with classical solvers for ordinary differential equations (ODE) without tuning. With the method of direct solution of discrete systems, such systems can be...
A class of optimization problems is the state change of a dynamic system while minimizing a functional as a quality criterion. Such problems may be solved with the help of the Hamiltonian function, which allows to find an optimal control variable for the process. Given the boundary conditions for the system state variables x, it is necessary to find initial conditions for the adjunct variables ψ....
A standard serial 6-DOF industrial robot was equipped with an electronic control unit designed especially for educational purposes. A fast Ethernet LAN with UDP communication allows a real-time control from a PC, which runs a widely used scientific software. Even inverse and direct kinematics are computed on the PC and hence are available for education. The configuration allows interactive reaction...
This article presents a new platform independent approach to the real-time solution of inverse problems on embedded systems. The class of problems addressed corresponds to ordinary differential equations (ODEs) with generalized linear constraints, whereby the data from an array of sensors forms the forcing function. The algebraic discretization of the problem enables an one-to-one mapping of the ODE...
Modern small-scale electronic systems based on ARM-processors provide surprising computing power and allow implementation of complex algorithms that usually are not applied in automation engineering. In this work a Hamiltonian-based optimal path control for a dynamical system of fourth order is implemented. It turns out that even the controller design that requires advanced numerical computation can...
This paper presents a mathematical model and partitioning for a software system for the solution of inverse problems involving arrays of sensors. Handling the data from the array of sensors as vectors and matrices, while defining the inverse problem as a least squares computation with linear constraints, leads naturally to the use of matrix algebra for the solution of the system of equations. The...
For a recently developed novel acoustic sensor for injection molding a signal processing unit was developed. Sensor elements inside the mold generate structure-borne sound in order to detect the filling level of the cavities. One acceleration sensor picks up the vibrations on the surface of the mold. The task of signal processing is to identify the source of the sound and to find the instant of time...
For the automation of a production system a hardware-in-the-loop (HIL) simulation model of the mechanical system was developed and embedded on the controller. In a second level, the controller was simulated on a PC for designing and testing the human-machine interface (HMI). The task of the system is a PVD (physical vapor deposition) coating process for materials, which involves pulsed laser deposition...
A cable-string driven robot was designed to move a camera with six degrees of freedom. Its motion is controlled by a human operator with a joystick. The intended purpose is to follow an object moving on a surface below the camera. Motion is controlled with the length of the strings, which requires the solution of the inverse kinematics by the electronic controller. Incremental encoders are used to...
Today Hardware-in-the-loop is standard testing procedure in controller design procedure. Once the design of the controller is completed using off-line desktop simulations and the algorithm is transferred in C code, it is necessary to test the code as well as the final controller for his capabilities of running in real-time. In the process of designing the hydro turbine speed governor this is more...
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