Gerhard Rath

Direct numerical solution of optimal control problems

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. Then the adjunct system can be solved in an iterative manner with classic ODE solvers. In this paper an alternative method based on recently developed methods for a direct numerical solution of such a problem is presented. The advantages are that it is not necessary to calculate an exponential matrix, and furthermore the approach is better suited for stiff systems than classical solvers.

Embedded simulation for automation of material manipulators in a PVD coating process

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 and magnetron sputtering. It requires positioning devices to move material probes as well as to manipulate laser target materials in a vacuum chamber. As a result of using simulation, the start-up phase was shortened and production was resumed faster. The need of software changes after deployment was reduced. With the increasing capabilities of modern simulation software and controller hardware it turns out, that virtual start-up, factory acceptance test and functional validation are practicable also for small projects.

Real-time optimal control and controller design on embedded systems

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 run on the system in a real-time manner. In order to verify the theoretical approach, the controller was tested on a mechanical model. Finally the performance data of the actual control task are given.

Mathematical model and software architecture for the solution of inverse problems involving sensor arrays

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 matrix algebra is also well suited for the use of automatic code generation to support the rapid development of embedded code. The full functionality of the proposed methods was demonstrated with an inclinometer based system for the monitoring of structural deformation.

Hardware-in-the-loop for simulation of hydraulic servo systems and their control

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 for implementation on real hardware. For this purpose digital controllers must be tested in real-time before they are implemented in the real machine. Hardware-in-the-loop (HIL) is technology which is available for this. In this paper a procedure for development of HIL simulator for servo valve driven system and SMISMO hydraulic systems is shown. First, mathematical model of hydraulic systems is developed using graphical environment. Then, real-time simulations are performed with a platform consisted from two industrial PLC and one PC. One PLC is used to simulate the real system (servo valve-cylinder) and the other one is real controller under test. PC is used for changing controller parameters and visualization.

Direct numerical solution of stiff ODE systems in optimal control

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 solved. To prove, that the resulting output is an optimal solution, the data were applied to a simulation model of the hydraulic system with good results.

Global least squares solution for LTI system response

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.

Teachers’ Beliefs About Subject Specific Competences and Inquiry Based Learning

The Austrian Ministry of Education has set up several measures as reaction to the low results in international student assessment studies like TIMSS or PISA: On the level of systematic monitoring, one strategy was to implement educational subject specific standards to change the focus of the educational system from input to output orientation. Subject specific standards and standardization has become one main issue in Austrian education in the last decade. There are several reasons why teachers encounter the issue of standards with resentments. One is that teachers were not provided with sufficient supportive measures in time, like teacher training courses or teaching materials, for a paradigmatic change in their teaching culture. Due to this shortfall, a number of beliefs and misconceptions about competence oriented teaching have spread. There seems to be a high tendency among teachers to interpret competence orientation only in terms of implementing open learning strategies which do not require guidance by the teachers at all. In the field of science teaching this idea of open, unguided learning manifests in the increase of Inquiry Based Learning (IBL), which of course can only be one way of promoting competence orientation. However, our work with teachers suggests that IBL is frequently just perceived as doing experimental work without any interference by the teacher. This situation served as the starting point for a research project which investigates teachers’ beliefs about competence orientation and IBL. As sample we chose teachers who applied for a continuous professional development programme (CMSE) focusing on the promotion of students’ subject specific competences. Our results show that even this preselected sample, which is about to take the challenge of competence orientation, struggles with competence orientation and the introduction of IBL.

Calibration verification of a mining machine using image processing

Recently developed mining machines are capable of cutting different profiles. Cutting desired profiles opens new fields of application for these machines. The precision of the profile, which is cut, depends on the kinematics of the machine and its calibration. The dimensions of the profiles up to 10 m wide and 5 m high make it difficult to calibrate and even measure. This paper presents an image processing system, which was developed to solve this problem. An ultra-bright infrared LED was mounted on the primary calibration point of the machine. The 2-R manipulator (i.e. the cutting arm) is moved so as to generate the desired outer profile. The 2-R kinematics of the machine result in the calibration point moving along the surface of a torus. The imaging system acquires a sequence of images, each of them captures the machine in one point along the profile. This delivers a 2-D central projection of the 3-D motion. The inverse projection is determined using projective geometry. The true position of the calibration points is determined by applying the inverse projection, which is then compared to the desired position. Measurements of a mining machine and a comparison with the desired profile are presented.