Safe Manual Control of Unstable Systems

This thesis deals with manual control of unstable systems, subject to control signal constraints. Allocation of control authority is critical in this situation. The manual control, or reference following, must not be performed at the risk of loosing stability. The conflicting objective is to achieve acceptable reference following performance. Design of control systems under such circumstances is critical, and has several important applications. One example is modern flight control systems for unstable fighter aircrafts. Experiments have been an important part of this work. An inverted pendulum of the Furuta type, has been used for experimental verification of the controller designs. This plant is unstable, but reasonably easy to analyze and perform experiments with. Theoretical as well as practical results are presented in this report. Controllers for the linearized pendulum model have been designed and simulated. Some of the designs were also implemented and evaluated on the real Furuta pendulum. The translation of the controllers from a simulation environment to the real plant proved quite difficult. Some modifications of the controllers had to be made, in order to achieve the desired results on the real Furuta pendulum. Compensation for friction also had to be done

Languages and Tools for Optimization of Large-Scale Systems

Modeling and simulation are established techniques for solving design problems in a wide range of engineering disciplines today. Dedicated computer languages, such as Modelica, and efficient software tools are available. In this thesis, an extension of Modelica, Optimica, targeted at dynamic optimization of Modelica models is proposed. In order to demonstrate the Optimica extension, supporting software has been developed. This includes a modularly extensible Modelica compiler, the JModelica compiler, and an extension that supports also Optimica. A Modelica library for paper machine dryer section modeling, DryLib, has been developed. The classes in the library enable structured and hierarchical modeling of dryer sections at the application user level, while offering extensibility for the expert user. Based on DryLib, a parameter optimization problem, a model reduction problem, and an optimization-based control problem have been formulated and solved. A start-up optimization problem for a plate reactor has been formulated in Optimica, and solved by means of the Optimica compiler. In addition, the robustness properties of the start-up trajectories have been evaluated by means of Monte-Carlo simulation. In many control systems, it is necessary to consider interaction with a user. In this thesis, a manual control scheme for an unstable inverted pendulum system, where the inputs are bounded, is presented. The proposed controller is based on the notion of reachability sets and guarantees semi global stability for all references. An inverted pendulum on a two wheels robot has been developed. A distributed control system, including sensor processing algorithms and a stabilizing control scheme has been implemented on three on-board embedded processors

Improving Newton's method for Initialization of Modelica models

Initializing a model written in Modelica translates to finding consistent initial values to the underlying DAE. Adding initial equations and conditions creates a system of non-linear equations that can be solved for the initial configuration. This paper reports an implementation of Newton's method to solve the non-linear initialization system. This implementation also uses a regularization method to deal with singular Jacobians as well as sparse solvers to exploit the sparsity structure of the Jacobian. The implementation is based on the open-source projects JModelica.org and Assimulo, KINSOL from the SUNDIALS suite and SuperLU

Flexible Implementation of Model Predictive Control Using Sub-Optimal Solutions

The on-line computational demands of model predictive control (MPC) often prevents its application to processes where fast sampling is necessary. This report presents a strategy for reducing the computational delay resulting from the on-line optimization inherent in many MPC formulations. Recent results have shown that feasibility, rather than optimality, is a prerequisite for stabilizing MPC algorithms, implying that premature termination of the optimization procedure may be valid, without compromising stability. The main result included in the report is a termination criterion for the on-line optimization algorithm giving rise to a sub-optimal, yet stabilizing, MPC algorithm. The termination criterion, based on an associated delay-dependent cost index, quantifies the trade-off between successively improved control profiles resulting form the optimization algorithm and the potential performance degradation due to increasing computational delay. It is also shown how the cost index may be used in a dynamic scheduling application, where the processor time is shared between two MPC tasks executing on the same CPU

Development of a CBM based service indicator for UFD replacements - An introductory study

Dialysis is a life-sustaining treatment for many people around the world. In or- der to meet the high demands on the dialysis machines, replaceable parts must be exchanged in proper time. Condition based maintenance (CBM) bases its service decisions on the actual health status of the component. The goal of this master’s thesis was to develop an algorithm based on machine learning, constituting the first step of a CBM based service indicator monitoring the dialysis ultra filter (UFD) of Baxter’s AK 98 dialysis machine. Real treatment data retrieved from ten dialysis machines have been an- alyzed. Signals believed to be relevant to the UFD status were preprocessed and analyzed. From them different features were extracted whereof some were found in CBM related literature. Two different feature selection methods were used to select 10 out of the 178 available features. Different labeling meth- ods were tested and evaluated together with other relevant parameters in the algorithm. The final algorithm used a k-nearest neighbors (kNN) classifier with k = 12. The classification accuracy was approximately twice as good as a ran- dom guess. The main reason for not achieving a better result was that only six features appeared to contain relevant information regarding the UFD status. Furthermore, these features were derived from the same signal and closely related. Despite this, the developed algorithm did show promising result in detecting the UFD degradation level but further development will be needed. The main focus should be to improve the signal quality and/or find more relevant signals and/or features.Utveckling av algoritm som avgör filterstatusen hos dialysmaskiner Många människor världen över dör för att de inte har råd med dialysbehandling. För att minska kostnaderna har det i detta exjobb utvecklats en algoritm som kan användas i en framtida serviceindikator för filter i dialysmaskiner. Resultaten ser lovande ut. Kronisk njursjukdom beskriver ett tillstånd av progressivt förlorad njurfunktion. När detta utvecklats tillräckligt långt krävs behandling, till exempel i form av dialys. Man räknar med att runt två miljoner människor världen över är i behov av regelbunden dialysbehandling för att överleva. Dock är mörkertalet stort vilket medför att siffran troligtvis är tio gånger så stor. Det dåliga allmäntillståndet hos dialyspatienter ställer stora krav på behandlingen. Inte minst i form av att se till att dialysvätskan är helt fri från bakterier och andra smittämnen vilket annars kan få katastrofala konsekvenser. Som en del i försvaret mot detta finns ett specifikt filter i vissa dialysmaskiner. De nuvarande rekommendationerna är att byta ut detta filter efter en viss tid alternativt efter att ett visst antal desinfektioner har utförts. Därmed tas ingen hänsyn till den faktiska statusen på filtret. För att inte riskera att filterna byts ut för sent är gränserna väl tilltagna. Tänk om det fanns ett sätt att optimera användandet av varje enskilt filter. Det skulle dels minska belastningen på miljön men framför allt leda till minskade kostnader för sjukvården. I slutändan skulle detta kunna leda till att dialysbehandlingen skulle kunna nå ut till fler drabbade personer även i den fattiga delen av världen och rädda liv. Ett sätt att optimera filteranvändningen skulle vara att utveckla en serviceindikator liknande den som finns i bilar som säger till när det är dags för service. Som ett första steg i att ta fram en sådan serviceindikator har vi i detta examensarbete utvecklat en algoritm som försöker avgöra statusen på filtret. Resultatet indikerar att möjligheterna att utveckla den önskade serviceindikatorn är mycket lovande, men det krävs fortsatta studier. Algoritmen var ungefär dubbelt så bra som en slumpmässig gissning på att avgöra filtrets status. Speciellt en signal som analyserades visade sig ha en väldigt nära koppling med tillståndet hos filtret. När denna signal studeras närmare gjordes en häpnadsväckande upptäckt. Den ursprungliga tanken var att filtret skulle sättas igen ju mer det användes och därmed få svårare att släppa igenom dialysvätskan. Vad resultatet däremot påvisade var motsatsen, nämligen att det blev lättare för dialysvätskan att passera filtret. Orsaken till detta var svår att finna då det inte fanns möjlighet att undersöka de studerade filterna. Dock fanns misstankar om att det kunde finnas ett samband med användandet av en viss typ av desinfektionsprogram

Parameter Optimization of a Paper Machine Model

In this paper, the problem of calibrating a paper machine dryer section model to measurement data is treated. The model, which is dynamic, nonlinear and of large scale, is implemented in Modelica and Dymola. The purpose of the model is to evaluate, in simulation, new control structures before application to the plant. This approach requires a well calibrated model in order for simulation results to be valid also on the real plant. In this paper, the problem is addressed by parameter optimization. A custom application integrating code generated by Dymola and packages for numerical optimization has been developed. Results are satisfactory, in that the mismatch between the calibrated model response and measured data is small

Kamratgranskning av rapporter i kursen Systemteknik

Traditionellt har examinationen av många kurser på LTH bestått av en skriftlig tentamen efter kursen avslutande. Detta instrument för att mäta och värdera studenternas kunskaper har ofta i stor utsträckning styrt studenternas studievanor, ofta med intensivt tentaläsande som följd. Kamratgranskning, eller ”Peer Review”, är en metod som kan användas som en del i en löpande examination under kursen gång. Metoden bygger på att studenterna utvärderar och ger synpunkter på varandras arbeten, vilket stimulerar till aktivitet och interaktion under en större del av kursen. På Institutionen för Reglerteknik har metoden med gott resultat tillämpas vid rapportskrivning i kursen Systemteknik som ges för tredjeårs­studenterna på Ekosystemteknikprogrammet. Erfarenheterna från det inledande försöket var mycket positiva, vilket lett till att kamratgranskning numera är ett permanent inslag i kursen

Collocation Methods for Optimization in a Modelica Environment

The solution of generic dynamic optimization problems described by Modelica, and its extension Optimica, code using direct collocation methods is discussed. We start by providing a description of dynamic optimization problems in general and how to solve them by means of direct collocation. Next, an existing implementation of a collocation algorithm in JModelica.org, using CasADi and IPOPT, is presented. The extensions made to this implementation are reported. The new implementation is compared to an old C-based collocation algorithm in JModelica.org in two benchmarks. The presented benchmarks are based on a continuously stirred tank reactor and a combined cycle power plant. The new algorithm and its surrounding framework is more flexible and shown to be several times more efficient than its predecessor

Tools and Languages for Modeling and Optimization of Large-Scale Dynamical Systems

High-level modeling languages are receiving increased industrial and academic interest within several domains, such as chemical engineering, thermo-fluid systems and automotive systems. One such modeling language is Modelica. Modelica is an open language, specifically targeted at multi-domain modeling and model re-use. Key features of Modelica include object oriented modeling, declarative equation modeling, a software component model enabling acausal connections of submodels, as well as support for hybrid/discrete behaviour. These features have proven very applicable to large-scale modeling problems in various fields. This contribution gives an overview of a project targeted at i) defining an extension of Modelica, Optimica, which enables high level formulation of optimization problems, ii) developing prototype tools for translating a Modelica model and a complementary Optimica description into a representation suited for numerical algorithms, and iii) performing case studies demonstrating the potential of the concept