Design and implementation of FPGA-based LQ control of active magnetic bearings

The need for high performance, high precision, and energy saving in rotating machinery demands an alternative solution to traditional bearings. Because of the contactless operation principle, the rotating machines employing active magnetic bearings (AMBs) provide many advantages over the traditional ones. The advantages such as contamination-free operation, low maintenance costs, high rotational speeds, low parasitic losses, programmable stiffness and damping, and vibration insulation come at expense of high cost, and complex technical solution. All these properties make the use of AMBs appropriate primarily for specific and highly demanding applications. High performance and high precision control requires model-based control methods and accurate models of the flexible rotor. In turn, complex models lead to high-order controllers and feature considerable computational burden. Fortunately, in the last few years the advancements in signal processing devices provide new perspective on the real-time control of AMBs. The design and the real-time digital implementation of the high-order LQ controllers, which focus on fast execution times, are the subjects of this work. In particular, the control design and implementation in the field programmable gate array (FPGA) circuits are investigated. The optimal design is guided by the physical constraints of the system for selecting the optimal weighting matrices. The plant model is complemented by augmenting appropriate disturbance models. The compensation of the force-field nonlinearities is proposed for decreasing the uncertainty of the actuator. A disturbance-observer-based unbalance compensation for canceling the magnetic force vibrations or vibrations in the measured positions is presented. The theoretical studies are verified by the practical experiments utilizing a custom-built laboratory test rig. The test rig uses a prototyping control platform developed in the scope of this work. To sum up, the work makes a step in the direction of an embedded single-chip FPGA-based controller of AMBs.

DTC-OHJATUN TAHTIKONEKÄYTÖN PYÖRIMISNOPEUSSÄÄDÖN ANALYYSI INTEGROIDUN SIMULOINTIMALLIN AVULLA

Työssä rakennettiin integroitu simulointimalli sähkökäytölle, jonka mekaniikka koostuu joustava-akselisesta kaksimassa systeemistä. Lisäksi tarkasteltiin kyseiselle sähkökäytölle ominaisia piirteitä ja niiden aiheuttamia ongelmia eri sovelluksissa, sekä tutkittiin teollisuudessa yleisesti esiintyvän pyörimisnopeussäädön, PI-säädön, parametrien vaikutusta kyseisen mekaniikan omaaviin sähkökäyttöihin. Taajuusmuuttajalle kehiteltiin yksinkertaistettu simulointimalli, jolla pystytään pienentämään merkittävästi simuloinnin laskenta-aikaa. Vääntövärähtelyiden kompensointiin tutkittiin optimaalista tilasäätöä, jossa Kalman suotimella estimoidaan systeemin tilojen lisäksi myös kuormamomentti ja jossa nopeussäätö suunnitellaan lineaarisella neliöllisellä menetelmällä (Linear Quadratic).

On the Analysis and Control of a Linear Synchronous Servomotor with a Flexible Load

Industry's growing need for higher productivity is placing new demands on mechanisms connected with electrical motors, because these can easily lead to vibration problems due to fast dynamics. Furthermore, the nonlinear effects caused by a motor frequently reduce servo stability, which diminishes the controller's ability to predict and maintain speed. Hence, the flexibility of a mechanism and its control has become an important area of research. The basic approach in control system engineering is to assume that the mechanism connected to a motor is rigid, so that vibrations in the tool mechanism, reel, gripper or any apparatus connected to the motor are not taken into account. This might reduce the ability of the machine system to carry out its assignment and shorten the lifetime of the equipment. Nonetheless, it is usually more important to know how the mechanism, or in other words the load on the motor, behaves. A nonlinear load control method for a permanent magnet linear synchronous motor is developed and implemented in the thesis. The purpose of the controller is to track a flexible load to the desired velocity reference as fast as possible and without awkward oscillations. The control method is based on an adaptive backstepping algorithm with its stability ensured by the Lyapunov stability theorem. As a reference controller for the backstepping method, a hybrid neural controller is introduced in which the linear motor itself is controlled by a conventional PI velocity controller and the vibration of the associated flexible mechanism is suppressed from an outer control loop using a compensation signal from a multilayer perceptron network. To avoid the local minimum problem entailed in neural networks, the initial weights are searched for offline by means of a differential evolution algorithm. The states of a mechanical system for controllers are estimated using the Kalman filter. The theoretical results obtained from the control design are validated with the lumped mass model for a mechanism. Generalization of the mechanism allows the methods derived here to be widely implemented in machine automation. The control algorithms are first designed in a specially introduced nonlinear simulation model and then implemented in the physical linear motor using a DSP (Digital Signal Processor) application. The measurements prove that both controllers are capable of suppressing vibration, but that the backstepping method is superior to others due to its accuracy of response and stability properties.

Centralized Motion Control of a Linear Tooth Belt Drive: Analysis of the Performance and Limitations

A centralized robust position control for an electrical driven tooth belt drive is designed in this doctoral thesis. Both a cascaded control structure and a PID based position controller are discussed. The performance and the limitations of the system are analyzed and design principles for the mechanical structure and the control design are given. These design principles are also suitable for most of the motion control applications, where mechanical resonance frequencies and control loop delays are present. One of the major challenges in the design of a controller for machinery applications is that the values of the parameters in the system model (parameter uncertainty) or the system model it self (non-parametric uncertainty) are seldom known accurately in advance. In this thesis a systematic analysis of the parameter uncertainty of the linear tooth beltdrive model is presented and the effect of the variation of a single parameter on the performance of the total system is shown. The total variation of the model parameters is taken into account in the control design phase using a Quantitative Feedback Theory (QFT). The thesis also introduces a new method to analyze reference feedforward controllers applying the QFT. The performance of the designed controllers is verified by experimentalmeasurements. The measurements confirm the control design principles that are given in this thesis.

Smooth height/age curves from stem analysis with linear programming

[Abstract]

Linear prediction application for modelling the relationships between a large number of stand characteristics of Norway spruce stands

Abstract

Multivariable regression analysis and hot-spot stress approach into fatigue life estimations of welded joints

Kolmen eri hitsausliitoksen väsymisikä arvio on analysoitu monimuuttuja regressio analyysin avulla. Regression perustana on laaja S-N tietokanta joka on kerätty kirjallisuudesta. Tarkastellut liitokset ovat tasalevy liitos, krusiformi liitos ja pitkittäisripa levyssä. Muuttujina ovat jännitysvaihtelu, kuormitetun levyn paksuus ja kuormitus tapa. Paksuus effekti on käsitelty uudelleen kaikkia kolmea liitosta ajatellen. Uudelleen käsittelyn avulla on varmistettu paksuus effektin olemassa olo ennen monimuuttuja regressioon siirtymistä. Lineaariset väsymisikä yhtalöt on ajettu kolmelle hitsausliitokselle ottaen huomioon kuormitetun levyn paksuus sekä kuormitus tapa. Väsymisikä yhtalöitä on verrattu ja keskusteltu testitulosten valossa, jotka on kerätty kirjallisuudesta. Neljä tutkimustaon tehty kerättyjen väsymistestien joukosta ja erilaisia väsymisikä arvio metodeja on käytetty väsymisiän arviointiin. Tuloksia on tarkasteltu ja niistä keskusteltu oikeiden testien valossa. Tutkimuksissa on katsottu 2mm ja 6mm symmetristäpitkittäisripaa levyssä, 12.7mm epäsymmetristä pitkittäisripaa, 38mm symmetristä pitkittäisripaa vääntökuormituksessa ja 25mm/38mm kuorman kantavaa krusiformi liitosta vääntökuormituksessa. Mallinnus on tehty niin lähelle testi liitosta kuin mahdollista. Väsymisikä arviointi metodit sisältävät hot-spot metodin jossa hot-spot jännitys on laskettu kahta lineaarista ja epälineaarista ekstrapolointiakäyttäen sekä paksuuden läpi integrointia käyttäen. Lovijännitys ja murtumismekaniikka metodeja on käytetty krusiformi liitosta laskiessa.

On Modelling, System Identification and Control of Servo-Systems with a Flexible Load

The present study was done with two different servo-systems. In the first system, a servo-hydraulic system was identified and then controlled by a fuzzy gainscheduling controller. The second servo-system, an electro-magnetic linear motor in suppressing the mechanical vibration and position tracking of a reference model are studied by using a neural network and an adaptive backstepping controller respectively. Followings are some descriptions of research methods. Electro Hydraulic Servo Systems (EHSS) are commonly used in industry. These kinds of systems are nonlinearin nature and their dynamic equations have several unknown parameters.System identification is a prerequisite to analysis of a dynamic system. One of the most promising novel evolutionary algorithms is the Differential Evolution (DE) for solving global optimization problems. In the study, the DE algorithm is proposed for handling nonlinear constraint functionswith boundary limits of variables to find the best parameters of a servo-hydraulic system with flexible load. The DE guarantees fast speed convergence and accurate solutions regardless the initial conditions of parameters. The control of hydraulic servo-systems has been the focus ofintense research over the past decades. These kinds of systems are nonlinear in nature and generally difficult to control. Since changing system parameters using the same gains will cause overshoot or even loss of system stability. The highly non-linear behaviour of these devices makes them ideal subjects for applying different types of sophisticated controllers. The study is concerned with a second order model reference to positioning control of a flexible load servo-hydraulic system using fuzzy gainscheduling. In the present research, to compensate the lack of dampingin a hydraulic system, an acceleration feedback was used. To compare the results, a pcontroller with feed-forward acceleration and different gains in extension and retraction is used. The design procedure for the controller and experimental results are discussed. The results suggest that using the fuzzy gain-scheduling controller decrease the error of position reference tracking. The second part of research was done on a PermanentMagnet Linear Synchronous Motor (PMLSM). In this study, a recurrent neural network compensator for suppressing mechanical vibration in PMLSM with a flexible load is studied. The linear motor is controlled by a conventional PI velocity controller, and the vibration of the flexible mechanism is suppressed by using a hybrid recurrent neural network. The differential evolution strategy and Kalman filter method are used to avoid the local minimum problem, and estimate the states of system respectively. The proposed control method is firstly designed by using non-linear simulation model built in Matlab Simulink and then implemented in practical test rig. The proposed method works satisfactorily and suppresses the vibration successfully. In the last part of research, a nonlinear load control method is developed and implemented for a PMLSM with a flexible load. The purpose of the controller is to track a flexible load to the desired position reference as fast as possible and without awkward oscillation. The control method is based on an adaptive backstepping algorithm whose stability is ensured by the Lyapunov stability theorem. The states of the system needed in the controller are estimated by using the Kalman filter. The proposed controller is implemented and tested in a linear motor test drive and responses are presented.

Non-Linear Journal Bearing Model for Analysis of Superharmonic Vibrations of Rotor Systems

A rotating machine usually consists of a rotor and bearings that supports it. The nonidealities in these components may excite vibration of the rotating system. The uncontrolled vibrations may lead to excessive wearing of the components of the rotating machine or reduce the process quality. Vibrations may be harmful even when amplitudes are seemingly low, as is usually the case in superharmonic vibration that takes place below the first critical speed of the rotating machine. Superharmonic vibration is excited when the rotational velocity of the machine is a fraction of the natural frequency of the system. In such a situation, a part of the machine’s rotational energy is transformed into vibration energy. The amount of vibration energy should be minimised in the design of rotating machines. The superharmonic vibration phenomena can be studied by analysing the coupled rotor-bearing system employing a multibody simulation approach. This research is focused on the modelling of hydrodynamic journal bearings and rotorbearing systems supported by journal bearings. In particular, the non-idealities affecting the rotor-bearing system and their effect on the superharmonic vibration of the rotating system are analysed. A comparison of computationally efficient journal bearing models is carried out in order to validate one model for further development. The selected bearing model is improved in order to take the waviness of the shaft journal into account. The improved model is implemented and analyzed in a multibody simulation code. A rotor-bearing system that consists of a flexible tube roll, two journal bearings and a supporting structure is analysed employing the multibody simulation technique. The modelled non-idealities are the shell thickness variation in the tube roll and the waviness of the shaft journal in the bearing assembly. Both modelled non-idealities may cause subharmonic resonance in the system. In multibody simulation, the coupled effect of the non-idealities can be captured in the analysis. Additionally one non-ideality is presented that does not excite the vibrations itself but affects the response of the rotorbearing system, namely the waviness of the bearing bushing which is the non-rotating part of the bearing system. The modelled system is verified with measurements performed on a test rig. In the measurements the waviness of bearing bushing was not measured and therefore it’s affect on the response was not verified. In conclusion, the selected modelling approach is an appropriate method when analysing the response of the rotor-bearing system. When comparing the simulated results to the measured ones, the overall agreement between the results is concluded to be good.

Control of permanent magnet linear synchronous motor in motion control applications

The aim of the thesis is to study the principles of the permanent magnet linear synchronous motor (PMLSM) and to develop a simulator model of direct force controlled PMLSM. The basic motor model is described by the traditional two-axis equations. The end effects, cogging force and friction model are also included into the final motor model. Direct thrust force control of PMLSM is described and modelled. The full system model is proven by comparison with the data provided by the motor manufacturer.