Development of linear modulation schemes has opened the way for spectrally efficient, high speed digital communication systems for voice and data applications. A trend has been to develop ultra wide and wide bandwidth modulation formats, which has meant feedback linearisation schemes (both analogue and digital) are no longer effective. This has in turn led to a number of approaches that involve predistorting the signal prior to amplification, with a characteristic that is the inverse to that of the power amplifier (PA). This thesis presents a polynomial based predistortion for linearisation of an RF PA. The predistortion characteristic is adaptive, using the LMS algorithm to minimise the mean squared error between output of the PA, and a scaled version of the baseband signal. This system can reduce third-order intermodulation by 40 dB when running in real time.

A gimbal is a pivoted device that decouples movements of a platform from its payload. The payload is a camera which must be stabilized to capture video without motion disturbances. A challenge with this type of gimbal is that a wide span of cameras with different sizes and weights can be used. The change of camera has significant effect on the dynamics of the gimbal and therefore the control system must be retuned. This tuning is inconvenient, especially for someone without knowledge of control engineering. This thesis reviews suitable methods to perform an automatic controller tuning directly on the gimbal's hardware.This tuning starts by exciting the system and then using data to estimate a model. This model is then used to control the gimbal, thus removing the need for manual tuning of the system. The foundation of this thesis is a physical model of the gimbal, derived through the Lagrange equation. The physical model has undetermined parameters such as inertias, centre of gravity and friction constants. System identification is used to determine these parameters. A problem discussed is how the system should be excited in order to achieve data with as much information as possible about the dynamics. This problem is approached by formulating an optimization problem that can be used find suitable trajectories. The identified model is then used to control the gimbal. Different methods for model based-control are discussed. By using a method called feedback linearisation all of the parameter-dependant dynamics of the gimbal can be compensated for. Apart from being independent of model parameters the new outer system is also decoupled and linear. A PID controller is used for feedback control of the outer system. The uncertainty of the feedback linearisation is analysed to find the effects of model errors.To assure robustness of the closed loop system a Lyapunov redesign controller is used to compensate for these model errors. Some experimental results are also presented. The quality of the estimated model is evaluated. Additionally, the reference tracking performance of the control system is tested and results reveal issues with the estimated model's performance.

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The first loudspeaker was invented almost 150 years ago and even though much has changed regarding the manufacturing, the main idea is still the same. To produce clean sound, modern loudspeaker consist of expensive materials that often need advanced manufacturing equipment. The relatively newly established company Actiwave AB uses digital signal processing to enhance the audio for loudspeakers with poor acoustic properties. Their algorithms concentrate on attenuating the linear distortion but there is no compensation for the loudspeakers' non-linear distortion, such as harmonic distortion. To attenuate the harmonic distortion, this thesis presents controllers based on exact input-output linearisation. This type of controller needs an accurate model of the system. A loudspeaker model has been derived based on the LR-2 model, an extension of the more common Thiele-Small model. A controller based on exact input-output linearisation also needs full state feedback, but since feedback risk being expensive, state estimators were used. The state estimators were based on feed-forward or observers using the extended Kalman filter or the unscented Kalman filter. A combination of feed-forward state estimation and a PID controller were designed as well. In simulations, the total harmonic distortion was attenuated for all controllers up to 180 Hz. The simulations also showed that the controllers are sensitive to inaccurate parameter values in the loudspeaker model. During real-life experiments, the controllers needed to be extended with a model of the used amplifier to function properly. The controllers that were able to attenuate the harmonic distortion were the two methods using feed-forward state estimation. Both controllers showed improvement compared to the uncontrolled case for frequencies up to 40 Hz.

Loudspeakers were invented over 150 years ago, but the loudspeakers used todayare still based on the same ideas. Traditionally, good sound quality has been obtainedby using expensive materials in the loudspeakers and by allowing themto be big. However, nowadays loudspeakers are wanted in applications such asmobile phones and tablets where size and weight are very limited and there is aconstant desire to decrease production costs. Special small loudspeakers, knownas micro loudspeakers, have been developed for this purpose but due to the severerestrictions in size and manufacturing costs, the sound quality in the microloudspeakers is relatively poor. One problem is that the nonlinearities of thesystem, present in any loudspeaker, become more evident in the case of microloudspeakers and cause noticeable distortion of the sound.This master’s thesis has been performed in cooperation with Opalum (formerlyActiwave), a company specializing in using digital signal processing to improvethe sound in loudspeakers with poor acoustic properties. The objective of thethesis is to investigate ways to increase the sound quality in micro loudspeakersby using nonlinear control. Focus has been on frequencies below the resonancefrequency since the distortion is more noticeable at low frequencies. First, a nonlinearmodel of the micro loudspeaker has been obtained using system identificationstrategies. The model describes the relationship between the voltage overthe voice-coil and the diaphragm displacement. Subsequently, input-output linearisationhas been used to design a controller for the system and the effect onthe distortion has been investigated through experiments. Two different modelstructures have been tested, a physical model based on the Thiele-Small modeland a black-box model with a Hammerstein-Wiener structure. In both cases, thenonlinearities were modelled as polynomials. The controller was then extendedwith an updating algorithm, making it adaptive.The efficiency of the controllers has been proved by experiments, where distortionwas decreased by up to 60 % compared to the case without control. The effectwas largest for low frequencies, around one third of the resonance frequency,but improvements were noted up to about two thirds of the resonance frequency,depending on the loudspeaker unit. The approach using a physical model andthat using a black-box model have shown similar results. / Högtalaren uppfanns för över 150 år sedan men de högtalare som används idagbygger till stora delar på samma teknik. Högkvalitativt ljud har traditionellt uppnåttsgenom att ge högtalaren goda akustiska egenskaper genom att tillåta den attvara stor och tillverkad av dyra material. Utmaningen idag ligger i att högtalarefinns inbyggda i exempelvis mobiltelefoner, vilket innebär att de behöver görassmå, lätta och billiga att producera. För att möta dessa krav har kompromisserkrävts vilket gör att dessa små högtalare, kallade mikrohögtalare, har sämre ljudkvalitet.Ett problem är att de olinjäriteter som finns i alla högtalare blir extraframträdande i små högtalare vilket leder till distorsion och övertoner i ljudsignalen.Detta examensarbete är gjort i samarbete med Opalum (tidigare Actiwave), vilketär ett företag som specialiserar sig på att med hjälp av digital signalbehandlingförbättra ljudkvaliteten för högtalare med akustiskt dåliga egenskaper. Syftetmed examensarbetet har varit att minska distorsionen i en mikrohögtalaremed hjälp av olinjär reglering. Fokus har legat på den lägre delen av frekvensbandet,under resonansfrekvensen, eftersom det är där distorsionen är mest märkbar.Först har en olinjär modell av högtalaren tagits fram genom systemidentifiering.Modellen förklarar sambandet mellan spänningen över högtalarens talspole ochmembranets utslag. I ett nästa steg har en regulator designats utifrån modellenoch regulatorns effekt på distorsionen har utvärderats genom experiment. Två olikamodellstrukturer har undersökts, dels en fysikalisk modell baserad på Thiele-Smallmodellen och dels en svartlådemodell med Hammerstein-Wienerstruktur.I båda fallen har olinjäriteterna modellerats som polynom. Regulatorn har sedanutökats med en uppdateringsalgoritm som gör den adaptiv.Experiment har visat att regleringen bidrog till att minska distorsionen med upptill 60 % jämfört med då systemet kördes utan reglering. Effekten har varit störstför låga frekvenser, kring en tredjedel av resonsnsfrekvensen, men förbättringarhar kunnat ses upp till frekvenser kring två tredjedelar av resonansfrekvensen.Både metoden med en fysikalisk modellstruktur och med en svartlådestrukturhar visat likartade resultat.

The development of new types of offshore wind turbine on floating platforms requires the development of new approaches to modelling the combined platform-turbine system. In this thesis a linearised frequency-domain approach is developed which gives fast but approximate results: linearised models of the structural dynamics, hydrodynamics, aerodynamics and control system dynamics are brought together to find the overall response of the floating wind turbine to harmonic wind and wave loading. Initially, a nonlinear flexible multibody dynamics code is developed and verified, which is then used to provide reference nonlinear simulation results. The structural dynamics of a wind turbine on a moving platform are shown to be nonlinear, but for realistic conditions the effects are small. An approximate analysis of the second-order response of floating cylinders to hydrodynamic loads suggests slow drift motion may be relatively small for floating wind turbines, compared to other floating offshore structures. The aerodynamic loads are linearised using both harmonic and tangent linearisation approaches; the harmonic linearisation gives improved results when stall occurs. The wake dynamics can also be included. The control system behaviour is linearised using the same method, which works well when the wind speed is far from the rated wind speed; close to the rated wind speed the nonlinearity is stronger, but further improvement should be possible. These sub-models are combined to give a simple but complete model of a floating wind turbine, with flexible blades and a flexible tower, but neglecting the control system behaviour, wake dynamics and nonlinear hydrodynamic loads. For the OC3-Hywind turbine, the accuracy of the results is assessed by comparison to nonlinear time-domain simulations using the commercial code Bladed. Peak-peak errors of less than 5 % are achievable for many harmonic wind and wave inputs, but certain conditions lead to larger errors. The effect of including linearised control system behaviour is demonstrated for a subset of conditions. Overall, the results are promising but more work is needed for practical application.

Time-Interleaved Analog to Digital Converters (TI ADC) consist of several individual sub-converters operating at a lower sampling rate, working in parallel, and in a circular loop. Thereby, they are increasing the sampling rate without compromising on the resolution during conversion, at high sampling rates. The latter is the main requirement in the area of radio frequency sampling. However, they suffer from mismatches caused by the different characteristics in each sub-converter and the TI structure. The output of the TI ADC under consideration contains a lot of harmonics and spurious tones due to the non-linearities mismatch between the sub-converters. Therefore, previously extensive frequency planning was performed to avoid the input signal from coinciding with these harmonic bins. More importance has been given to digital calibration in recent years where algorithms are developed and implemented outside ADC in a Digital signal processor (DSP), whereas the compensation is done in real time. In this work, we model the distortions and the harmonics present in the TI ADC output to get a clear understanding of the TI ADC. A post-correction block is developed for the cancellation of the characterized harmonics. The suggested method is tested on the TI ADCs working at radio frequencies, but is valid also for other types of ADCs, such as pipeline ADCs and sigma-delta ADCs.

This final year project describes the linearisation method Cartesian feedback and the design of such a feedback with a 2.4GHz power amplifier. To investigate the functionality of the Cartesian feedback ideal blocks with no current consumption were made and then gradually analog circuits were introduced into the feedback. The Cartesian feedback design consists of a subtracter, a modulator and a preamplifier in the top path and a demodulator and a filter in the feedback path. The blocks that are discussed in this report are the subtracter and the modulator unit. The circuits are designed in a 0.35µm SiGe BiCMOS technology. The result of the Cartesian feedback showed an increase in 1dB compression point by 6.2dBm and the IMD was improved by 17dB.

<p>This final year project describes the linearisation method Cartesian feedback and the design of such a feedback with a 2.4GHz power amplifier. </p><p>To investigate the functionality of the Cartesian feedback ideal blocks with no current consumption were made and then gradually analog circuits were introduced into the feedback. The Cartesian feedback design consists of a subtracter, a modulator and a preamplifier in the top path and a demodulator and a filter in the feedback path. The blocks that are discussed in this report are the subtracter and the modulator unit. The circuits are designed in a 0.35µm SiGe BiCMOS technology. </p><p>The result of the Cartesian feedback showed an increase in 1dB compression point by 6.2dBm and the IMD was improved by 17dB.</p>

In this document we review the status of existing techniques for nonlinear model order reduction by investigating how well these techniques perform for typical industrial needs. In particular the TPWL-method (Trajectory Piecewise Linear-method) and the POD-approach (Proper Orthogonal Decomposion) is taken under consideration. We address several questions that are (closely) related to both the theory and application of nonlinear model order reduction techniques. The goal of this document is to provide an overview of available methods together with a classification of nonlinear problems that in principle could be handled by these methods.