University reports

The fol­lo­wing three reports might be hel­pful for peo­p­le who are inte­res­ted in topics of non-line­ar or adap­ti­ve con­trol and mathe­ma­ti­cal model­ling. Fur­ther mate­ri­al e. g. MATLAB® code is available upon request.

Control of an Inverted Pendulum

The sin­gle inver­ted pen­dulum is a clas­si­cal pro­blem in the the field of non-line­ar con­trol theo­ry. Essen­ti­al­ly, the sys­tem as it is dis­cus­sed here con­sists of a cart and a pen­dulum atta­ched to it. App­ly­ing a force to the cart, for ins­tance through a built-in elec­tri­cal motor, and thus moving it for­wards and back­wards will cau­se the pen­dulum to swing. Howe­ver, model­ling the­se dyna­mics yields a high­ly non-line­ar pro­blem. It is the aim of the con­trol­ler to app­ly the right amount of force which will sta­bi­li­ze the pen­dulum in the upright position.

Con­trol of an Inver­ted Pendulum

Analysis and Performance Evaluation of Model Reference Adaptive Control

In con­trast to clas­si­cal con­trol theo­ry, adap­ti­ve von­trol tech­ni­ques allow to con­trol sys­tems whe­re cer­tain sys­tem para­me­ters are not known
or chan­ge over time, for ins­tance due to chan­ging ope­ra­ting envi­ron­ment. Two methods based on the MIT rule and Lyapu­n­ov rule are deri­ved and then appli­ed to a line­ar first order sys­tem. The sys­tem is simu­la­ted and it is ana­ly­sed how chan­ges to the adapt­a­ti­on gain affect the sys­tem per­for­mance. Last­ly, varia­ti­ons in the refe­rence model para­me­ters, that is chan­ging the desi­red clo­sed-loop beha­viour are examinded.

Model Refe­rence Adap­ti­ve Control

Modelling Chlamydia Transmission Dynamics

In this report, a mathe­ma­ti­cal model is crea­ted to under­stand the dyna­mics of geni­tal Chla­my­dia trachoma­tis infec­tions. By under­stan­ding the dyna­mics of how the infec­tion spreads, the effect of exe­cu­ting a scree­ning pro­gram for 20–24 year olds in Aus­tra­lia can be investigated.

Model­ling Chla­my­dia Trans­mis­si­on Dynamics