The topic of this thesis is the theoretical and numerical research of optimal control problems for uncertain nonlinear systems, described by semilinear parabolic differential equations with additive noise, where the state is not completely available. Based on a paper by Kazufumi Ito and Karl Kunisch, which was published in 2006 with the title "Receding Horizon Control with Incomplete Observations", we analyze a Model Predictive Control (MPC) approach where the resulting linear problems on small intervals are solved with a Linear Quadratic Gaussian (LQG) design. Further we define a performance index for the MPC/LQG approach, find estimates for it and present bounds for the solutions of the underlying Riccati equations. Another large part of the thesis is devoted to extensive numerical studies for an 1+1- and 3+1-dimensional problem to show the robustness of the MPC/LQG strategy. The last part is a generalization of the MPC/LQG approach to infinite-dimensional problems.

Στην διατριβή αυτή μελετήθηκαν και εξακριβώθηκαν θεωρητικά όλες οι φυσικές διεργασίες που υπεισέρχονται στις μετρήσεις του διαμορφωμένου φωτορεύματος. Με βάση αυτές δείξαμε ότι μπορούμε να εξάγουμε όλες τις πιθανές διεργασίες παγίδευσης και επανασύνδεσης σε διάφορες κατηγορίες ανόργανων ημιαγωγών. Σαν μελλοντική μελέτη μπορεί να γίνει η επέκταση της θεωρητικής ανάλυσης για υλικά όπου έχουμε ατέλειες που μπορούν να βρεθούν σε περισσότερες από δύο καταστάσεις φορτίου όπως είναι οι αιωρούμενοι δεσμοί του άμορφου . Επίσης η ανάλυση που προτείνουμε μπορεί να εφαρμοστεί και στην κατηγορία των οργανικών ημιαγωγών. / In this thesis we studied and verified theoretically, all the physical processes involved in modulated photocurrent measurements. Based on these measurements, we show that we can extract all possible trapping and recombination processes in different classes of inorganic semiconductors. As future study, we can extend the theoretical analysis for materials which have defects that may be found in more than two charge states such as the dangling bonds in amorphous silicon. Also, the analysis we propose can be applied to the class of organic semiconductors.

Arbetet har utförts på Saab Bofors Dynamics i Karlskoga och dess syfte var att undersöka om det är möjligt att använda modellbaserad prediktionsreglering, MPC, vid slutfasstyrning av en viss typ av robot. Som referensram används linjärkvadratisk reglering, LQ, eftersom denna reglermetod har undersökts tidigare och visat sig fungera bra vid slutfasstyrning, dock för en annan typ av robot. Anledningen till att man vill undersöka om det är möjligt att använda MPC är att styrlagen enkelt tar hand om begränsningar på systemet på ett direkt och intuitivt sätt. Styrlagarnas uppgift är att styra en robot i dess slutfas då det finns krav och önskemål på roboten som bör vara uppfyllda. Till exempel finns det begränsningar på styrsignalen samt önskemål om att träff ska ske i en viss träffpunkt och även med en viss träffvinkel. För att utvärdera resultaten undersöks och jämförs de två styrlagarnas prestanda och robusthet. För att kunna utvärdera styrlagarnas egenskaper och jämföra dem implementeras de båda i en befintlig detaljerad simuleringsmiljö, som har utvecklats på Saab Bofors Dynamics i Karlskoga. De prestanda och robusthetstester som har utförts uppvisar små skillnader på de två styrlagarna och slutsatsen blir därmed att det är möjligt att använda modellbaserad prediktionsreglering vid slutfasstyrning av en viss typ av robot eftersom det sedan tidigare är känt att linjärkvadratisk reglering är en bra styrlag att använda. För att se vilken av de två styrlagarna som är bäst vid slutfasstyrning av en viss typ av robot behöver det göras vissa ändringar och mer detaljerade undersökningar utföras.

År 2012 gick ca 30 % av den totala energianvändningen till uppvärmning av bostäder och lokaler. Av den utgör uppvärmning av flerbostadshus och lokaler 60 % (79,5 TWh). Det finns därmed stor potential att minska energianvändningen inom bostadssektorn. En del i effektiviseringsarbetet är att se över regleringen av utrustningen som styr uppvärmningssystemen i bostäderna. Dagens reglering innefattar oftast en styrning som är direkt kopplad till utomhustemperaturen. Denna form av reglering lämpar sig bäst till system där ändring av tillstånd kan ske fort. När det gäller bostäder med hög massa tar det däremot tid innan en ändring får effekt. I vissa fall kan trögheten vara bortåt ett dygn för bostäder med hög intern massa. Ett alternativt till dagens enkla metoder är den så kallade MPC-regulatorn som står för Model Predictive Control. MPC är en reglermetod som kan ta hänsyn till trögheten och dynamiken hos byggnader. MPC-regulatorn arbetar dessutom proaktiv snarare än retroaktivt vilket de flesta av dagens reglermetoder gör. Ett problem med MPC-regulatorn är att den kräver stora beräkningsresurser samt energiteknisk kunskap om byggnaden där den ska implementeras. Detta gör att den har haft svårt att slå igenom. Syftet med examensarbetet var därför att konstruera en enkel MPC-regulator och utvärdera dess funktion. Detta gjordes genom att konstruera en bänktestmodell som utvärderade funktionen av regulatorn. Utöver att konstruera en simpel MPC-regulator har en studie gjorts på hur den nuvarande reglermetoden kan energieffektiviseras utan att behöva investera i ny utrustning. Målet var att få en jämn inomhustemperatur och förbättra driftsekonomin för byggnaden som studerades. Studien har genomförts hos Karlstads Bostads Aktiebolag (KBAB) som förvaltar och äger 7300 lägenheter i Karlstad. Studien presenterar ett antal enkla MPC-regulatorer som kan användas för att uppnå jämnare inomhustemperatur och bättre driftsekonomi. Det bedöms dock att den MPC-regulatorn som endast tar hänsyn till utetemperaturen i sin prediktering är den mest lämpliga. MPC-regulatorn har potential att sänka värmebehovet med 3,12 MWh/år (-4 %) och minska inomhustemperaturens variationer med 96 %. Årsmedeltemperaturen skulle hamna på 21,1 °C och energiförbrukningen på 113 kWh/m2. Studien presenterar dessutom ett alternativ till dagens reglermetod som inte kräver några extra resurser eller investeringskostnader. Den har potential att sänka värmebehovet med 8,3 MWh/år (-10 %) och minska inomhustemperaturens variationer med 65 %. Energiförbrukningen skulle då bli 106 kWh/m2 för byggnaden. / In 2012, 30% of the total energy consumption was used by apartments and buildings. Heating of apartment buildings and commercial buildings represents 60% (79.5 TWh) of that energy consumption. There is thus great potential for reducing energy use in the residential sector. Part of the overall efficiency work is to review the control of heating systems. Today's control often involves simple on / off systems where an upper and lower limit controls when to start and stop a process. This form of control is therefore best suited to systems where the change of state occurs quickly. When it comes to homes with high mass however, it takes time before a change takes effect. In some cases, it can take up to 24h before a change is noticed for buildings with high thermal inertia. An alternative to the traditional temperature based control is the so-called MPC controller which stands for Model Predictive Control. MPC is a control method that can take into account the thermal inertia and the dynamics of buildings. MPC controller also controls the system proactive rather than retroactive, which is the technique most of current control methods use. One problem with the MPC controller thou is that it requires large computational resources and technical knowledge of the building where it will be implemented. The aim of the thesis was to design a simple MPC controller and evaluate its performance. This was done by constructing a bench test model that can evaluate the function of the MPC controller. In addition to constructing a simple MPC-controller, a study has been done on how the current control method can be more energy efficient without having to invest in new equipment. The goal was to reduce the variations in indoor temperature and improve operating economics of the building. The study was conducted at Karlstad Bostads Aktiebolag (KBAB) that owns and manages 7,300 apartments in Karlstad. The Bench test model calculated indoor temperature using the weather conditions as solar radiation, cloud cover, outside temperature and wind speed. The study presents a number of simple MPC controllers that can be used to minimize indoor temperature variations and improving operating economy. It is estimated, however, that the MPC controller that only takes into account the outside temperature in its prediction is the most appropriate. The MPC controller has the potential to reduce heating requirements by 3.12 MWh (-4%) and reduce indoor temperature variations with 96%. The mean annual temperature would be 21.1 ° C and the energy consumption 113 kWh/m2 for the building. The study also presents an alternative to current control method that does not require any additional resources or investments. It has the potential to reduce heating requirements by 8.3 MWh (10%) and reduce indoor temperature variations by 65%. The energy consumption would then be 106 kWh/m2.

In this master’s thesis we study how Model Predictive Control (MPC) can be fitted into an existing control system to handle state constraints. We suggest the use of reference governing based on the predictive control methodology. The platform for the survey is Saabs unmanned helicopter Skeldar. We develop and investigate different Reference Governor(RG) formulations that can be used together with the already existing stabilizing control system. These different setups show various features regarding model predictive control. One setup is complemented with a pre-filter to prevent aggressive actuator control in response to set-point changes, while the other is developed to handle this in the MPC framework. We also show that one of these RGs can be extended to guarantee stability and convergence. Implementation and real time requirements are also considered in this thesis. For this two different QP-solvers have been used for online solving of the optimization problem that arises from the MPC formulations. For evaluation and analysis the solutions are implemented in an advanced simulation environment developed at Saab and in a hardware-in-the-loop avionics test rig for the Skeldar system.

Antibiotic-resistant bacteria are increasingly a major healthcare problem but very few new classes of antibiotics have been discovered or launched in recent decades. Approaches to dealing with the problem include learning how bacteria evolve to resistance and improving dosing regimens with current antibiotics so as to reduce the selection of resistant bacteria. This thesis presents studies examining whether antibiotic dosing at high levels can prevent the selection of fluoroquinolone-resistant mutants in Escherichia coli. It also addresses the genetics of fluoroquinolone resistance in E. coli in relation to fitness costs for the resistant bacteria, and the evolution of E. coli to reduce the costs of resistance. The mutant prevention concentration (MPC) of ciprofloxacin was measured for a set of clinical urinary tract infection E. coli strains showing that MPC could not be predicted from the minimum inhibitory concentration (MIC). Results from an in vitro kinetic model showed that an AUC/MPC >22 for ciprofloxacin was the single best pharmacodynamic index that predicted prevention of resistance emergence in the wild-type. Simulating currently approved dosing regimens for three different fluoroquinolones it was found that only a few were effective in preventing the selection of a small sub-population of pre-existing mutants. Step-wise selection of fluoroquinolone resistance showed that the accumulation of mutations usually reduced bacterial fitness in vitro and in vivo. Systematic construction of isogenic resistant strains confirmed this result and revealed that some combinations of resistance mutations mutually compensate and increase both resistance and fitness. It was discovered that mutations altering RNA polymerase could ameliorate the fitness costs of fluoroquinolone resistance. Thus, the major fitness cost of fluoroquinolone resistance is due to defective transcription. The finding that fluoroquinolone resistance mutations can increase resistance while mutually compensating their fitness costs, shows that resistance to fluoroquinolones can continue to evolve in the absence of antibiotic selection.

Sorption Behaviour of Selected Dairy Powder Mixtures: A Study of The Effects of Composition and Mixing Methods Abstract As water mediates physico-chemical reactions (i.e. Maillard reactions, phase changes of sugars and minerals, protein conformational changes), water-powder interactions during storage are critical for dairy powder stability. Therefore, the mechanisms of moisture adsorption from the environment and water distribution among components in the dry state need to be investigated, especially in mixed systems. In order to achieve this goal, the research reported in this thesis had two key objectives. The first was to examine the effect of the sorption properties and phase changes of individual components in relation to the sorption properties of the mixed system. This was achieved by adding three level concentrations of lactose and mineral rich dairy powder (10, 20 and 30%) to Milk Protein Concentrate containing 85% of protein (MPC-85). The second objective was to examine the effect of mixing methods on the sorption behaviour of mixed systems, by applying two different mixing methods, solution mixing and mechanical mixing (particulate mixing). In the solution mixing method, the components were mixed in the same water and then spray dried. In the mechanical mixing method, two individual powder components were physically mixed. For both mixed systems, the kinetics of moisture adsorption were determined at 4 different equilibrium relative humidity levels (22.5, 43.2, 65.4 and 84.3%) and the final equilibrium moisture contents were determined at 8 different equilibrium relative humidity levels (11.3, 22.5, 32.8, 43.2, 52.9, 65.4, 75.3 and 84.3%) at 25°C. The effect of lactose addition to the MPC powder tended to retard the moisture sorption of the mixtures. The increase of concentration level of the lactose that was introduced to the MPC system, through either solution or mechanical mixing, resulted in less moisture adsorption when compared to MPC itself (p-value<0.05). This effect tended to be greater with the increase in relative humidity. A similar effect was observed for MPC/mineral rich milk calcium powder (MC) mixtures. The application of different mixing methods modified the equilibrium moisture content of MPC/Lactose mixtures, even though both mixing methods resulted in similar monolayer moisture value. The monolayer moisture values calculated for both mixing methods were significantly lower than their theoretical values (p-value< 0.05). This suggested that a lactose-protein interaction might exist in both powders prepared by solution and mechanical mixing. Even though the interaction itself is hypothetical, the effect of interaction could be reflected by significant different adsorption rate (p-value < 0.05) of powders produced by different mixing method. A similar type of interaction might exist for the solution mixed MPC/MC system, even though different results were obtained for MPC/MC mixtures prepared by mechanical mixing. The addition of lactose to MPC tended to slow the rate of moisture adsorption. This deceleration might have been contributed to by a reduction of the protein hydration sites by the association of lactose molecules to these sites. In contrast to the MPC/lactose system, the addition of mineral rich MC powder to MPC did not significantly change the rate of adsorption (p-value<0.05). Different mixing methods were found to change the rate of moisture adsorption for the MPC/Lactose systems (p-value<0.05). Even though the mechanically mixed powder adsorbed faster than that of solution mixed powder and X-Ray measurement indicated lactose crystal formation, a drop of moisture during the sorption study was not observed. This suggests that water released during crystallisation might be adsorbed by protein. Meanwhile, the application of two different mixing methods did not modify adsorption rate of MPC/MC system, except for samples stored at RH 84.3%. At this environment, mechanically mixed MPC/MC powders were adsorbed more slowly than the solution mixed powder (p-value<0.05). It might reflect powder compaction or a collapse of the porous structure, leading to limited moisture transfer at the interface. Lactose proportions and different mixing methods influenced the glass-rubber transition temperature (Tg-r) of the MPC/Lactose mixtures. An increase in the proportion of lactose tended to depress Tg-r of the mixtures (p-value<0.05). The Tg-r of the mechanically mixed powder was lower than that of solution mixed powder, presumably on account of the Tg-r for mechanically mixed powder being dominated by phase separated sugar components. Meanwhile, the Tg-r of MPC/MC mixtures was not influenced by either MC proportion or mixing method, particularly for samples stored at below RH 65.4%. The XRD-pattern suggested that the crystal formed during storage of MPC/Lactose mixtures was α-lactose monohydrate. As confirmed by XRD, a drop in moisture for the mixture corresponded to the presence of a peak in the XRD pattern, except for mechanically mixed powder. In this type of powder, even though a peak was detected, a moisture drop was not observed. Within the sensitivity limits of XRD, a crystalline form was not observed for MPC/MC mixtures.

Sorption Behaviour of Selected Dairy Powder Mixtures: A Study of The Effects of Composition and Mixing Methods Abstract As water mediates physico-chemical reactions (i.e. Maillard reactions, phase changes of sugars and minerals, protein conformational changes), water-powder interactions during storage are critical for dairy powder stability. Therefore, the mechanisms of moisture adsorption from the environment and water distribution among components in the dry state need to be investigated, especially in mixed systems. In order to achieve this goal, the research reported in this thesis had two key objectives. The first was to examine the effect of the sorption properties and phase changes of individual components in relation to the sorption properties of the mixed system. This was achieved by adding three level concentrations of lactose and mineral rich dairy powder (10, 20 and 30%) to Milk Protein Concentrate containing 85% of protein (MPC-85). The second objective was to examine the effect of mixing methods on the sorption behaviour of mixed systems, by applying two different mixing methods, solution mixing and mechanical mixing (particulate mixing). In the solution mixing method, the components were mixed in the same water and then spray dried. In the mechanical mixing method, two individual powder components were physically mixed. For both mixed systems, the kinetics of moisture adsorption were determined at 4 different equilibrium relative humidity levels (22.5, 43.2, 65.4 and 84.3%) and the final equilibrium moisture contents were determined at 8 different equilibrium relative humidity levels (11.3, 22.5, 32.8, 43.2, 52.9, 65.4, 75.3 and 84.3%) at 25°C. The effect of lactose addition to the MPC powder tended to retard the moisture sorption of the mixtures. The increase of concentration level of the lactose that was introduced to the MPC system, through either solution or mechanical mixing, resulted in less moisture adsorption when compared to MPC itself (p-value<0.05). This effect tended to be greater with the increase in relative humidity. A similar effect was observed for MPC/mineral rich milk calcium powder (MC) mixtures. The application of different mixing methods modified the equilibrium moisture content of MPC/Lactose mixtures, even though both mixing methods resulted in similar monolayer moisture value. The monolayer moisture values calculated for both mixing methods were significantly lower than their theoretical values (p-value< 0.05). This suggested that a lactose-protein interaction might exist in both powders prepared by solution and mechanical mixing. Even though the interaction itself is hypothetical, the effect of interaction could be reflected by significant different adsorption rate (p-value < 0.05) of powders produced by different mixing method. A similar type of interaction might exist for the solution mixed MPC/MC system, even though different results were obtained for MPC/MC mixtures prepared by mechanical mixing. The addition of lactose to MPC tended to slow the rate of moisture adsorption. This deceleration might have been contributed to by a reduction of the protein hydration sites by the association of lactose molecules to these sites. In contrast to the MPC/lactose system, the addition of mineral rich MC powder to MPC did not significantly change the rate of adsorption (p-value<0.05). Different mixing methods were found to change the rate of moisture adsorption for the MPC/Lactose systems (p-value<0.05). Even though the mechanically mixed powder adsorbed faster than that of solution mixed powder and X-Ray measurement indicated lactose crystal formation, a drop of moisture during the sorption study was not observed. This suggests that water released during crystallisation might be adsorbed by protein. Meanwhile, the application of two different mixing methods did not modify adsorption rate of MPC/MC system, except for samples stored at RH 84.3%. At this environment, mechanically mixed MPC/MC powders were adsorbed more slowly than the solution mixed powder (p-value<0.05). It might reflect powder compaction or a collapse of the porous structure, leading to limited moisture transfer at the interface. Lactose proportions and different mixing methods influenced the glass-rubber transition temperature (Tg-r) of the MPC/Lactose mixtures. An increase in the proportion of lactose tended to depress Tg-r of the mixtures (p-value<0.05). The Tg-r of the mechanically mixed powder was lower than that of solution mixed powder, presumably on account of the Tg-r for mechanically mixed powder being dominated by phase separated sugar components. Meanwhile, the Tg-r of MPC/MC mixtures was not influenced by either MC proportion or mixing method, particularly for samples stored at below RH 65.4%. The XRD-pattern suggested that the crystal formed during storage of MPC/Lactose mixtures was α-lactose monohydrate. As confirmed by XRD, a drop in moisture for the mixture corresponded to the presence of a peak in the XRD pattern, except for mechanically mixed powder. In this type of powder, even though a peak was detected, a moisture drop was not observed. Within the sensitivity limits of XRD, a crystalline form was not observed for MPC/MC mixtures.

Sorption Behaviour of Selected Dairy Powder Mixtures: A Study of The Effects of Composition and Mixing Methods Abstract As water mediates physico-chemical reactions (i.e. Maillard reactions, phase changes of sugars and minerals, protein conformational changes), water-powder interactions during storage are critical for dairy powder stability. Therefore, the mechanisms of moisture adsorption from the environment and water distribution among components in the dry state need to be investigated, especially in mixed systems. In order to achieve this goal, the research reported in this thesis had two key objectives. The first was to examine the effect of the sorption properties and phase changes of individual components in relation to the sorption properties of the mixed system. This was achieved by adding three level concentrations of lactose and mineral rich dairy powder (10, 20 and 30%) to Milk Protein Concentrate containing 85% of protein (MPC-85). The second objective was to examine the effect of mixing methods on the sorption behaviour of mixed systems, by applying two different mixing methods, solution mixing and mechanical mixing (particulate mixing). In the solution mixing method, the components were mixed in the same water and then spray dried. In the mechanical mixing method, two individual powder components were physically mixed. For both mixed systems, the kinetics of moisture adsorption were determined at 4 different equilibrium relative humidity levels (22.5, 43.2, 65.4 and 84.3%) and the final equilibrium moisture contents were determined at 8 different equilibrium relative humidity levels (11.3, 22.5, 32.8, 43.2, 52.9, 65.4, 75.3 and 84.3%) at 25°C. The effect of lactose addition to the MPC powder tended to retard the moisture sorption of the mixtures. The increase of concentration level of the lactose that was introduced to the MPC system, through either solution or mechanical mixing, resulted in less moisture adsorption when compared to MPC itself (p-value<0.05). This effect tended to be greater with the increase in relative humidity. A similar effect was observed for MPC/mineral rich milk calcium powder (MC) mixtures. The application of different mixing methods modified the equilibrium moisture content of MPC/Lactose mixtures, even though both mixing methods resulted in similar monolayer moisture value. The monolayer moisture values calculated for both mixing methods were significantly lower than their theoretical values (p-value< 0.05). This suggested that a lactose-protein interaction might exist in both powders prepared by solution and mechanical mixing. Even though the interaction itself is hypothetical, the effect of interaction could be reflected by significant different adsorption rate (p-value < 0.05) of powders produced by different mixing method. A similar type of interaction might exist for the solution mixed MPC/MC system, even though different results were obtained for MPC/MC mixtures prepared by mechanical mixing. The addition of lactose to MPC tended to slow the rate of moisture adsorption. This deceleration might have been contributed to by a reduction of the protein hydration sites by the association of lactose molecules to these sites. In contrast to the MPC/lactose system, the addition of mineral rich MC powder to MPC did not significantly change the rate of adsorption (p-value<0.05). Different mixing methods were found to change the rate of moisture adsorption for the MPC/Lactose systems (p-value<0.05). Even though the mechanically mixed powder adsorbed faster than that of solution mixed powder and X-Ray measurement indicated lactose crystal formation, a drop of moisture during the sorption study was not observed. This suggests that water released during crystallisation might be adsorbed by protein. Meanwhile, the application of two different mixing methods did not modify adsorption rate of MPC/MC system, except for samples stored at RH 84.3%. At this environment, mechanically mixed MPC/MC powders were adsorbed more slowly than the solution mixed powder (p-value<0.05). It might reflect powder compaction or a collapse of the porous structure, leading to limited moisture transfer at the interface. Lactose proportions and different mixing methods influenced the glass-rubber transition temperature (Tg-r) of the MPC/Lactose mixtures. An increase in the proportion of lactose tended to depress Tg-r of the mixtures (p-value<0.05). The Tg-r of the mechanically mixed powder was lower than that of solution mixed powder, presumably on account of the Tg-r for mechanically mixed powder being dominated by phase separated sugar components. Meanwhile, the Tg-r of MPC/MC mixtures was not influenced by either MC proportion or mixing method, particularly for samples stored at below RH 65.4%. The XRD-pattern suggested that the crystal formed during storage of MPC/Lactose mixtures was α-lactose monohydrate. As confirmed by XRD, a drop in moisture for the mixture corresponded to the presence of a peak in the XRD pattern, except for mechanically mixed powder. In this type of powder, even though a peak was detected, a moisture drop was not observed. Within the sensitivity limits of XRD, a crystalline form was not observed for MPC/MC mixtures.

Sorption Behaviour of Selected Dairy Powder Mixtures: A Study of The Effects of Composition and Mixing Methods Abstract As water mediates physico-chemical reactions (i.e. Maillard reactions, phase changes of sugars and minerals, protein conformational changes), water-powder interactions during storage are critical for dairy powder stability. Therefore, the mechanisms of moisture adsorption from the environment and water distribution among components in the dry state need to be investigated, especially in mixed systems. In order to achieve this goal, the research reported in this thesis had two key objectives. The first was to examine the effect of the sorption properties and phase changes of individual components in relation to the sorption properties of the mixed system. This was achieved by adding three level concentrations of lactose and mineral rich dairy powder (10, 20 and 30%) to Milk Protein Concentrate containing 85% of protein (MPC-85). The second objective was to examine the effect of mixing methods on the sorption behaviour of mixed systems, by applying two different mixing methods, solution mixing and mechanical mixing (particulate mixing). In the solution mixing method, the components were mixed in the same water and then spray dried. In the mechanical mixing method, two individual powder components were physically mixed. For both mixed systems, the kinetics of moisture adsorption were determined at 4 different equilibrium relative humidity levels (22.5, 43.2, 65.4 and 84.3%) and the final equilibrium moisture contents were determined at 8 different equilibrium relative humidity levels (11.3, 22.5, 32.8, 43.2, 52.9, 65.4, 75.3 and 84.3%) at 25°C. The effect of lactose addition to the MPC powder tended to retard the moisture sorption of the mixtures. The increase of concentration level of the lactose that was introduced to the MPC system, through either solution or mechanical mixing, resulted in less moisture adsorption when compared to MPC itself (p-value<0.05). This effect tended to be greater with the increase in relative humidity. A similar effect was observed for MPC/mineral rich milk calcium powder (MC) mixtures. The application of different mixing methods modified the equilibrium moisture content of MPC/Lactose mixtures, even though both mixing methods resulted in similar monolayer moisture value. The monolayer moisture values calculated for both mixing methods were significantly lower than their theoretical values (p-value< 0.05). This suggested that a lactose-protein interaction might exist in both powders prepared by solution and mechanical mixing. Even though the interaction itself is hypothetical, the effect of interaction could be reflected by significant different adsorption rate (p-value < 0.05) of powders produced by different mixing method. A similar type of interaction might exist for the solution mixed MPC/MC system, even though different results were obtained for MPC/MC mixtures prepared by mechanical mixing. The addition of lactose to MPC tended to slow the rate of moisture adsorption. This deceleration might have been contributed to by a reduction of the protein hydration sites by the association of lactose molecules to these sites. In contrast to the MPC/lactose system, the addition of mineral rich MC powder to MPC did not significantly change the rate of adsorption (p-value<0.05). Different mixing methods were found to change the rate of moisture adsorption for the MPC/Lactose systems (p-value<0.05). Even though the mechanically mixed powder adsorbed faster than that of solution mixed powder and X-Ray measurement indicated lactose crystal formation, a drop of moisture during the sorption study was not observed. This suggests that water released during crystallisation might be adsorbed by protein. Meanwhile, the application of two different mixing methods did not modify adsorption rate of MPC/MC system, except for samples stored at RH 84.3%. At this environment, mechanically mixed MPC/MC powders were adsorbed more slowly than the solution mixed powder (p-value<0.05). It might reflect powder compaction or a collapse of the porous structure, leading to limited moisture transfer at the interface. Lactose proportions and different mixing methods influenced the glass-rubber transition temperature (Tg-r) of the MPC/Lactose mixtures. An increase in the proportion of lactose tended to depress Tg-r of the mixtures (p-value<0.05). The Tg-r of the mechanically mixed powder was lower than that of solution mixed powder, presumably on account of the Tg-r for mechanically mixed powder being dominated by phase separated sugar components. Meanwhile, the Tg-r of MPC/MC mixtures was not influenced by either MC proportion or mixing method, particularly for samples stored at below RH 65.4%. The XRD-pattern suggested that the crystal formed during storage of MPC/Lactose mixtures was α-lactose monohydrate. As confirmed by XRD, a drop in moisture for the mixture corresponded to the presence of a peak in the XRD pattern, except for mechanically mixed powder. In this type of powder, even though a peak was detected, a moisture drop was not observed. Within the sensitivity limits of XRD, a crystalline form was not observed for MPC/MC mixtures.