Distributed parameter systems (DPS) are systems defined on infinite dimensional spaces. This includes problems governed by partial differential equations (PDEs) and delay differential equations. In order to numerically implement a controller for a physical system we often first approximate the PDE and the PDE controller using some finite dimensional scheme. However, control design at this level will typically give rise to controllers that are inherently large-scale. This presents a challenge since we are interested in the design of robust, real-time controllers for physical systems. Therefore, a reduction in the size of the model and/or controller must take place at some point. Traditional methods to obtain lower order controllers involve reducing the model from that for the PDE, and then applying a standard control design technique. One such model reduction technique is balanced truncation. However, it has been argued that this type of method may have an inherent weakness since there is a loss of physical information from the high order, PDE approximating model prior to control design. In an attempt to capture characteristics of the PDE controller before the reduction step, alternative techniques have been introduced that can be thought of as controller reduction methods as opposed to model reduction methods. One such technique is LQG balanced truncation. Only recently has theory for LQG balanced truncation been developed in the infinite dimensional setting. In this work, we numerically investigate the viability of LQG balanced truncation as a suitable means for designing low order, robust controllers for distributed parameter systems. We accomplish this by applying both balanced reduction techniques, coupled with LQG, MinMax and central control designs for the low order controllers, to the cable mass, Klein-Gordon, and Euler-Bernoulli beam PDE systems. All numerical results include a comparison of controller performance and robustness properties of the closed loop systems. / Ph. D.

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In vibration-based damage detection in structures, often changes in the dynamic properties such as natural frequencies, modeshapes, and derivatives of modeshapes are used to identify the damaged elements. If only a partial list of natural frequencies is known, optimization methods may need to be used to identify the damage. In this research, the algorithm proposed by Podlevskyi & Yaroshko (2013) is used to determine the stiffness distribution in shear building models. The lateral load resisting elements are presented as a single equivalent spring, and masses are lumped at floor levels. The proposed method calculates stiffness values directly, i.e., without optimization, from the known partial list of natural frequency data and mass distribution. It is shown that if the number of stories with reduced stiffness is smaller than the number of known natural frequencies, the stories with reduced stiffnesses can be identified. Numerical studies on building models with two stories and four stories are used to illustrate the solution method. Effect of error or noise in given natural frequencies on stiffness estimates and, conversely, sensitivity of natural frequencies to changes in stiffness are studied using 7-, 15-, 30-, and 50-story numerical models. From the studies, it is learnt that as the number of stories increases, the natural frequencies become less sensitive to stiffness changes. Additionally, eight laboratory experiments were conducted on a five-story aluminum structural model. Ten slender columns were used in each story of the specimen. Damage was simulated by removing columns in one, two, or three stories. The method can locate and quantify the damage in cases presented in the experimental studies. It is also applied to a 1/3 scaled 18-story steel moment frame building tested on an earthquake simulator (Suita et al., 2015) to identify the reduction in the stiffness due to fractures of beam flanges. Only the first two natural frequencies are used to determine the reductions in the stiffness since the third mode of the tower is torsional and no reasonable planar spring-mass model can be developed to present all of the translational modes. The method produced possible cases of the softening when the damage was assumed to occur at a single story.

his Disertation thesis involves the creating of the simulation model of the C axis drive over mentioned machine and them verification on the prototype of this machine. C axis is controlled with position feedback. Simulation model was created before the realisation of the machine prototype for the preliminary identification of the dynamic behaviours in the working cycles and them opportunity of the realisation this conception. C axis is constructed with worm gear and is controlled with help of Master-Slave drive. This torque drive eliminates the production backlash in the worm gear. The multifunction turning center, where is used this C axis, is determinate for heavy duty roughing cutting of the forged peaces, where is problem with dynamic stability of the cutting process. Simulation model includes the problems with multi-body mass system, friction on the worm gear, self locking, damping on the worm gear and the optimization of the parametrs for many regulators. Simulation model was verified on the prototype of the machine. Achieved results bring the new knowledge, which are used for simulation complicated machine nodes and this knowledge is used for research and developing of the similar mechatronics system.