Legged robots have the potential to be a valuable technology that provides agile and adaptive locomotion over complex terrain. To realize legged locomotion's full abilities a control design must consider the nonlinear piecewise dynamics of the systems. This paper aims to develop a controller for the planar bounding of a quadrupedal robot. The bounding of the quadruped robot is characterized by a simplified hybrid model that consists of two subsystems for stance and flight phases and the switching laws between the two states. An additional model, the Multibody model, with fewer simplifications, is used concurrently to best approximate real-world behavior. The bounding gait (periodic orbit) of the robot is predicted by an optimization method based on the numerical integration of the differential equations of subsystems. To stabilize the gait, a switching controller is applied which can be split into two separate phases: stance-phase and swing-phase control. The stance phase implements reaction force control utilizing a body state feedback controller and a gait stabilizer, while the swing phase deploys position control in conjunction with a trajectory planning algorithm to ensure proper footfall. Numerical simulations are carried out for the system with/without control. The control strategy is further validated by simulations of the Simscape multibody model. The overall simulated controller results are promising and demonstrate stable bounding for four system cycles.

Laser interferometry, commonly used in high-precision motion control systems, is rarely adopted in experimental vibration analysis because its installation and mounting is invasive to dynamical systems. However, metrology systems that already utilize laser interferometry, such as profilometry in semiconductor manufacturing, may benefit from interferometer feedback for signal processing. This study investigates the use of laser interferometry for system identification through a piezoelectrically actuated cantilevered beam. The model of the beam including piezo actuators and optical measurement components are established through the Euler-Bernoulli beam theory. From the method of separation of variables, the continuous system is transformed into a discrete system represented in a state-space form. By performing the Laplace transformation of the state-space form, we obtain the analytical transfer function of interferometer displacement versus actuator input, which is then validated numerically and experimentally. Adaptive filters based on FIR and IIR are designed to identify the transfer function. Because of the slow convergence of such filters, a recursive LMS algorithm is designed to accelerate computation. It is experimentally demonstrated that the precision measurement of interferometer can lead to highly accurate results of system identification.

<ul> <li>Energy Optimization Stategies</li> <li>Hydraulic Models for Water Distribution Systems</li> <li>Heuristic Multi-objective Optimization Algorithms</li> <li>Multi-objective Optimization Problems</li> <li>System Constraints</li> <li>Encoding Techniques</li> <li>Optimal Pumping Operations</li> <li>Sovling Real-World Optimization Problems </li> </ul> / <p>The water supply industry is a very important element of a modern economy; it represents a key element of urban infrastructure and is an integral part of our modern civilization. Billions of dollars per annum are spent internationally in pumping operations in rural water distribution systems to treat and reliably transport water from source to consumers.</p> <p>In this dissertation, a new multi-objective optimization approach referred to as energy optimization strategy is proposed for minimizing electrical energy consumption for pumping, the cost, pumps maintenance cost, and the cost of maximum power peak, while optimizing water quality and operational reliability in rural water distribution systems. Minimizing the energy cost problem considers the electrical energy consumed for regular operation and the cost of maximum power peak. Optimizing operational reliability is based on the ability of the network to provide service in case of abnormal events (e.g., network failure or fire) by considering and managing reservoir levels. Minimizing pumping costs also involves consideration of network and pump maintenance cost that is imputed by the number of pump switches. Water quality optimization is achieved through the consideration of chlorine residual during water transportation.</p> <p>An Adaptive Parallel Clustering-based Multi-objective Particle Swarm Optimization (APC-MOPSO) algorithm that combines the existing and new concept of Pareto-front, operating-mode specification, selecting-best-efficiency-point technique, searching-for-gaps method, and modified K-Means clustering has been proposed. APC-MOPSO is employed to optimize the above-mentioned set of multiple objectives in operating rural water distribution systems.</p> <p>Saskatoon West is, a rural water distribution system, owned and operated by Sask-Water (i.e., is a statutory Crown Corporation providing water, wastewater and related services to municipal, industrial, government, and domestic customers in the province of Saskatchewan). It is used to provide water to the city of Saskatoon and surrounding communities. The system has six main components: (1) the pumping stations, namely Queen Elizabeth and Aurora; (2) The raw water pipeline from QE to Agrium area; (3) the treatment plant located within the Village of Vanscoy; (4) the raw water pipeline serving four major consumers, including PCS Cogen, PCS Cory, Corman Park, and Agrium; (5) the treated water pipeline serving a domestic community of Village of Vanscoy; and (6) the large Agrium community storage reservoir.</p> <p>In this dissertation, the Saskatoon West WDS is chosen to implement the proposed energy optimization strategy. Given the data supplied by Sask-Warer, the scope of this application has resulted in savings of approximately 7 to 14% in energy costs without adversely affecting the infrastructure of the system as well as maintaining the same level of service provided to the Sask-Water’s clients.</p> <p>The implementation of the energy optimization strategy on the Saskatoon West WDS over 168 hour (i.e., one-week optimization period of time) resulted in savings of approximately 10% in electrical energy cost and 4% in the cost of maximum power peak. Moreover, the results showed that the pumping reliability is improved by 3.5% (i.e., improving its efficiency, head pressure, and flow rate). A case study is used to demonstrate the effectiveness of the multi-objective formulations and the solution methodologies, including the formulation of the system-operational optimization problem as five objective functions. Beside the reduction in the energy costs, water quality, network reliability, and pumping characterization are all concurrently enhanced as shown in the collected results. The benefits of using the proposed energy optimization strategy as replacement for many existing optimization methods are also demonstrated.</p> / Doctor of Science (PhD)

It is shown that the relationship between an impedance change and the dynamic response of a linear system is in the form of the Moebius transformation. The Moebius transformation is a conformal complex transformation that maps straight lines and circles in one complex plane into straight lines and circles in another complex plane. The center and radius of the mapped circle can be predicted provided that all the complex coefficients are known. This feature enables rapid determination of the optimal impedance change to achieve desired performance. This dissertation is primarily focused on the application of the Moebius transformation to enhance vibro-acoustic performance of exhaust systems and expedite the assessment due to modifications. It is shown that an optimal acoustic impedance change can be made to improve both structural and acoustic performance, without increasing the overall dimension and mass of the exhaust system. Application examples include mufflers and enclosures. In addition, it is demonstrated that the approach can be used to assess vibration isolators. In many instances, the source properties (source strength and source impedance) will also greatly influence exhaust system performance through sound reflections and resonances. Thus it is of interest to acoustically characterize the sources and assess the sensitivity of performance towards source impedance. In this dissertation, the experimental characterization of source properties is demonstrated for a diesel engine. Moreover, the same approach can be utilized to characterize other sources like refrigeration systems. It is also shown that the range of variation of performance can be effectively determined given the range of source impedance using the Moebius transformation. This optimization approach is first applied on conventional single-inlet single-outlet exhaust systems and is later applied to multi-inlet multi-outlet (MIMO) systems as well, with proper adjustment. The analytic model for MIMO systems is explained in details and validated experimentally. The sensitivity of MIMO system performance due to source properties is also investigated using the Moebius transformation.

The goal of this dissertation consists of improving the efficiency of energy harvesting using pyroelectric and piezoelectric materials in a system by the proper characterization of electrical parameters, widening frequency, and coupling of both effects with the appropriate parameters. A new simple stand-alone method of characterizing the impedance of a pyroelectric cell has been demonstrated. This method utilizes a Pyroelectric single pole low pass filter technique, PSLPF. Utilizing the properties of a PSLPF, where a known input voltage is applied and capacitance Cp and resistance Rp can be calculated at a frequency of 1 mHz to 1 Hz. This method demonstrates that for pyroelectric materials the impedance depends on two major factors: average working temperature, and the heating rate. Design and implementation of a hybrid approach using multiple piezoelectric cantilevers is presented. This is done to achieve mechanical and electrical tuning, along with bandwidth widening. In addition, a hybrid tuning technique with an improved adjusting capacitor method was applied. An toroid inductor of 700 mH is shunted in to the load resistance and shunt capacitance. Results show an extended frequency range up to 12 resonance frequencies (300% improvement) with improved power up to 197%. Finally, a hybrid piezoelectric and pyroelectric system is designed and tested. Using a voltage doubler, circuit for rectifying and collecting pyroelectric and piezoelectric voltages individually is proposed. The investigation showed that the hybrid energy is possible using the voltage doubler circuit from two independent sources for pyroelectrictity and piezoelectricity due to marked differences of optimal performance.

Empirical models based on flow resistivity are commonly used to determine the bulk properties of porous sound absorbing materials. The bulk properties include the complex wavenumber and complex characteristic impedance which can be used directly in simulation models. Moreover, the bulk properties can also be utilized to determine the normal incidence sound absorption and specific acoustic impedance for sound absorbing materials of any thickness and for design of layered materials. The sound absorption coefficient of sound absorbing materials is measured in an impedance tube using wave decomposition and the measured data is used to determine the flow resistivity of the materials by least squares curve fitting to empirical equations. Results for several commonly used foams and fibers are tabulated to form a rudimentary materials database. The same approach is then used to determine the flow resistivity of compressed sound absorbing materials. The flow resistivities of the compressed materials are determined as a function of the compression ratio. Results are then used in conjunction with transfer matrix theory to predict the sound absorptive performance of layered compressed absorbers with good agreement to measurement.

Partial enclosures are commonly used to reduce machinery noise. However, it is well known in industry that enclosures sometimes amplify the sound at low frequencies due to strong acoustic resonances compromising the performance. These noise issues are preventable if predicted prior to prototyping and production. Though boundary and finite element approaches can be used to accurately predict partial enclosure insertion loss, modifications to the model require time for remeshing and solving. In this work, partial enclosure performance at low frequencies is simulated using a plane wave transfer matrix approach. Models can be constructed and the effect of design modifications can be predicted rapidly. Results are compared to finite element analysis and measurement with good agreement. The approach is then used to design and place resonators into a sample enclosure. Improvements in enclosure performance are predicted using plane wave simulation, compared with acoustic finite element analysis, and then validated via measurement.

Scale modeling has been commonly used for architectural acoustics but use in other noise control areas is nominal. Acoustic scale modeling theory is first reviewed and then feasibility for small-scale applications, such as is common in the electronics industry, is investigated. Three application cases are used to examine the viability. In the first example, a scale model is used to determine the insertion loss of a rectangular barrier. In the second example, the transmission loss through parallel tubes drilled through a cylinder is measured and results are compared to a 2.85 times scale model with good agreement. The third example is a rectangular cuboid with a smaller cylindrical well bored into it. A point source is placed above the cuboid. The transfer function was measured between positions on the top of the cylinder and inside of the cylindrical well. Treatments were then applied sequentially including a cylindrical barrier around the well, a membrane cover over the opening, and a layer of sound absorption over the well. Results are compared between the full scale and a 5.7 times scale model and correlation between the two is satisfactory.

Mufflers and silencers are commonly used to attenuate noise sources such as internal combustion engines and HVAC systems. Typically, these environments contain mean flow that can affect the acoustic properties of the muffler components and may produce flow generated noise. To characterize the muffler performance, common metrics such as insertion and transmission loss and noise reduction are used in industry. Though transmission loss without flow is often measured and is a relatively simple bench top experiment and useful for model validation purposes, mean flow can significantly affect the muffler performance. There are a few existing and commercial transmission loss rigs that incorporate flow into the measurement procedure. These rigs are useful for model verification including flow but do not predict how the muffler will perform in the system since the source, termination, and pipe lengths significantly impact performance. In this research, the development of an insertion loss test rig is detailed. This testing strategy has the advantage of being simpler, quantifying the self-generated noise due to flow, and taking into account the effect of tailpipe length and a realistic termination. However, the test does not include the actual source and is not as useful for model validation. An electric blower produces the flow and a silencer quiets the flow. Loudspeakers are positioned just downstream of the flow silencer and they are used as the sound source. The low frequency source is a subwoofer installed in a cylindrical enclosure that includes a conical transition from speaker to pipe. Special care is taken to reduce any flow generated noise. Qualification of the system is detailed by comparing the measured transmission loss, noise reduction, and insertion loss to one-dimensional plane wave models. The results demonstrate that the developed rig should be useful as a muffler evaluation tool after a prototype has been constructed. The rig can also be used for transmission loss and noise reduction determination which will prove beneficial for laboratory testing.

The goal of this thesis is to use the Cal Poly Spacecraft Attitude Dynamics Simulator to provide proof of concept of two adaptive control theories developed by former Cal Poly students: Nonlinear Direct Model Reference Adaptive Control and Adaptive Output Feedback Control. The Spacecraft Attitude Dynamics Simulator is a student-built air bearing spacecraft simulator controlled by four reaction wheels in a pyramidal arrangement. Tests were performed to determine the effectiveness of the two adaptive control theories under nominal operating conditions, a “plug-and-play” spacecraft scenario, and under simulated actuator damage. Proof of concept of the adaptive control theories applied to attitude control of a spacecraft is provided. The adaptive control theories are shown to attain similar or improved performance over a Full State Feedback controller. However, the measurement capabilities of the simulator need to be improved before strong comparisons between the adaptive controllers and Full State Feedback can be achieved.