M.Ing. / Experimental tests have indicated that limit cycles are likely to occur in hydraulic drive systems, where backlash in the actuator seals is the dominant nonlinearity'. This study primarily deals with the analysis and synthesis of existing hydraulic drive systems to eliminate limit cycles and with establishing a design tool for the design of hydraulic drives with the object of avoiding limit cycles. Most analytical results were verified experimentally. The most general methods for the design of practical nonlinear systems are discussed. It is concluded that some form of synthesis and analysis is necessary, and that the need exists for general methods to evaluate the stability of nonlinear systems and design tools for nonlinear system design. Ageneral procedure of system analysis is given. Amathematical model of the system needs to be obtained, which can be done with the aid of bond graphs. Simulations of complex systems are recommended to verify system performance only. The first procedure of system analysis that should be followed is to systematically identify elements of the system which are not related to the cause of the limit cycle. Experimental testing is a good first step in identifying the non-critical elements. Signal flow diagrams enable the engineer quickly to determine all feedback loops of a complicated system which might be critical. Block diagrams are necessary for the application of nonlinear analysis and synthesis techniques. Hydraulic resonance, where the actuator seal acts as an oscillating mechanism, is identified as a possible cause of the limit cycle. An unusual application of the describing function, where the describing function is applied to optimize the hydraulic supply, is discussed. The transfer function of flow in a hydraulic pipe is given. With the use of the describing function, the gain margin can be studied versus different parameters of the plant. This gives insight into slightly damped conditions of the hydraulic supply that might be the cause of a limit cycle in the system. A control gain does not change the dynamic behaviour of the hydraulic supply, but only amplifies certain natural modes of the system. The design application of the describing function to nonlinear hydraulic drives is discussed. Procedures to eliminate an existing limit cycle and to design a nonlinear hydraulic drive system are proposed. Most important of all, is to design the system so that the natural frequencies of the mechanical structure and the hydraulic supply do not have any common multiples.

This paper was written to investigate whether or not systems theory could be usefully applied to the control of advertising programs in business. A theoretical framework integrating systems, mass communication and advertising was developed and then applied to an existing real-estate marketing firm. It was concluded that the systems approach can be useful in a practical situation but a great deal of work remains to be done in this area. The paper closes with a number of suggestions for future research. / Business, Sauder School of / Graduate

Lyapunov functions are applied to the power system studies. Three types of power system problems are investigated, namely, the determination of asymptotic stability regions of a nonlinear power system for fault and switching transient stability studies, the systematic optimum parameter setting of power system controllers, and the determination of linear and nonlinear optimum stabilising signals as functions of state variables for both nonlinear and linearized power systems. To investigate and construct the transient stability region of a synchronous machine connected to infinite bus through a transmission system after fault and switching, high degree Lyapunov function series generated by Zubov's method is applied. For the optimum parameter setting of a power system, a computation technique based on the method of gradient has been developed to adjust the system parameters simultaneously so as to minimise a system performance function which is evaluated from a Lyapunov function of the second degree. For the computation of the second degree Lyapunov function a method based on the concept of similarity transformation has been developed and applied so that the simultaneous solution of a large number of algebraic equations can be avoided. To determine the optimum stabilizing signals for a power system, the concept of the Lyapunov function of the optimum system is applied. To compute the Lyapunov function of the optimum nonlinear power system, a general iterative scheme and algorithm have been developed. / Applied Science, Faculty of / Electrical and Computer Engineering, Department of / Graduate

A relatively new body of literature dealing with the concept of system has become more noticeable on the horizons of business thought in recent years. At the same time, some of this new systems literature has begun to permeate marketing thinking and is being reflected in the marketing literature. This thesis is concerned with surveying both the systems and marketing literatures in an attempt to establish some consensus as to the usage and understanding of the systems concept when applied to marketing. Due to the very broad possible nature of such a survey, only channels of distribution are involved in a depth surveying. Necessarily, however, the concept of "marketing system" has to be developed in order to integrate the channels of distribution literature with that of marketing and to provide a useful first step in integrating the systems concept into marketing thinking. The research question involves investigation of how the term "system" is employed in the marketing literature dealing with channels of distribution. The methodology employed to conduct the survey involves three major and clearly distinct steps. In the first step the literature dealing with the concept of system is surveyed and an attempt is made to establish a consensus as to the general content of that body of writings. This first step is necessarily brief and, while it is not contended that a consensus from the literature is established, at least a position is taken of describing the nature, meaning, and content of systems. The second step is a transitional one involving an integration of the systems literature with the marketing literature. Thus, a broad framework is established to permit a more detailed integration of particular aspects of marketing with the systems literature. The last step involves a somewhat more detailed survey of the literature dealing with channels of distribution that appears to utilize some aspects of the systems concept. This literature is appraised and evaluated and some statements are made as to how such writings can be improved and clarified. The conclusions that this thesis presents are general in nature. A first step in integrating the marketing literature that can employ the systems concept is provided. At the same time, a great many irregularities and inconsistencies are clarified and some attempts made to correct them. Some suggestions are made as to topics in marketing requiring elaboration before it is possible to talk extensively and meaningfully of the concept of marketing channel systems. Finally, some tenative hypotheses are postulated as to usage of systems concepts in marketing. / Business, Sauder School of / Graduate

Elastic wave propagation in a multilayered crust with causally or acausally attenuating layers is formulated directly in terms of linear systems theory. The solution of the linear systems analog determines the wave motions at the free surface, motions of all internal boundaries and the waveforms propagated into the mantle in response to plane P or S waves generated within the layering or entering into the crust. The particular problem solved is the determination of the response of an n-layered crust to teleseismic P or S waves incident with arbitrary angle at the crustal base. Trivial extensions of this problem would allow reflection solutions. Numerical solutions have been accomplished in both the frequency domain and the time domain. The Fourier solution restricted to a non-attenuating crust is equivalent to the standard Haskell matrix solution of elastic wave equations. Direct time domain solutions allow the syntheses of seismograms considering internal crustal absorption. For demonstration of the utility and advantages of the theory, the linear systems formulation has been applied to studies of the elastic wave response of the central Alberta crust using P waves from 6 teleseismic events. Frequency domain comparisons between the theoretical and experimental spectral amplitude V/H ratios have shown that, although the theoretical effect of attenuation within the crust can be considerable, little improvement in correlations between theory and experiment has been achieved by considering plausible crustal absorption models. Although significant similarities between the theoretical and experimental V/H ratios were found below 2 Hz, little correlation was apparent at higher frequencies. Background and scattering noise partly contributed to this effect and it is also probable that insufficient detail and accuracy was available for the model crustal sections. Time domain synthetic seismograms have been determined which well correspond to the early P coda of several of the experimental records. Assumptions on the event source motions and the mantle properties are required to determine incident P waveforms for these solutions. Causal attenuation within the crustal layering was included. Correlations between the synthetic seismograms and the experimental records has been found to decrease rapidly with time following the P onset. It is suggested that this effect is primarily due to background noise and possible scattering of the waves within the crust. Furthermore, it is probable that the waveforms used for these solutions based on the source motion and mantle attenuation assumptions were not sufficient. A major apparent advantage of the new formulation is that causal and acausal attenuation solutions are permitted in both the frequency and time domains. Also, the large body of communications theory mathematics can now be applied directly to the propagation problem and could prove useful in attempts at the solution of the non-normal incidence inverse problem. / Science, Faculty of / Earth, Ocean and Atmospheric Sciences, Department of / Graduate

Rain fed maize is an important staple food crop for rural communities in Southern Africa as it plays a major role in ensuring food security and improving livelihoods. Rainfall consistency and intensity is an essential requirement for successful maize growing seasons. The variability of intra-seasonal rainfall characteristics such as onset, cessation and wet and dry spells threatens maize yields in Southern Africa. Previous studies have focused on the impacts of seasonal rainfall totals on maize yields. The aim of this study is to investigate the impacts of intra-seasonal rainfall variability on the maize growing season of Limpopo Province, South Africa from 1990 to 2014. A Self-Organizing Map (SOM) is used to identify and distinguish synoptic states and patterns that are conducive for growing maize in the province from those that are not. The SOM is trained using daily mean Geopotential height reanalysis data, composites for rainfall and moisture are then analysed to understand surface responses. CHIRPS daily rainfall data is used to analyse the variability of rainfall characteristics. The relationship between these rainfall characteristics and maize yield is evaluated to assess the impacts of variability on maize yields. The SOM shows that summer maize growing season is characterised by low pressure systems over the mainland which act as tropical sources of moisture and the formation of cloud-bands associated with Tropical Temperate Troughs. There is a trend in late rainfall onset and earlier cessation leading to a shift and shortening of the rainy season. The shifted and shortened rainy seasons are characterised by dry spells and high intensity rainfall events and are potentially more suitable for planting the shorter season maize cultivars. Regardless of these agrometeorological conditions being detrimental to yields, district level and provincially averaged maize yields show an overall increasing trend. This is a result of improved farming methods such as planting drought resistant short season yellow maize cultivars which can withstand dry spells.

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