This thesis studies in detail the dynamics of ball screw feed drives and expands understanding of the factors that impose limitations on their performance. This knowledge is then used for developing control strategies that provide adequate command following and disturbance rejection. High performance control strategies proposed in this thesis are designed for, and implemented on, a custom-made ball screw drive. A hybrid Finite Element (FE) model for the ball screw drive is developed and coded in Matlab programming language. This FE model is employed for prediction of natural frequencies, mode shapes, and Frequency Response Functions (FRFs) of the ball screw setup. The accuracy of FRFs predicted for the ball screw mechanism alone is validated against the experimental measurements obtained through impact hammer testing. Next, the FE model for the entire test setup is validated. The dynamic characteristics of the actuator current controller are also modeled. In addition, the modal parameters of the mechanical structure are extracted from measured FRFs, which include the effects of current loop dynamics. To ensure adequate command following and disturbance rejection, three motion controllers with active vibration damping capability are developed. The first is based on the sensor averaging concept which facilitates position control of the rigid body dynamics. Active damping is added to suppress vibrations. To achieve satisfactory steady state response, integral action over the tracking error is included. The stability analysis and tuning procedure for this controller is presented together with experimental results that prove the effectiveness of this method in high-speed tracking and cutting applications. The second design uses the pole placement technique to move the real component of two of the oscillatory poles further to the left along the real axis. This yields a faster rigid body response with less vibration. However, the time delay from the current loop dynamics imposes a limitation on how much the poles can be shifted to the left without jeopardizing the system???s stability. To overcome this issue, a lead filter is designed to recover the system phase at the crossover frequency. When designing the Pole Placement Controller (PPC) and the lead filter concurrently, the objective is to minimize the load side disturbance response against the disturbances. This controller is also tested in high-speed tracking and cutting experiments. The third control method is developed around the idea of using the pole placement technique for active damping of not only the first mode of vibration, but also the second and third modes as well. A Kalman filter is designed to estimate a state vector for the system, from the control input and the position measurements obtained from the rotary and linear encoders. The state estimates are then fed back to the PPC controller. Although for this control design, promising results in terms of disturbance rejection are obtained in simulations, the Nyquist stability analysis shows that the closed loop system has poor stability margins. To improve the stability margins, the McFarlane-Glover robustness optimization method is attempted, and as a result, the stability margins are improved, but at the cost of degraded performance. The practical implementation of the third controller, was, unfortunately, not successful. This thesis concludes by addressing the problem of harmonic disturbance rejection in ball screw drives. It is shown that for cases where a ball screw drive is subject to high-frequency disturbances, the dynamic positioning accuracy of the ball screw drive can be improved significantly by adopting an additional control scheme known as Adaptive Feedforward Cancellation (AFC). Details of parameter tuning and stability analysis for AFC are presented. At the end, successful implementation and effectiveness of AFC is demonstrated in applications involving time periodic or space periodic disturbances. The conclusions drawn about the effectiveness of the AFC are based on results obtained from the high-speed tracking and end-milling experiments.

Small Unmanned Aerial Vehicles (UAVs) have seen continual growth in both research and commercial applications. Attractive features such as their small size, light weight and low cost are a strong driver of this growth. However, these factors also bring about some drawbacks. The light weight and small size means that small UAVs are far more susceptible to performance degradation from factors such as wind gusts. Due to the generally low cost, available sensors are somewhat limited in both quality and available measurements. For example, it is very unlikely that angle of attack is sensed by a small UAV. These aircraft are usually constructed by the end user, so a tangible amount of variation will exist between different aircraft of the same type. Depending on application, additional variation between flights from factors such as battery placement or additional sensors may exist. This makes the application of optimal model based control methods difficult. Research literature on the topic of small UAV control is very rich in regard to high level control, such as path planning in wind. A common assumption in such literature is the existence of a low level control method which is able to track demanded aircraft attitudes to complete a task. Design of such controllers in the presence of significant wind or modelling errors (factors collectively addressed as lumped disturbances herein) is rarely considered. Disturbance Observer Based Control (DOBC) is a means of improving the robustness of a baseline feedback control scheme in the presence of lumped disturbances. The method allows for the rejection of the influence of unmeasurable disturbances much more quickly than traditional integral control, while also enabling recovery of nominal feedback con- trol performance. The separation principle of DOBC allows for the design of a nominal feedback controller, which does not need to be robust against disturbances. A DOBC augmentation can then be applied to ensure this nominal performance is maintained even in the presence of disturbances. This method offers highly attractive properties for control design, and has seen a large rise in popularity in recent years. Current literature on this subject is very often conducted purely in simulation. Ad- ditionally, very advanced versions of DOBC control are now being researched. To make the method attractive to small UAV operators, it would be beneficial if a simple DOBC design could be used to realise the benefits of this method, as it would be more accessible and applicable by many. This thesis investigates the application of a linear state space disturbance observer to low level flight control of a small UAV, along with developments of the method needed to achieve good performance in flight testing. Had this work been conducted purely in simulation, it is likely many of the difficulties encountered would not have been addressed or discovered. This thesis presents four main contributions. An anti-windup method has been devel- oped which is able to alleviate the effect of control saturation on the disturbance observer dynamics. An observer is designed which explicitly considers actuator dynamics. This development was shown to enable faster observer estimation dynamics, yielding better disturbance rejection performance. During initial flight testing, a significant aeroelastic oscillation mode was discovered. This issue was studied in detail theoretically, with a pro- posed solution developed and applied. The solution was able to fully alleviate the effect in flight. Finally, design and development of an over-actuated DOBC method is presented. A method for design of DOBC for over actuated systems was developed and studied. The majority of results in this thesis are demonstrated with flight test data.

This research investigates the harmonic and narrowband disturbance rejection problem for linear time-periodic (LTP) systems. The consequence of disturbances on LTP systems is similar to their linear time-invariant (LTI) counterparts, but is complicated by the interaction of the disturbance and plant acting at different frequencies, which manifests itself in the modulation of the disturbance signal. The result, for an m-periodic plant and disturbance containing a single tone, is that the output contains m tones. Using various disturbance rejection architectures, harmonic and narrowband disturbance rejection is investigated for linear time-periodic plants. Included are classical and multivariable feedback controllers, fixed-gain feedforward designs using finite impulse response (FIR) filters and H-infinity synthesis tools, and adaptive feedforward controllers. The objective of time-periodic, narrowband, disturbance rejection seeks to place a zero in the controlled system's disturbance path and align the zero direction, defined by the null space of the controlled system at the disturbance frequency, with the disturbance. In this research, constraints on controlled system infinity-norms specify nominal performance and robust stability objectives. Periodic controllers are found using existing LTI H-infinity control theory, and causality is satisfied using two techniques which can be added easily to H-infinity solvers: loop-shifting and Q-parameterization. The resulting controllers are high-gain, narrowband-pass, periodic filters; the closed-loop sensitivity has a zero at the disturbance frequency, and the disturbance is in the sensitivity's null space. It is also shown that classical designs do not achieve the same performance levels as periodic controllers. Similar developments are made using the feedforward disturbance rejection architecture. Objectives are given which minimize the weighted infinity-norm of the controlled system. Such feedforward controllers achieve perfect disturbance rejection. A multivariable equivalent of the tapped-delay line is used in the description of periodic FIR filters. In addition, periodic FIR filters are made adaptive using an algorithm similar to filtered-X least mean square (LMS) but modified for periodic systems. / Ph. D.

An alternate method for mitigating the depredating physiological affects of a soldiers marksmanship due to combat stressors can be achieved through the design and implementation of a active stabilization system for small arms weapons. The INSTAR system is an innovative active stabilization system designed to decouple the shooter's disturbance effects from the barrel movement. The INSTAR system uses an piezoelectric actuator separating the barrel of the rifle from its stock to stabilize barrel movement. This paper uses various control techniques to develop control algorithms for simulation. The level of performance for each control algorithm is based on how well each they measure up to the criteria developed from the INSTAR system. This paper furthers research on INSTAR by developing and comparing four control designs that may be implemented within the INSTAR system. / Master of Science

In a roll-to-roll web system lateral motion of a web caused by disturbances, which are often periodic, results in poor product quality. To reduce the effect of such disturbances, two control strategies are applied. First, the internal model principle is used to reject a sinusoidal disturbance. Second, repetitive control theory is used to reject a general periodic disturbance. We provide the synthesis procedure for both strategies, and demonstrate its use in several simulation studies on a five-roller web system. The simulation results show that the effect of disturbances, either sinusoidal or triangular, on lateral motion are significantly reduced with the internal model controller or the modified repetitive controller.

This thesis focuses on deadbeat disturbance rejection for discrete-time linear multi-agent systems. The multi-agent systems, on which Spieser and Shams’ decentralized deadbeat output regulation problem is based, are extended by including disturbance agents. Specifically, we assume that there are one or more disturbance agents interacting with the plant agents in some known manner. The disturbance signals are assumed to be unmeasured and, for simplicity, constant. Control agents are introduced to interact with the plant agents, and each control agent is assigned a target plant agent. The goal is to drive the outputs of all plant agents to zero in finite time, despite the presence of the disturbances. In the decentralized deadbeat output regulation problem, two analysis schemes were introduced: targeting analysis, which is used to determine whether or not control laws can be found to regulate, not all the agents, but only the target agents; and growing analysis, which is used to determine the behaviour of all the non-target agents when the control laws are applied. In this thesis these two analyses are adopted to the deadbeat disturbance rejection problem. A new necessary condition for successful disturbance rejection is derived, namely that a control agent must be connected to the same plant agent to which a disturbance agent is connected. This result puts a bound on the minimum number of control agents and constraints the locations of control agents. Then, given the premise that both targeting and growing analyses succeed in the special case where the disturbances are all ignored, a new control approach is proposed for the linear case based on the idea of integral control and the regulation methods of Spieser and Shams. Preliminary studies show that this approach is also suitable for some nonlinear systems.

In a roll-to-roll web system lateral motion of a web caused by disturbances, which are often periodic, results in poor product quality. To reduce the effect of such disturbances, two control strategies are applied. First, the internal model principle is used to reject a sinusoidal disturbance. Second, repetitive control theory is used to reject a general periodic disturbance. We provide the synthesis procedure for both strategies, and demonstrate its use in several simulation studies on a five-roller web system. The simulation results show that the effect of disturbances, either sinusoidal or triangular, on lateral motion are significantly reduced with the internal model controller or the modified repetitive controller.

This thesis focuses on deadbeat disturbance rejection for discrete-time linear multi-agent systems. The multi-agent systems, on which Spieser and Shams’ decentralized deadbeat output regulation problem is based, are extended by including disturbance agents. Specifically, we assume that there are one or more disturbance agents interacting with the plant agents in some known manner. The disturbance signals are assumed to be unmeasured and, for simplicity, constant. Control agents are introduced to interact with the plant agents, and each control agent is assigned a target plant agent. The goal is to drive the outputs of all plant agents to zero in finite time, despite the presence of the disturbances. In the decentralized deadbeat output regulation problem, two analysis schemes were introduced: targeting analysis, which is used to determine whether or not control laws can be found to regulate, not all the agents, but only the target agents; and growing analysis, which is used to determine the behaviour of all the non-target agents when the control laws are applied. In this thesis these two analyses are adopted to the deadbeat disturbance rejection problem. A new necessary condition for successful disturbance rejection is derived, namely that a control agent must be connected to the same plant agent to which a disturbance agent is connected. This result puts a bound on the minimum number of control agents and constraints the locations of control agents. Then, given the premise that both targeting and growing analyses succeed in the special case where the disturbances are all ignored, a new control approach is proposed for the linear case based on the idea of integral control and the regulation methods of Spieser and Shams. Preliminary studies show that this approach is also suitable for some nonlinear systems.

This thesis considers the problem of robust geometric regulation for tracking and disturbance rejection of systems governed by delay differential equations. It is well known that geometric regulation can be highly sensitive to system parameters and hence such designs are not always robust. In particular, when employing numerical approximations to delay systems, the resulting finite dimensional models inherit natural approximation errors that can impact robustness. This demonstrates this lack of robustness and then addresses robustness by employing versions of robust regulation that have been developed for infinite dimensional systems. Numerical examples are given to illustrate the ideas and to test the robustness of the regulator. / M.S. / Recent years have seen a surge in the everyday application of complex mechanical and electrical systems. These systems can perform complex tasks; however, the increased complexity makes it harder to control them. An example of such a system is a semi-autonomous car designed to stay within a designated lane. One of the most commonly used approaches for controlling such systems is called output regulation. In the above example, the output regulator regulates the output of the car (position of the car) to follow the reference output (the road lane). Traditionally, the design of output regulators assumes complete knowledge of the system. However, it is impossible to derive equations that govern complex systems like a car. This thesis analyzes the robustness of output regulators in the presence of errors in the system. In particular, the focus is on analyzing output regulators implemented to delay-differential equations. These are differential equations where the rate of change of states at the current time depends on the states at previous times. Furthermore, this thesis addresses this problem by employing the robust versions of the output regulators.

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