It is well known that Fourier series of discontinuous functions converge slowly and that the derivatives of the series may not converge at all. Since modal expansion of structural response is a generalization of the Fourier series, slow convergence of modal expansion can be expected when the applied loads exhibit discontinuities in time or space. Thus, in a structure controlled by point actuators, slow convergence of derivatives of structural response with respect to system parameters can be expected. To demonstrate this, the sensitivity of the closed-loop response to structural changes is calculated for a multi-span beam with three control systems of increasing complexity that utilize point actuators. Reduced models based on the natural modes of the structure are formed and derivatives of the damping ratios of the closed-loop eigenvalues are calculated. As expected, the convergence of the derivatives of the damping ratios with increasing number of modes is slower than the convergence of the damping ratios themselves. The convergence is improved when distributed actuators replace the point actuators. When the control system is designed based on a reduced model, the damping ratios also converge slowly. In transient response problems, it is known that complementing the vibration modes with a mode representing static response to the loads can greatly improve convergence. Indeed, for the examples studied, when Ritz vectors corresponding to static responses due to unit loads at the actuators are added to the basis vectors, the convergence of the reduced-model derivatives is greatly enhanced. Also, when the control system is designed using a reduced model containing both vibration modes and Ritz vectors, its prediction of the full-model response is greatly improved. / Ph. D.

Digital control needs discrete time models, but conversion from continuous time, fed by a zero order hold, to discrete time introduces sampling zeros which are outside the unit circle, i.e. non-minimum phase (NMP) zeros, in the majority of the systems. Also, some systems are already NMP in continuous time. In both cases, the inverse problem to find the input required to maintain a desired output tracking, produces an unstable causal control action. The control action will grow exponentially every time step, and the error between time steps also grows exponentially. This prevents many control approaches from making use of inverse models. The problem statement for the existing stable inverse theorem is presented in this work, and it aims at finding a bounded nominal state-input trajectory by solving a two-point boundary value problem obtained by decomposing the internal dynamics of the system. This results in the causal part specified from the minus infinity time; and its non-causal part from the positive infinity time. By solving for the nominal bounded internal dynamics, the exact output tracking is achieved in the original finite time interval. The new stable inverses concepts presented and developed here address this instability problem in a different way based on the modified versions of problem states, and in a way that is more practical for implementation. The statements of how the different inverse problems are posed is presented, as well as the calculation and implementation. In order to produce zero tracking error at the addressed time steps, two modified statements are given as the initial delete and the skip step. The development presented here involves: (1) The detection of the signature of instability in both the nonhomogeneous difference equation and matrix form for finite time problems. (2) Create a new factorization of the system separating maximum part from minimum part in matrix form as analogous to transfer function format, and more generally, modeling the behavior of finite time zeros and poles. (3) Produce bounded stable inverse solutions evolving from the minimum Euclidean norm satisfying different optimization objective functions, to the solution having no projection on transient solutions terms excited by initial conditions. Iterative Learning Control (ILC) iterates with a real world control system repeatedly performing the same task. It adjusts the control action based on error history from the previous iteration, aiming to converge to zero tracking error. ILC has been widely used in various applications due to its high precision in trajectory tracking, e.g. semiconductor manufacturing sensors that repeatedly perform scanning maneuvers. Designing effective feedback controllers for non-minimum phase (NMP) systems can be challenging. Applying Iterative Learning Control (ILC) to NMP systems is particularly problematic. Incorporating the initial delete stable inverse thinkg into ILC, the control action obtained in the limit as the iterations tend to infinity, is a function of the tracking error produced by the command in the initial run. It is shown here that this dependence is very small, so that one can reasonably use any initial run. By picking an initial input that goes to zero approaching the final time step, the influence becomes particularly small. And by simply commanding zero in the first run, the resulting converged control minimizes the Euclidean norm of the underdetermined control history. Three main classes of ILC laws are examined, and it is shown that all ILC laws converge to the identical control history, as the converged result is not a function of the ILC law. All of these conclusions apply to ILC that aims to track a given finite time trajectory, and also apply to ILC that in addition aims to cancel the effect of a disturbance that repeats each run. Having these stable inverses opens up opportunities for many control design approaches. (1) ILC was the original motivation of the new stable inverses. Besides the scenario using the initial delete above, consider ILC to perform local learning in a trajectory, by using a quadratic cost control in general, but phasing into the skip step stable inverse for some portion of the trajectory that needs high precision tracking. (2) One step ahead control uses a model to compute the control action at the current time step to produce the output desired at the next time step. Before it can be useful, it must be phased in to honor actuator saturation limits, and being a true inverse it requires that the system have a stable inverse. One could generalize this to p-step ahead control, updating the control action every p steps instead of every one step. It determines how small p can be to give a stable implementation using skip step, and it can be quite small. So it only requires knowledge of future desired control for a few steps. (3) Note that the statement in (2) can be reformulated as Linear Model Predictive Control that updates every p steps instead of every step. This offers the ability to converge to zero tracking error at every time step of the skip step inverse, instead of the usual aim to converge to a quadratic cost solution. (4) Indirect discrete time adaptive control combines one step ahead control with the projection algorithm to perform real time identification updates. It has limited applications, because it requires a stable inverse.

There is a considerable scope for improving the temperature control of exothermic processes. In this thesis, a sub-optimal control strategy is developed through utilizing the dynamic, simulation tool. This scheme is built around easily obtained knowledge of the system and still retains flexibility. It can be applied to both exothermic batch and fed-batch processes. It consists of servo and regulatory modes, where a Generalized Predictive Controller (GPC) was used to provide self-tuning facilities. The methods outlined allow for limited thermal runaway whilst keeping some spare cooling capacity to ensure that operation at constraints are not violated. A special feature of the method proposed is that switching temperatures and temperature profiles can be readily found from plant trials whilst the addition rate profile Is capable of fairly straightforward computation. The work shows that It is unnecessary to demand stability for the whole of the exothermic reaction cycle, permitting a small runaway has resulted in a fast temperature response within the given safety margin. The Idea was employed for an exothermic single Irreversible reaction and also to a set of complex reactions. Both are carried out in a vessel with a heating/cooling coil. Two constraints are Imposed; (1) limited heat transfer area, and (11) a maximum allowable reaction temperature Tmax. The non-minimum phase problem can be considered as one of the difficulties in managing exothermic fed-batch process when cold reactant Is added to vessel at the maximum operating temperature. The control system coped with this within limits, a not unexpected result. In all cases, the new strategy out-performed the conventional controller and produced smoother variations in the manipulated variable. The simulation results showed that batch to batch variations and disturbances In cooling were successfully handled. GPC worked well but can be susceptible to measurement noise.

Thesis (MTech (Electrical Engineering))--Cape Peninsula University of Technology, 2014. / The application of digital control techniques has become dominant in power electronics owing to several advantages they present, when compared to analogue solutions. Their development is based on the use of microprocessors and microcontrollers, such as Application Specific Integrated Circuit (ASIC), Digital signal processors (DSP), Field Programmable Gate Arrays (FPGA), or a combination of these devices. This thesis presents an investigation of a soft-core based FPGA control system as a solution for power electronic applications. The aim was the development and implementation of a conversion controller, which purpose is to supply control inputs in the form of digital Pulse Width Modulation (PWM) signals, to a number of power electronic applications, such as single half and full bridge DC-DC converters, three phase and multicell inverters. The PWM control technique is achieved via their power semiconductor switching devices. These PWM control signals are necessary for the high frequency conversion of an analog input voltage (AC, DC or unregulated) to an analog output voltage of another level (AC or DC). This was intended to be achieved by exploiting and combining the advantages that FPGA and embedded processors provide such as high reconfigurability and multipurpose ability. This controller’s digital outputs, namely PWM switching signals, can be directly delivered to an analog signal amplification circuit to create an adequate voltage level before being processed by the converters’ switches.

Unmanned aerial vehicles (UAV's) have recently gained popularity in military, civil service, agriculture, commercial, and hobby use. This is due in part to their affordability, which comes from advances in component technology. That technology includes microelectromechanical systems (MEMS) for inertial sensing, microprocessor technology for sequential algorithm processing, field programmable gate arrays (FPGA's) for parallel data processing, camera technology, global navigation satellite systems (GNSS's) for navigation, and battery technology such as the high energy density of lithium polymer batteries. Despite the success of the technology to date, there remains development before UAV's should be flying alongside manned aircraft or over populated areas. One concern is that UAV electronics are not as safe, reliable or robust as manned-aircraft electronics because UAV's are not certified by the FAA. Another concern for UAV operation is with control algorithms and sensors, particularly in the estimation of the aircraft state, which is the position, velocity, and orientation of the aircraft. Some problems, such as numerical stability of a control algorithm or flight in windy and turbulent conditions have only been solved for certain conditions of wind, weather, or maneuvers. Outside those conditions, the actual orientation of a flying craft can mislead to the control system, and the control system may not be able to recover without a crash. When pilots fly manned aircraft in instrument meteorological conditions, or conditions of limited visibility of the ground, terrain, and obstacles, the pilot must fly in a manner which avoids abrupt maneuvers which could disturb accuracy of the aircraft's instruments. In a UAV without a pilot, there is a need to estimate the position and orientation of a UAV in an absolute manner unambiguous relative to the Earth. The position and orientation estimate must not depend on carefully controlled flight paths, but instead the estimate must be robust in the presence of UAV flight dynamics. This thesis describes the design, implementation, and evaluation of a hardware platform for GPS based orientation sensing research. In this work, we considered a receiver with three or four RF sections, each connected to an antenna in a triangular or tetrahedral pyramid constellation. Specific requirements for the receiver hardware and functionality were created. Circuitry was designed to meet the requirements using commercial off-the-shelf (COTS) radio frequency (RF) modules, a mid-sized microcontroller, an FPGA, and other supporting components. A printed circuit board (PCB) was designed, fabricated, assembled, and tested. A GPS baseband processor was designed and coded in Verilog hardware description language. The design was synthesized and loaded to the FPGA, and the microcontroller was programmed to track satellites. With the hardware platform implemented, live satellite signals were found and tracked, and experiments were performed to explore the validity of GPS based orientation sensing using short antenna baselines. The platform successfully allows the user to develop correlator designs and explore carrier phase based orientation measurement using only software/Verilog modifications. Initial results of carrier phase based orientation sensing are promising, but the presence of multipath signal interference shows room for improvement to the baseband processing code.

There is a considerable scope for improving the temperature control of exothermic processes. In this thesis, a sub-optimal control strategy is developed through utilizing the dynamic, simulation tool. This scheme is built around easily obtained knowledge of the system and still retains flexibility. It can be applied to both exothermic batch and fed-batch processes. It consists of servo and regulatory modes, where a Generalized Predictive Controller (GPC) was used to provide self-tuning facilities. The methods outlined allow for limited thermal runaway whilst keeping some spare cooling capacity to ensure that operation at constraints are not violated. A special feature of the method proposed is that switching temperatures and temperature profiles can be readily found from plant trials whilst the addition rate profile Is capable of fairly straightforward computation. The work shows that It is unnecessary to demand stability for the whole of the exothermic reaction cycle, permitting a small runaway has resulted in a fast temperature response within the given safety margin. The Idea was employed for an exothermic single Irreversible reaction and also to a set of complex reactions. Both are carried out in a vessel with a heating/cooling coil. Two constraints are Imposed; (1) limited heat transfer area, and (11) a maximum allowable reaction temperature Tmax. The non-minimum phase problem can be considered as one of the difficulties in managing exothermic fed-batch process when cold reactant Is added to vessel at the maximum operating temperature. The control system coped with this within limits, a not unexpected result. In all cases, the new strategy out-performed the conventional controller and produced smoother variations in the manipulated variable. The simulation results showed that batch to batch variations and disturbances In cooling were successfully handled. GPC worked well but can be susceptible to measurement noise. / Higher Education Ministry and Scientific Research

A single-layer neural network-based voltage compensation technique which generates minimum-distortion sinusoidal output voltages from a three-phase PWM inverter used for uninterruptible power supplies (UPS) is described. The proposed compensation technique is implemented in a microprocessor-based controller constructed in the stationary d-q frame where the controller sampling rate is twice the inverter switching frequency. The structure of a feed-forward artificial neural network connects network inputs and outputs through multiple linear or nonlinear neuron models, and processes these input/output data associations in a parallel distributed manner. Network inputs in the form of UPS load voltage commands and load current feedback are propagated forward in the network each controller sampling period generating the inverter output voltage commands, the network outputs, which are converted to three phase inverter switching Signals using the space vector PWM waveform generation process. / Ph. D.

This thesis considers the development of a Hammerstein-bilinear approach to non-linear systems modelling, analysis and control systems design, which builds on and extends the applicability of an existing bilinear approach. The underlying idea of the Hammerstein-bilinear approach is to use the Hammerstein-bilinear system models to capture various physical phenomena of interest and subsequently use these for model based control system designs with the premise being that of achieving enhanced control performance. The advantage of the Hammerstein-bilinear approach is that the well-structured system models allow techniques that have been originally developed for linear systems to be extended and applied, while retaining moderate complexity of the corresponding system identification schemes and nonlinear model based control designs. In recognition of the need to be able to identify the Hammerstein-bilinear models a unified suite of algorithms, being the extensions to the simplified refined instrumental variable method for parameter estimation of linear transfer function models is proposed. These algorithms are able to operate in both the continuous-time and discrete-time domains to reflect the requirements of the intended purposes of the identified models with the emphasis being placed on straightforward applicability of the developed algorithms and recognising the need to be able to operate under realistic practical system identification scenarios. Moreover, the proposed algorithms are also applicable to parameter estimation of Hammerstein and bilinear models, which are special cases of the wider Hammerstein-bilinear model class. The Hammerstein-bilinear approach has been applied to an industrial heating, ventilation and air conditioning (HVAC) system, which has also been the underlying application addressed in this thesis. A unique set of dynamic control design purpose oriented air temperature and humidity Hammerstein-bilinear models of an environmentally controlled clear room manufacturing zone has been identified. The greater insights afforded by the knowledge of the system nonlinearities then allow for enhanced control tuning of the associated commercial HVAC control system leading to an improved overall control performance.

Biomimetic flapping-wing vehicles have attracted recent interest because of their numerous potential military and civilian applications. In this dissertation is described the design of a multi-agent adaptive controller for such a vehicle. This controller is responsible for estimating the vehicle pose (position and orientation) and then generating four parameters needed for split-cycle control of wing movements to correct pose errors. These parameters are produced via a subsumption architecture rule base. The control strategy is fault tolerant. Using an online learning process, an agent continuously monitors the vehicle's behavior and initiates diagnostics if the behavior has degraded. This agent can then autonomously adapt the rule base if necessary. Each rule base is constructed using a combination of extrinsic and intrinsic evolution. Details of the vehicle, the multi-agent system architecture, agent task scheduling, rule base design, and vehicle control are provided.

This thesis presents the design of various controllers for a highly maneuverable, high performance aircraft, namely the modified F-18. The aircraft was required to perform high angle-of-attack maneuvers, for which the aircraft behaves in as a highly nonlinear system. An adaptive PID controller was used to control the aircraft through these high angle-of-attack maneuvers. Several nonlinear controllers were then developed based on the adaptive PID control, and were tested for robustness. This thesis also looks at an improvement in the aircraft which may improve performance in high angle-of-attack maneuvers. The contributions of this thesis are in the areas of control, in general, and specifically in the area of aircraft control. Successful application of linear adaptive control and nonlinear control were presented. In the area of aircraft control, controllers were presented which produce good performance for high angle-of-attack maneuvers, while maintaining implementability. Also, some insight is gained into what aircraft changes could improve performance. / Graduation date: 1995