Control Methods for High-Speed Supercavitating Vehicles

Supercavitation is an emerging technology that enables underwater vehicles to reach un- precedented speed. With proper design of cavitator attached to the vehicle nose, the vehicle body is surrounded by water vapor cavity, eliminating skin friction drag. This technology offers unprecedented drag reduction, though poses problems for vehicle design. The gas bubble surrounding the hull introduces highly coupled dynamic behavior, representing a challenge for the control designer. Development of stable, controllable supercavitating vehi- cles requires solution for several open problems. This dissertation addresses the problem of control oriented modeling, stability augmentation, and reference tracking using parameter dependent control techniques for supercavitating vehicles.\ud The thesis is divided into three parts. A nonlinear dynamical model capturing the most important properties of the vehicle motion is developed from a control design perspective. The model includes memory effects associated with the time evolution of the cavity and uses lookup tables to determine forces.\ud To aid understanding the cavity-vehicle interaction, a longitudinal control scenario is developed for a simplified longitudinal dynamical model with guaranteed properties. Sig- nificant insight is gained on planing behavior and operating envelope using constrained control inputs.\ud Extending the longitudinal control problem, a linear parameter varying model of the coupled motion is developed to provide a platform for parameter dependent control syn- thesis. The mathematical model is scheduled with aerodynamic angles, uses steady-state approximation of the cavity, leading to uncertainty in the governing equations. Two Linear Parameter Varying (LPV) controllers are synthesized for the angle rate tracking problem, taking uncertainty into account. One uses traditional decoupled loops for pitch-, roll- and yaw-rate tracking. Ignoring the cross coupling, leads to more tractable subproblems . A controller, taking advantage of the coupling, is also presented in the thesis. The complexity of the coupled dynamics prohibits the synthesis of the controller as a single entity. Sev- eral LPV controllers synthesized for smaller overlapping regions of the parameter space are blended together, providing a single controller for the full flight envelope. Time-domain simulations of different vehicle-controller configurations, implemented on high-fidelity sim- ulations, provide insight into the capabilities of the supercavitating vehicle

Inverse modelling and inverse simulation for system engineering and control applications

Following extensive development over the past two decades, techniques of inverse simulation have led to a range of successful applications, mainly in the fields of helicopter flight mechanics, aircraft handling qualities and associated issues in terms of model validation. However, the available methods still have some well-known limitations. The traditional methods based on the Newton-Raphson algorithm suffer from numerical problems such as high-frequency oscillations and can have limitations in their applicability due to problems of input-output redundancy. The existing approaches may also show a phenomenon which has been termed “constraint oscillations” which leads to low-frequency oscillatory behaviour in the inverse solutions. Moreover, the need for derivative information may limit their applicability for situations involving manoeuvre discontinuities, model discontinuities or input constraints. Two new methods are developed to overcome these issues. The first one, based on sensitivity-analysis theory, allows the Jacobian matrix to be calculated by solving a sensitivity equation and also overcomes problems of input-output redundancy. In addition, it can improve the accuracy of results compared with conventional methods and can deal with the problem of high-frequency oscillations to some extent. The second one, based on a constrained Nelder-Mead search-based optimisation algorithm, is completely derivative-free algorithm for inverse simulation. This approach eliminates problems which make traditional inverse simulation techniques difficult to apply in control applications involving discontinuous issues such as actuator amplitude or rate limits. This thesis also offers new insight into the relationship between mathematically based techniques of model inversion and the inverse simulation approach. The similarities and shortcomings of both these methodologies are explored. The findings point to the possibility that inverse simulation can be used successfully within the control system design process for feedforward controllers for model-based output-tracking control system structures. This avoids the more complicated and relatively tedious techniques of model inversion which have been used in the past for feedforward controller design. The methods of inverse simulation presented in this thesis have been applied to a number of problems which are concerned mainly with helicopter and ship control problems and include cases involving systems having nonminimum-phase characteristics. The analysis of results for these practical applications shows that the approaches developed and presented in this thesis are of practical importance. It is believed that these developments form a useful step in moving inverse simulation methods from the status of an academic research topic to a practical and robust set of tools for engineering system design

Acoustically driven control of mobile robots for source localization in complex ocean environments

Ocean based robotic systems are an opportunity to combine the power of acoustic sensing in the water with sophisticated control schemes. Together these bodies of knowledge could create autonomous systems for mapping acoustic fields and localizing underwater sources. However, existing control schemes have often been designed for land and air robots. This creates challenges for applying these algorithms to complex ocean environments. Acoustic fields are strongly frequency dependent, can rarely be realistically modeled analytically, have complex contours where the feature of interest is not always located at the peak pressure, and include many sources of background noise. This work addresses these challenges for control schemes from three categories: feedback and observer control, gradient ascent control and optimal control. In each case the challenges of applying the control scheme to an acoustic field are enumerated and addressed to create a suite of acoustically driven control schemes. For many of these algorithms, the largest issue is the processing and collection of acoustic data, particularly in the face of noise. Two new methods are developed to solve this issue. The first is the use of Principal Component Analysis as a noise filter for acoustic signals, which is shown to address particularly high levels of noise, while providing the frequency dependent sound pressure levels necessary for subsequent processing. The second method addresses the challenge that an analytical expression of the pressure field is often lacking, due to uncertainties and complexities in the environmental parameters. Basis functions are used to address this. Several candidates are considered, but Legendre polynomials are selected for their low error and reasonable processing time. Additionally, a method of intermediate points is used to approximate high frequency pressure fields with low numbers of collected data points. Following this work, the individual control schemes are explored. A method of observer feedback control is proposed to localize sources by linearizing the acoustic fields. A gradient ascent method for localizing sources in real time is proposed which uses Matched Field Processing and Bayesian filters. These modifications allow the gradient ascent algorithm to be compatible with complex acoustic fields. Finally, an optimal control method is proposed using Pontryagin's Maximum Principle to derive trajectories in real time that balance information gain with control energy. This method is shown to efficiently map an acoustic field, either for optimal sensor placement or to localize sources. The contribution of this work is a new collection of control schemes that use acoustic data to localize acoustically complex sources in a realistic noisy environment, and an understanding of the tradeoffs inherent in applying each of these to the acoustic domain

Underwater Vehicles

For the latest twenty to thirty years, a significant number of AUVs has been created for the solving of wide spectrum of scientific and applied tasks of ocean development and research. For the short time period the AUVs have shown the efficiency at performance of complex search and inspection works and opened a number of new important applications. Initially the information about AUVs had mainly review-advertising character but now more attention is paid to practical achievements, problems and systems technologies. AUVs are losing their prototype status and have become a fully operational, reliable and effective tool and modern multi-purpose AUVs represent the new class of underwater robotic objects with inherent tasks and practical applications, particular features of technology, systems structure and functional properties

Investigations of Model-Free Sliding Mode Control Algorithms including Application to Autonomous Quadrotor Flight

Sliding mode control is a robust nonlinear control algorithm that has been used to implement tracking controllers for unmanned aircraft systems that are robust to modeling uncertainty and exogenous disturbances, thereby providing excellent performance for autonomous operation. A significant advance in the application of sliding mode control for unmanned aircraft systems would be adaptation of a model-free sliding mode control algorithm, since the most complex and time-consuming aspect of implementation of sliding mode control is the derivation of the control law with incorporation of the system model, a process required to be performed for each individual application of sliding mode control. The performance of four different model-free sliding mode control algorithms was compared in simulation using a variety of aerial system models and real-world disturbances (e.g. the effects of discretization and state estimation). The two best performing algorithms were shown to exhibit very similar behavior. These two algorithms were implemented on a quadrotor (both in simulation and using real-world hardware) and the performance was compared to a traditional PID-based controller using the same state estimation algorithm and control setup. Simulation results show the model-free sliding mode control algorithms exhibit similar performance to PID controllers without the tedious tuning process. Comparison between the two model-free sliding mode control algorithms showed very similar performance as measured by the quadratic means of tracking errors. Flight testing showed that while a model-free sliding mode control algorithm is capable of controlling realworld hardware, further characterization and significant improvements are required before it is a viable alternative to conventional control algorithms. Large tracking errors were observed for both the model-free sliding mode control and PID based flight controllers and the performance was characterized as unacceptable for most applications. The poor performance of both controllers suggests tracking errors could be attributed to errors in state estimation, which effectively introduce unknown dynamics into the feedback loop. Further testing with improved state estimation would allow for more conclusions to be drawn about the performance characteristics of the model-free sliding mode control algorithms

Fault-tolerant Synchronization of Autonomous Underwater Vehicles

The main objective of this thesis is to develop a fault-tolerant and reconfigurable synchronization scheme based on model-based control protocols for stern and sail hydroplanes that are employed as actuators in the attitude control subsystem (ACS) of an autonomous underwater vehicle (AUV). In this thesis two control approaches are considered for synchronization, namely i) state feedback synchronization, and ii) output feedback synchronization. Both problems are tackled by proposing a passive control approach as well as an active reconfiguration (re-designing the control gains). For the ”state feedback” synchronization scheme, to achieve consensus the relative/absolute measurements of the AUV’s states (position and attitude) are available. The states of a longitudinal model of an AUV are mainly heave, pitch, and their associated rates. For the state feedback problem we employ a static protocol, and it is shown that the multi-agent system will synchronize in the stochastic mean square sense in the presence of measurement noise. However, the resulting performance index defined as the accumulated sum of variations of control inputs and synchronization errors is high. To deal with this problem, Kalman filtering is used for states estimation that are used in synchronization protocol. Moreover, the e�ffects of parameter uncertainty of the agent’s dynamics are also investigated through simulation results. By employing the static protocol it is demonstrated that when a loss of e�ffectiveness (LOE) or float fault occurs the synchronization can still be achieved under some conditions. Finally, one of the main problems that is tackled in the state feedback scenario is our proposed proportional-integral (PI) control methodology to deal with the lock in place (LIP) fault. It is shown that if the LIP fault occurs, by employing a PI protocol the synchronization could still be achieved. Finally, our proposed dynamic synchronization protocol methodology is applied given that the fault (LOE/float) severity is known. Since after a fault occurrence the agents become heterogeneous, employing the dynamic scheme makes the task of reconfiguration (redesigning the gains) more e�ffective. For the ”output feedback” synchronization approach, to achieve consensus relative/absolute measurements of the AUV’s states except the pitch rate are available. For the output feedback problem a dynamic protocol through a Luenberger observer is first employed for state estimation and the synchronization achievement is demonstrated. Then, a system under state and measurement noise is considered, and it is shown that by employing a Kalman filter for the state estimation; the multi-agent system will synchronize in the stochastic mean square sense. Furthermore, by employing the static protocol, it is shown that when a LOE/float fault occurs the synchronization is still achieved under certain conditions. Finally, one of the main problems that is tackled in the output feedback scenario is our proposed dynamic controller methodology. The results of this scheme are compared with another approach that exploits both dynamic controller and dynamic observer. The former approach has less computational e�ort and results in more a robust control with respect to the actuator fault. The reason is that the later method employs an observer that uses the control input matrix information. When fault occurs, this information will not be correct any more. However, if there is a need to redesign the synchronization gains under faulty scenario, the later methodology is preferred. The reason is that the former approach becomes complicated when there is a fault even though its severity is known. In this thesis, fault-tolerant synchronization of autonomous underwater vehicles is considered. In the first chapter a brief introduction on the motivation, problem definition, objectives and the methodologies that are used in the dissertation are discussed. A literature review on research dedicated to synchronization, fault diagnosis, and fault-tolerant control is provided. In Chapter 2, a through literature review on unmanned underwater vehicles is covered. It also comprises a comprehensive background information and definitions including algebraic graph theory, matrix theory, and fault modeling. In the problem statement, the two main problems in this thesis, namely state feedback synchronization and output feedback synchronization are discussed. Chapters 3 and 4 will cover these two problems, their solutions, and the corresponding simulation results that are provided. Finally, Chapter 5 includes a discussion of conclusions and future work

Methods of system identification, parameter estimation and optimisation applied to problems of modelling and control in engineering and physiology

Mathematical and computer-based models provide the foundation of most methods of engineering design. They are recognised as being especially important in the development of integrated dynamic systems, such as “control-configured” aircraft or in complex robotics applications. These models usually involve combinations of linear or nonlinear ordinary differential equations or difference equations, partial differential equations and algebraic equations. In some cases models may be based on differential algebraic equations. Dynamic models are also important in many other fields of research, including physiology where the highly integrated nature of biological control systems is starting to be more fully understood. Although many models may be developed using physical, chemical, or biological principles in the initial stages, the use of experimentation is important for checking the significance of underlying assumptions or simplifications and also for estimating appropriate sets of parameters. This experimental approach to modelling is also of central importance in establishing the suitability, or otherwise, of a given model for an intended application – the so-called “model validation” problem. System identification, which is the broad term used to describe the processes of experimental modelling, is generally considered to be a mature field and classical methods of identification involve linear discrete-time models within a stochastic framework. The aspects of the research described in this thesis that relate to applications of identification, parameter estimation and optimisation techniques for model development and model validation mainly involve nonlinear continuous time models Experimentally-based models of this kind have been used very successfully in the course of the research described in this thesis very in two areas of physiological research and in a number of different engineering applications. In terms of optimisation problems, the design, experimental tuning and performance evaluation of nonlinear control systems has much in common with the use of optimisation techniques within the model development process and it is therefore helpful to consider these two areas together. The work described in the thesis is strongly applications oriented. Many similarities have been found in applying modelling and control techniques to problems arising in fields that appear very different. For example, the areas of neurophysiology, respiratory gas exchange processes, electro-optic sensor systems, helicopter flight-control, hydro-electric power generation and surface ship or underwater vehicles appear to have little in common. However, closer examination shows that they have many similarities in terms of the types of problem that are presented, both in modelling and in system design. In addition to nonlinear behaviour; most models of these systems involve significant uncertainties or require important simplifications if the model is to be used in a real-time application such as automatic control. One recurring theme, that is important both in the modelling work described and for control applications, is the additional insight that can be gained through the dual use of time-domain and frequency-domain information. One example of this is the importance of coherence information in establishing the existence of linear or nonlinear relationships between variables and this has proved to be valuable in the experimental investigation of neuromuscular systems and in the identification of helicopter models from flight test data. Frequency-domain techniques have also proved useful for the reduction of high-order multi-input multi-output models. Another important theme that has appeared both within the modelling applications and in research on nonlinear control system design methods, relates to the problems of optimisation in cases where the associated response surface has many local optima. Finding the global optimum in practical applications presents major difficulties and much emphasis has been placed on evolutionary methods of optimisation (both genetic algorithms and genetic programming) in providing usable methods for optimisation in design and in complex nonlinear modelling applications that do not involve real-time problems. Another topic, considered both in the context of system modelling and control, is parameter sensitivity analysis and it has been found that insight gained from sensitivity information can be of value not only in the development of system models (e.g. through investigation of model robustness and the design of appropriate test inputs), but also in feedback system design and in controller tuning. A technique has been developed based on sensitivity analysis for the semi-automatic tuning of cascade and feedback controllers for multi-input multi-output feedback control systems. This tuning technique has been applied successfully to several problems. Inverse systems also receive significant attention in the thesis. These systems have provided a basis for theoretical research in the control systems field over the past two decades and some significant applications have been reported, despite the inherent difficulties in the mathematical methods needed for the nonlinear case. Inverse simulation methods, developed initially by others for use in handling-qualities studies for fixed-wing aircraft and helicopters, are shown in the thesis to provide some important potential benefits in control applications compared with classical methods of inversion. New developments in terms of methodology are presented in terms of a novel sensitivity based approach to inverse simulation that has advantages in terms of numerical accuracy and a new search-based optimisation technique based on the Nelder-Mead algorithm that can handle inverse simulation problems involving hard nonlinearities. Engineering applications of inverse simulation are presented, some of which involve helicopter flight control applications while others are concerned with feed-forward controllers for ship steering systems. The methods of search-based optimisation show some important advantages over conventional gradient-based methods, especially in cases where saturation and other nonlinearities are significant. The final discussion section takes the form of a critical evaluation of results obtained using the chosen methods of system identification, parameter estimation and optimisation for the modelling and control applications considered. Areas of success are highlighted and situations are identified where currently available techniques have important limitations. The benefits of an inter-disciplinary and applications-oriented approach to problems of modelling and control are also discussed and the value in terms of cross-fertilisation of ideas resulting from involvement in a wide range of applications is emphasised. Areas for further research are discussed