A Geometric Control System with Applications to Helicopters

This thesis introduces an Automatic Flight Control System for single rotor helicopters which gives a new relevance to the traditional techniques based on the Linear Control Theory. This design was obtained by applying concepts of differential geometry tailored for engineering purposes through the Nonlinear System Theory. The development of this thesis follows the traditional path of applied sciences. First the need to establish techniques for theoretical analysis of flight machanics, where the small disturbance methods are no longer valid, is reviewed. This is followed by a presentation of the nonlinear problem and a survey of the development of the theoretical tools available. At this stage the process, a single rotor helicopter, is modelled. The model is then cast in a form suitable for Nonlinear System Theory techniques. Next, the mathematical theory to be applied is fully developed. It consists of finding the conditions required by a nonlinear system to be transformable under state feedback to a linear canonical form; the construction of the feedback is also presented. A Flight Control System is designed by applying this theory to the helicopter model previously formulated. The above application requires the development of Symbolic Algebraic Manipulation programmes, which are also included. Finally, a set of simulation studies demonstrate the performance of the design

Induction motor control: multivariable analysis and effective decentralized control of stator currents for high performance applications

Adequate control of the stator currents is a fundamental requirement for several high-performance induction motor (IM) control schemes. In this context, classical linear controllers remain widely employed due to their simplicity and success in industrial applications. However, the models and methods commonly used for control design lack valuable information –which is fundamental to guarantee robustness and high performance. Following this line, the design and existence of linear fixed controllers is examined using individual channel analysis and design. The studies here presented aim to establish guidelines for the design of simple (time-invariant, low order, stable, minimum-phase and decentralized), yet robust and highperformance linear controllers. Such characteristics ease the implementation task and are well suited for engineering applications, making the resulting controllers a good alternative for the stator currents control required for high-performance IM schemes; e.g., field oriented, passivity-based and intelligent control. Illustrative examples are presented to demonstrate the analysis and controller design of an IM, with results validated in a real-time experimental platform. It is shown that it is possible to completely decouple the stator currents subsystem without the use of additional decoupling elements

Analysis of the damping characteristics of two power electronics-based Devices using 'individual channel analysis and design'

A comparison of the capabilities of two quite distinct power electronics-based ‘flexible AC transmission systems’ devices is presented. In particular, the damping of low frequency electromechanical oscillations is investigated aiming at improving the performance of power systems. The comparison is made using frequency domain methods under the ‘individual channel analysis and design’ framework. A synchronous generator feeding into a system with large inertia is used for such a purpose. Two system configurations including compensation are analysed: (a) in series in the form of a thyristor-controlled series compensator, and (b) in shunt through a static VAr compensator featuring a damping controller. Analyses are carried out to elucidate the dynamic behaviour of the synchronous generator in the presence of the power electronics-based controllers and for the case when no controller is present. Performance and robustness assessments are given particular emphasis. The crux of the matter is the comparison between the abilities of the static VAr compensator and the thyristor-controlled series compensator to eliminate the problematic switch-back characteristic intrinsic to synchronous generator operation by using the physical insight afforded by ‘individual channel analysis and design’

Flux-torque cross-coupling analysis of FOC schemes: Novel perturbation rejection characteristics

Field oriented control (FOC) is one of the most successful control schemes for electrical machines. In this article new properties of FOC schemes for induction motors (IMs) are revealed by studying the cross-coupling of the flux-torque subsystem. Through the use of frequency-based multivariable tools, it is shown that FOC has intrinsic stator currents disturbance rejection properties due to the existence of a transmission zero in the flux-torque subsystem. These properties can be exploited in order to select appropriate feedback loop configurations. One of the major drawbacks of FOC schemes is their high sensitivity to slip angular velocity perturbations. These perturbations are related to variations of the rotor time constant, which are known to be problematic for IM control. In this regard, the effect that slip angular velocity perturbations have over the newly found perturbation rejection properties is also studied. In particular, although perturbation rejection is maintained, deviations to the equilibrium point are induced; this introduces difficulties for simultaneous flux and torque control. The existence of equilibrium point issues when flux and torque are simultaneously controlled is documented for the first time in this article

Structural robustness assessment of electric machine applications using individual channel analysis and design

Adequate control of three-phase machines, such as induction motors -IMs- and synchronous generators, is of paramount importance for the electric power industry. These are multivariable, non-linear systems. In this paper, the individual channel analysis and design framework is used to formally demonstrate that the electrical subsystems of the IM and of the permanent magnet SG, due to their inherent structural robustness, are the multivariable equivalent to stable, minimum-phase, single-input single-output systems. As a cnsequence, an adequate performance and robustness may be achieved through fixed, stable, minimum-phase, diagonal controllers –justifying the widespread use of control schemes based on fixed, classical linear controllers such as PI

The multivariable structure function as an extension of the RGA matrix: relationship and advantages

It is common practice to specify the performance of control design tasks in terms of an output response to a given input. In spite of a greater complexity, this is also the case for multivariable plants, where for clarity of performance specification and design remains desirable to consider the inputs and outputs in pairs. Regardless of the structure and internal coupling of the plant, it is convenient to establish if decentralized control is capable of meeting design specifications: the control structure will be easy to implement, economic (less programming burden upon implementation), and may provide further physical insight. In line with this, the analysis and design of decentralized controllers using the relative gain array (RGA) and the multivariable structure function (MSF) are presented for the general multivariable case. It is demonstrated that the RGA matrix can be expressed in terms of the MSF. Moreover, it is shown that the correct interpretation of the MSF offers significative advantages over the RGA matrix analysis. While the RGA offers insight about the adequate pairing of input-output signals in a multivariable system, the MSF, besides providing this information, plays a crucial role in the design of stabilizing controllers (and their requirements) and the subsequent robustness and performance assessment of the closed loop control system. Theoretical results are drawn for a general n×n plant, with examples from electrical power systems and laboratory tank processes included to illustrate key concepts

MIMO Passive Control Systems Are Not Necessarily Robust

Via several cases of study it is shown that a passive multivariable linear control system, contrary to its single input single output counterpart, may not be robust. Moreover, it is shown that lack of robustness can be exposed via the multivariable structure function

Fundamental analysis of the static VAr compensator performance using individual channel analysis and design

In this paper the performance of a synchronous generator – SVC system is evaluated using Individual Channel Analysis and Design (ICAD), a control-oriented framework suitable for small-signal stability assessments. The SVC is already a mature piece of technology, which has become very popular for providing fast-acting reactive power support. The great benefits of ICAD in control system design tasks are elucidated. Fundamental analysis is carried out explaining the generator dynamic behavior as affected by the SVC. A multivariable control system design for the system is presented, with particular emphasis in the closed-loop performance and stability and structural robustness assessment. It is formally shown in the paper that although the addition of the SVC with no damping control loop does not improve the dynamic of the system, its inclusion is very effective in enhancing voltage stability. Moreover, ICAD analysis shows that with the use of the SVC the dynamical structure of the system is preserved and no considerable coupling or adverse dynamics are added to the plant

MIMO Passive Control Systems Are Not Necessarily Robust

Via several cases of study it is shown that a passive multivariable linear control system, contrary to its single input single output counterpart, may not be robust. Moreover, it is shown that lack of robustness can be exposed via the multivariable structure function