The objective of adaptive control is to design a controller that can adjust its behaviour to tolerate uncertain or time-varying parameters. An adaptive controller typically consists of a linear time-invariant (LTI) compensator together with a tuning mechanism which adjusts the compensator parameters and yields a nonlinear controller. Because of the nonlinearity, the transient closed-loop behaviour is often poor and the control signal may become unduly large. Although the initial objective of adaptive control was to deal with time-varying plant parameters, most classical adaptive controllers cannot handle rapidly changing parameters. Recently, the use of a linear periodic (LP) controller has been proposed as a new approach in the field of model reference adaptive control [1]. In this new approach, instead of estimating plant parameters, the “ideal control signal” (what the control signal would be if the plant parameters and states were measurable) is estimated. The resulting controller has a number of desirable features: (1) it handles rapid changes in the plant parameters, (2) it provides nice transient behaviour of the closed-loop system, (3) it guarantees that the effect of the initial conditions declines to zero exponentially, and (4) it generates control signals which are modest in size. Although the linear periodic controller (LPC) has the above advantages, it has some imperfections. In order to achieve the desirable features, a rapidly varying control signal and a small sampling period are used. The rapidly time-varying control signal requires fast actuators which may not be practical. The second weakness of the LPC [1] is poor noise rejection behaviour. The small sampling period results in large controller gains and correspondingly poor noise sensitivity, since there is a clear trade-off between tracking and noise tolerance. As the last drawback, this controller requires knowledge of the exact plant relative degree. Here we extend this work in several directions: (i) In [1], the infinity-norm is used to measure the signal size. Here we redesign the controller to yield a new version which provides comparable results when the more common 2-norm is used to measure signal size, (ii) A key drawback of the controller of [1] is that the control signal moves rapidly. Here we redesign the control law to significantly alleviate this problem, (iii) The redesigned controller can handle large parameter variation and in the case that the sign of high frequency gain is known, the closed-loop system is remarkably noise-tolerant, (iv) We prove that in an important special case, we can replace the requirement of knowledge of the exact relative degree with that of an upper bound on the relative degree, at least from the point of view of providing stability, and (v) A number of approaches to improve the noise behaviour of the controller are presented. Reference: [1] D. E. Miller, “A New Approach to Model Reference Adaptive Control”, IEEE Transaction on Automatic Control, Vol. 48, No. 5, pages 743-756, May 2003.

The objective of adaptive control is to design a controller that can adjust its behaviour to tolerate uncertain or time-varying parameters. An adaptive controller typically consists of a linear time-invariant (LTI) compensator together with a tuning mechanism which adjusts the compensator parameters and yields a nonlinear controller. Because of the nonlinearity, the transient closed-loop behaviour is often poor and the control signal may become unduly large. Although the initial objective of adaptive control was to deal with time-varying plant parameters, most classical adaptive controllers cannot handle rapidly changing parameters. Recently, the use of a linear periodic (LP) controller has been proposed as a new approach in the field of model reference adaptive control [1]. In this new approach, instead of estimating plant parameters, the “ideal control signal” (what the control signal would be if the plant parameters and states were measurable) is estimated. The resulting controller has a number of desirable features: (1) it handles rapid changes in the plant parameters, (2) it provides nice transient behaviour of the closed-loop system, (3) it guarantees that the effect of the initial conditions declines to zero exponentially, and (4) it generates control signals which are modest in size. Although the linear periodic controller (LPC) has the above advantages, it has some imperfections. In order to achieve the desirable features, a rapidly varying control signal and a small sampling period are used. The rapidly time-varying control signal requires fast actuators which may not be practical. The second weakness of the LPC [1] is poor noise rejection behaviour. The small sampling period results in large controller gains and correspondingly poor noise sensitivity, since there is a clear trade-off between tracking and noise tolerance. As the last drawback, this controller requires knowledge of the exact plant relative degree. Here we extend this work in several directions: (i) In [1], the infinity-norm is used to measure the signal size. Here we redesign the controller to yield a new version which provides comparable results when the more common 2-norm is used to measure signal size, (ii) A key drawback of the controller of [1] is that the control signal moves rapidly. Here we redesign the control law to significantly alleviate this problem, (iii) The redesigned controller can handle large parameter variation and in the case that the sign of high frequency gain is known, the closed-loop system is remarkably noise-tolerant, (iv) We prove that in an important special case, we can replace the requirement of knowledge of the exact relative degree with that of an upper bound on the relative degree, at least from the point of view of providing stability, and (v) A number of approaches to improve the noise behaviour of the controller are presented. Reference: [1] D. E. Miller, “A New Approach to Model Reference Adaptive Control”, IEEE Transaction on Automatic Control, Vol. 48, No. 5, pages 743-756, May 2003.

This dissertation describes the development and modeling of a low-cost, open source, and reliable small fixed-wing unmanned aerial vehicle (UAV) for advanced control implementation. The platform is mostly constructed of low-cost commercial off-the-shelf (COTS) components. The only non-COTS components are the airdata probes which are manufactured and calibrated in-house, following a procedure provided herein. The airframe used is the commercially available radio-controlled 6-foot Telemaster airplane from Hobby Express. The airplane is chosen mainly for its adequately spacious fuselage and for being reasonably stable and sufficiently agile. One noteworthy feature of this platform is the use of two separate low-cost open source onboard computers for handling the data management/hardware interfacing and control computation. Specifically, the single board computer, Gumstix Overo Fire, is used to execute the control algorithms, whereas the autopilot, Ardupilot Mega, is mostly used to interface the Overo computer with the sensors and actuators. The platform supports multi-vehicle operations through the use of a radio modem that enables multi-point communications. As the goal of the development of this platform is to implement rigorous control algorithms for real-time trajectory tracking and distributed control, it is important to derive an appropriate flight dynamic model of the platform, based on which the controllers will be synthesized. For that matter, reasonably accurate models of the vehicle, servo motors and propulsion system are developed. Namely, the output error method is used to estimate the longitudinal and lateral-directional aerodynamic parameters from flight test data. The moments of inertia of the platform are determined using the simple pendulum test method, and the frequency response of each servomotor is also obtained experimentally. The Javaprop applet is used to obtain lookup tables relating airspeed to propeller thrust at constant throttle settings. Control systems are also designed for the regulation of this UAV along real-time trajectories. The reference trajectories are generated in real-time from a library of pre-specified motion primitives and hence are not known a priori. Two concatenated primitive trajectories are considered: one formed from seven primitives exhibiting a figure-8 geometric path and another composed of a Split-S maneuver that settles into a level-turn trim trajectory. Switched control systems stemming from l2-induced norm synthesis approaches are designed for discrete-time linearized models of the nonlinear UAV system. These controllers are analyzed based on simulations in a realistic operational environment and are further implemented on the physical UAV. The simulations and flight tests demonstrate that switched controllers, which take into account the effects of switching between constituent sub-controllers, manage to closely track the considered trajectories despite the various modeling uncertainties, exogenous disturbances and measurement noise. These switched controllers are composed of discrete-time linear sub-controllers designed separately for a subset of the pre-specified primitives, with the uncertain initial conditions, that arise when switching between primitives, incorporated into the control design. / Ph. D.