Robust adaptive control of uncertain nonlinear systems

Ph.DDOCTOR OF PHILOSOPH

Dynamic Inversion and Backstepping Controller Robustness Analysis for a Reusable Launch Vehicle

The Air Force has been working towards developing technology for operationally responsive space (ORS), which is the ability to launch military assets into space without the long set up time currently required. Part of the solution to ORS is to develop a reusable booster vehicle capable of sending any vehicle into orbit, then descending back to the atmosphere and landing unpowered so that it may take another vehicle into orbit with a 48 hour turnaround time. Currently classical gain tuning techniques are used to design a controller for a specific mission, which may hinder the vehicle’s ability to perform multiple missions if gains have to be re-tuned. Advanced nonlinear control methods like dynamic inversion and backstepping may eliminate the need to use classical gain tuning techniques that may increase quick turnaround time, reliability, and performance. Both methods consider the dynamics of the vehicle allowing the controller to be applied to the whole flight envelope. However, they are model-based methods that require knowledge of plant aerodynamics. The objective was to develop a backstepping outer loop and dynamic inversion inner loop controller for a reusable launch vehicle configuration and evaluate its robustness characteristics by inserting aerodynamic uncertainties into the static and control surface aerodynamic data separately and together. Both dynamic inversion and backstepping were susceptible to control surface aerodynamic uncertainties more than static aerodynamics. The benefit of using dynamic inversion and backstepping was that it was formulated so that it decouples the system of equations as long as the dynamics were modeled accurately. The control variable became a bank of decoupled integrators. However, when uncertainties were introduced into the plant model, the controller was unable to accurately model the dynamics, which re-introduced axes coupling inherent in the plant. The coupling caused performance in one axis to degrade if another axis degraded

Development of Fault Tolerant Adaptive Control Laws for Aerospace Systems

The main topic of this dissertation is the design, development and implementation of intelligent adaptive control techniques designed to maintain healthy performance of aerospace systems subjected to malfunctions, external parameter changes and/or unmodeled dynamics. The dissertation is focused on the development of novel adaptive control configurations that rely on non-linear functions that appear in the immune system of living organisms as main source of adaptation. One of the main goals of this dissertation is to demonstrate that these novel adaptive control architectures are able to improve overall performance and protect the system while reducing control effort and maintaining adequate operation outside bounds of nominal design. This research effort explores several phases, ranging from theoretical stability analysis, simulation and hardware implementation on different types of aerospace systems including spacecraft, aircraft and quadrotor vehicles. The results presented in this dissertation are focused on two main adaptivity approaches, the first one is intended for aerospace systems that do not attain large angles and use exact feedback linearization of Euler angle kinematics. A proof of stability is presented by means of the circle Criterion and Lyapunov’s direct method. The second approach is intended for aerospace systems that can attain large attitude angles (e.g. space systems in gravity-less environments), the adaptation is incorporated on a baseline architecture that uses partial feedback linearization of quaternions kinematics. In this case, the closed loop stability was analyzed using Lyapunov’s direct method and Barbalat’s Lemma. It is expected that some results presented in this dissertation can contribute towards the validation and certification of direct adaptive controllers

Parameter Estimation for a Sinusoidal Signal with a Time-Varying Amplitude

This paper addresses the parameter estimation problem of a non-stationary sinusoidal signal with a timevarying amplitude, which is given by a known function of time multiplied by an unknown constant coefficient. A robust estimation algorithm is proposed for identifying the unknown frequency and the amplitude coefficient in real-time. The estimation algorithm is constructed based on the Volterra integral operator with suitably designed kernels and sliding mode adaptation laws. It is shown that the parameter estimation error converges to zero within an arbitrarily small finite time, and the robustness against bounded additive disturbances is certified by bounded-input-bounded-output arguments. The effectiveness of the estimation technique is evaluated and compared with other existing tools through numerical simulations

Task-space dynamic control of underwater robots

This thesis is concerned with the control aspects for underwater tasks performed by marine robots. The mathematical models of an underwater vehicle and an underwater vehicle with an onboard manipulator are discussed together with their associated properties. The task-space regulation problem for an underwater vehicle is addressed where the desired target is commonly specified as a point. A new control technique is proposed where the multiple targets are defined as sub-regions. A fuzzy technique is used to handle these multiple sub-region criteria effectively. Due to the unknown gravitational and buoyancy forces, an adaptive term is adopted in the proposed controller. An extension to a region boundary-based control law is then proposed for an underwater vehicle to illustrate the flexibility of the region reaching concept. In this novel controller, a desired target is defined as a boundary instead of a point or region. For a mapping of the uncertain restoring forces, a least-squares estimation algorithm and the inverse Jacobian matrix are utilised in the adaptive control law. To realise a new tracking control concept for a kinematically redundant robot, subregion tracking control schemes with a sub-tasks objective are developed for a UVMS. In this concept, the desired objective is specified as a moving sub-region instead of a trajectory. In addition, due to the system being kinematically redundant, the controller also enables the use of self-motion of the system to perform sub-tasks (drag minimisation, obstacle avoidance, manipulability and avoidance of mechanical joint limits)

Model-based Friction Compensation

Friction is present in all mechanical systems and causes a wide range of problems for control. The development of model-based strategies accounting for Friction in the designed control has been a vast area of Research since these last decades. A promising Friction model which received a lot of attention these last years is the so-called LuGre model, which originates in the collaboration between the two control Research groups of Lund (Sweden) and Grenoble (France). This model is quite simple and is capable of capturing a wide range of well known friction phenomena, such as the Stribeck effect or the frictionnal lag. In particular this model is used in [Robertsson et al., 2004], where a general method for friction compensation for nonlinear systems is presented. The compensation strategy is simple: it just consists in adding to the control signal a friction estimate, computed using a LuGre model based observer. This thesis deals with the application of the theory of this article on a real experiment: the stabilization of the Furuta pendulum in the upright position. First, attention is paid so that the initial hypothesis of this article be satisfied. These hypotheses consist in finding a stabilizing control for the system when Friction is neglected, and an associated Lyapunov function verifying some properties. Then, Friction is included by following the procedure presented in the article. The friction estimate is computed according to the discretized LuGre form, presented in fFreidovich et al., 2006g, and the main result of the article is verified both in Simulation and on the real process, the simulations being carried out with Matlab-Simulink and the real experiments by using a dSPACE device. From a practical point of view, the implemented compensation scheme works perfectly in Simulation: the limit cycles originating from an uncompensated friction are totally annihilated, while for real experiments this oscillating behaviour is still remaining, but happens to be significantly reduced. From a theoretical point of view, the results of [Robertsson et al., 2004] are fully verified in Simulation, while for real experiments the presence of remaining limit cycles prevents a perfect verification of the theory

MIT Space Engineering Research Center

The Space Engineering Research Center (SERC) at MIT, started in Jul. 1988, has completed two years of research. The Center is approaching the operational phase of its first testbed, is midway through the construction of a second testbed, and is in the design phase of a third. We presently have seven participating faculty, four participating staff members, ten graduate students, and numerous undergraduates. This report reviews the testbed programs, individual graduate research, other SERC activities not funded by the Center, interaction with non-MIT organizations, and SERC milestones. Published papers made possible by SERC funding are included at the end of the report

Adaptive-Optimal Control of Spacecraft near Asteroids

Spacecraft dynamics and control in the vicinity of an asteroid is a challenging and exciting problem. Currently, trajectory tracking near asteroid requires extensive knowledge about the asteroid and constant human intervention to successfully plan and execute proximity operation. This work aims to reduce human dependency of these missions from a guidance and controls perspective. In this work, adaptive control and model predictive control are implemented to generating and tracking obstacle avoidance trajectories in asteroid’s vicinity. Specifically, direct adaptive control derived from simple adaptive control is designed with e modification to track user-generated trajectories in the presence of unknown system and sensor noise. This adaptive control methodology assumes no information on the system dynamics, and it is shown to track trajectories successfully in the vicinity of the asteroid. Then a nonlinear model predictive control methodology is implemented to generate obstacle avoidance trajectories with minimal system information namely mass and angular velocity of the asteroid. Ultimately, the adaptive control system is modified to include feed-forward control input from the nonlinear model predictive control. It is shown through simulations that the new control methodology names direct adaptive model predictive control (DAMPC), is able to generate sub-optimal trajectories. A comparative study is done with Asteroid Bennu, Kleopatra and Eros to show the benefits of DAMPC over adaptive control and MPC. A study on effect of noisy measurements and model is also conducted on adaptive control and direct adaptive model predictive control