Tools for Nonlinear Control Systems Design

This is a brief statement of the research progress made on Grant NAG2-243 titled "Tools for Nonlinear Control Systems Design", which ran from 1983 till December 1996. The initial set of PIs on the grant were C. A. Desoer, E. L. Polak and myself (for 1983). From 1984 till 1991 Desoer and I were the Pls and finally I was the sole PI from 1991 till the end of 1996. The project has been an unusually longstanding and extremely fruitful partnership, with many technical exchanges, visits, workshops and new avenues of investigation begun on this grant. There were student visits, long term.visitors on the grant and many interesting joint projects. In this final report I will only give a cursory description of the technical work done on the grant, since there was a tradition of annual progress reports and a proposal for the succeeding year. These progress reports cum proposals are attached as Appendix A to this report. Appendix B consists of papers by me and my students as co-authors sorted chronologically. When there are multiple related versions of a paper, such as a conference version and journal version they are listed together. Appendix C consists of papers by Desoer and his students as well as 'solo' publications by other researchers supported on this grant similarly chronologically sorted

Performance limits and robustness issues in the control of flexible link manipulators

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 1992.Includes bibliographical references (leaves 179-186).by Carlos Eduardo Padilla Santos.Ph.D

On Observer-Based Control of Nonlinear Systems

Filtering and reconstruction of signals play a fundamental role in modern signal processing, telecommunications, and control theory and are used in numerous applications. The feedback principle is an important concept in control theory. Many different control strategies are based on the assumption that all internal states of the control object are available for feedback. In most cases, however, only a few of the states or some functions of the states can be measured. This circumstance raises the need for techniques, which makes it possible not only to estimate states, but also to derive control laws that guarantee stability when using the estimated states instead of the true ones. For linear systems, the separation principle assures stability for the use of converging state estimates in a stabilizing state feedback control law. In general, however, the combination of separately designed state observers and state feedback controllers does not preserve performance, robustness, or even stability of each of the separate designs. In this thesis, the problems of observer design and observer-based control for nonlinear systems are addressed. The deterministic continuous-time systems have been in focus. Stability analysis related to the Positive Real Lemma with relevance for output feedback control is presented. Separation results for a class of nonholonomic nonlinear systems, where the combination of independently designed observers and state-feedback controllers assures stability in the output tracking problem are shown. In addition, a generalization to the observer-backstepping method where the controller is designed with respect to estimated states, taking into account the effects of the estimation errors, is presented. Velocity observers with application to ship dynamics and mechanical manipulators are also presented

Nonlinear Tracking Control Using a Robust Differential-Algebraic Approach.

This dissertation presents the development and application of an inherently robust nonlinear trajectory tracking control design methodology which is based on linearization along a nominal trajectory. The problem of trajectory tracking is reduced to two separate control problems. The first is to compute the nominal control signal that is needed to place a nonlinear system on a desired trajectory. The second problem is one of stabilizing the nominal trajectory. The primary development of this work is the development of practical methods for designing error regulators for Linear Time Varying systems, which allows for the application of trajectory linearization to time varying trajectories for nonlinear systems. This development is based on a new Differential Algebraic Spectral Theory. The problem of robust tracking for nonlinear systems with parametric uncertainty is studied in relation to the Linear Time Varying spectrum. The control method presented herein constitutes a rather general control strategy for nonlinear dynamic systems. Design and simulation case studies for some challenging nonlinear tracking problems are considered. These control problems include: two academic problems, a pitch autopilot design for a skid-to-turn missile, a two link robot controller, a four degree of freedom roll-yaw autopilot, and a complete six degree of freedom Bank-to-turn planar missile autopilot. The simulation results for these designs show significant improvements in performance and robustness compared to other current control strategies

Practical Solutions to the Non-Minimum Phase and Vibration Problems Under the Disturbance Rejection Paradigm

This dissertation tackles two kinds of control problems under the disturbance rejection paradigm (DRP): 1) the general problem of non-minimum phase (NMP) systems, such as systems with right half plane (RHP) zeros and those with time delay 2) the specific problem of vibration, a prevailing problem facing practicing engineers in the real world of industrial control. It is shown that the DRP brings to the table a refreshingly novel way of thinking in tackling the persistently challenging problems in control. In particular, the problem of NMP has confounded researchers for decades in trying to find a satisfactory solution that is both rigorous and practical. The active disturbance rejection control (ADRC), originated from DRP, provides a potential solution. Even more intriguingly, the DRP provides a new framework to tackle the ubiquitous problem of vibration, whether it is found in the resonant modes in industrial motion control with compliant load, which is almost always the case, or in the microphonics of superconducting radio frequency (SRF) cavities in high energy particle accelerators. That is, whether the vibration is caused by the environment or by the characteristics of process dynamics, DRP provides a single framework under which the problem is better understood and resolved. New solutions are tested and validated in both simulations and experiments, demonstrating the superiority of the new design over the previous ones. For systems with time delay, the stability characteristic of the proposed solution is analyze

Asymmetric order-doubling and robust state estimation for uncertain nonminimum phase systems

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 1999.Includes bibliographical references (leaves 145-148).by Muralidhar Ravuri.Ph.D

Practical Solutions to the Non-Minimum Phase and Vibration Problems Under the Disturbance Rejection Paradigm

This dissertation tackles two kinds of control problems under the disturbance rejection paradigm (DRP): 1) the general problem of non-minimum phase (NMP) systems, such as systems with right half plane (RHP) zeros and those with time delay 2) the specific problem of vibration, a prevailing problem facing practicing engineers in the real world of industrial control. It is shown that the DRP brings to the table a refreshingly novel way of thinking in tackling the persistently challenging problems in control. In particular, the problem of NMP has confounded researchers for decades in trying to find a satisfactory solution that is both rigorous and practical. The active disturbance rejection control (ADRC), originated from DRP, provides a potential solution. Even more intriguingly, the DRP provides a new framework to tackle the ubiquitous problem of vibration, whether it is found in the resonant modes in industrial motion control with compliant load, which is almost always the case, or in the microphonics of superconducting radio frequency (SRF) cavities in high energy particle accelerators. That is, whether the vibration is caused by the environment or by the characteristics of process dynamics, DRP provides a single framework under which the problem is better understood and resolved. New solutions are tested and validated in both simulations and experiments, demonstrating the superiority of the new design over the previous ones. For systems with time delay, the stability characteristic of the proposed solution is analyze