Explicit Reference Governor for Continuous Time Nonlinear Systems Subject to Convex Constraints

This paper introduces a novel closed-form strategy that dynamically modifies the reference of a pre-compensated nonlinear system to ensure the satisfaction of a set of convex constraints. The main idea consists of translating constraints in the state space into constraints on the Lyapunov function and then modulating the reference velocity so as to limit the value of the Lyapunov function. The theory is introduced for general nonlinear systems subject to convex constraints. In the case of polyhedric constraints, an explicit solution is provided for the large and highly relevant class of nonlinear systems whose Lyapunov function is lower-bounded by a quadratic form. In view of improving performances, further specializations are provided for the relevant cases of linear systems and robotic manipulators.Comment: Submitted to: IEEE Transactions on Automatic Contro

Non-linear PID predictive controller

A new class of nonlinear PID controllers are derived for nonlinear systems using a Nonlinear Generalised Predictive Control (NGPC) approach. First the disturbance decoupling ability of the nonlinear generalised predictive controller is discussed. For a nonlinear system where the disturbance cannot be decoupled, a nonlinear observer is designed to estimate the offset. By selecting the nonlinear gain function in the observer, it is shown that the closed-loop system under optimal generalised predictive control with the nonlinear observer is asymptotically stable. It is pointed out that this composite controller is equivalent to a nonlinear controller with integral action. As a special case, for a nonlinear system with a low relative degree, the proposed nonlinear controller reduces to a nonlinear PI or PID predictive controller, which consists of a nonlinear PI or PID controller and a prediction controller. The design method is illustrated by an example nonlinear mechanical system

Supervisory-plus-regulatory control design for efficient operation of industrial furnaces

A two-level system engineering design approach to integrated control and supervision of industrial multi-zone furnaces has been elaborated and tested. The application case study is the three-zone 25 MW RZS furnace plant at Skopje Steelworks. The integrated control and supervision design is based on combined use of general predictive control optimization of set-points and steady-state decoupling,at the upper level, and classical two-term laws with stady-state decouling, at the executive control level. This design technique exploits the intrinsic stability of thermal processes and makes use of constrained optimization, standard non-parametric time-domain process models, identified under operating conditions, using truncated k-time sequence matrices, controlled autoregressive moving average models. Digital implementations are sought within standard computer process control platform for practical engineering and maintenance reasons

Gradient projection anti-windup scheme

Thesis (Sc. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2011.Cataloged from PDF version of thesis.Includes bibliographical references (p. 205-217).It is a well-recognized fact that control saturation affects virtually all practical control systems. It leads to controller windup, which degrades/limits the system's closed-loop performance, and may cause catastrophic failures if it induces instability. Anti-windup compensation is one of two main approaches to mitigate the effects of windup, and is conceptually and practically attractive. For the idealized case of constrained linear time invariant (LTI) plants driven by LTI controllers, numerous anti-windup schemes exist. However, most practical control systems are inherently nonlinear, and anti-windup compensation for nonlinear systems remains largely an open problem. To this end, we propose the gradient projection anti-windup (GPAW) scheme, which is an extension of the conditional integration method to multi-input-multi-output (MIMO) nonlinear systems, using Rosen's gradient projection method for nonlinear programming. It achieves controller state-output consistency by projecting the controller state onto the unsaturated region induced by the control saturation constraints. The GPAW-compensated controller is a hybrid controller defined by the online solution to either a combinatorial optimization subproblem, a convex quadratic program, or a projection onto a convex polyhedral cone problem. We show that the GPAW-compensated system is obtained by modifying the uncompensated system with a passive operator. Qualitative weaknesses of some existing anti-windup results are established, which motivated a new paradigm to address the anti-windup problem. It is shown that for a constrained first order LTI plant driven by a first order LTI controller, GPAW compensation can only maintain/enlarge its region of attraction (ROA). In this new paradigm, we derived some ROA comparison and stability results for MIMO nonlinear as well as MIMO LTI systems. The thesis is not that the GPAW scheme solves a centuries-old open problem of immense practical importance, but rather, that it provides a potential path to a solution. We invite the reader to join us in this quest at the confluence of nonlinear systems, hybrid systems, projected dynamical systems, differential equations with discontinuous right-hand sides, combinatorial optimization, convex analysis and optimization, and passive systems.by Chun Sang Justin Teo.Sc.D