Output-input stability and minimum-phase nonlinear systems

This paper introduces and studies the notion of output-input stability, which represents a variant of the minimum-phase property for general smooth nonlinear control systems. The definition of output-input stability does not rely on a particular choice of coordinates in which the system takes a normal form or on the computation of zero dynamics. In the spirit of the ``input-to-state stability'' philosophy, it requires the state and the input of the system to be bounded by a suitable function of the output and derivatives of the output, modulo a decaying term depending on initial conditions. The class of output-input stable systems thus defined includes all affine systems in global normal form whose internal dynamics are input-to-state stable and also all left-invertible linear systems whose transmission zeros have negative real parts. As an application, we explain how the new concept enables one to develop a natural extension to nonlinear systems of a basic result from linear adaptive control.Comment: Revised version, to appear in IEEE Transactions on Automatic Control. See related work in http://www.math.rutgers.edu/~sontag and http://black.csl.uiuc.edu/~liberzo

Reverse Engineering Biological Control Systems for Applications in Process Control.

The main emphasis of this dissertation is the development of nonlinear control strategies based on biological control systems. Commonly utilized biological control schemes have been studied in order to reverse engineer the important concepts for applications in process control. This approach has led to the development of a nonlinear habituating control strategy and nonlinear model reference adaptive control schemes. Habituating control is a controller design strategy for nonlinear systems with more manipulated inputs than controlled outputs. Nonlinear control laws that provide input-output linearization while simultaneously minimizing the cost of affecting control are derived. Local stability analysis shows the controller can provide a simple solution to singularity and non-minimum phase problems. A direct adaptive control strategy for a class of single-input, single-output non-linear systems is presented. The major advantage is that a detailed dynamic non-linear model is not required for controller design. Unknown controller functions in the associated input-output linearizing control law are approximated using locally supported radial basis functions. Lyapunov stability analysis is used to derive parameter update laws which ensure the state vector remains bounded and the plant output asymptotically tracks the output of a linear reference model. A nonlinear model reference adaptive control strategy in which a linear model (or multiple linear models) is embedded within the nonlinear controller is presented. The nonlinear control law is constructed by embedding linear controller gains derived from models obtained using standard linear system identification techniques within the associated input-output linearizing control law. Higher-order controller functions are approximated with radial basis functions. Lyapunov stability analysis is used to derive stable parameter update laws. The major disadvantage of the previous techniques is computational expense. Two modifications have been developed. First, the effective dimension is reduced by applying nonlinear principal component analysis to the state variable data obtained from open-loop tests. This allows basis functions to be placed in a lower dimensional space than the original state space. Second, the total number of basis functions is fixed a priori and an algorithm which adds/prunes basis function centers to surround the current operating point on-line is utilized

Real Time Trajectory Generation for Differentially Flat Systems

This paper considers the problem of real time trajectory generation and tracking for nonlinear control systems. We employ a two degree of freedom approach that separates the nonlinear tracking problem into real time trajectory generation followed by local (gain-scheduled) stabilization. The central problem which we consider is how to generate, possibly with some delay, a feasible state space and input trajectory in real time from an output trajectory that is given online. We propose two algorithms that solve the real time trajectory generation problem for differentially flat systems with (possibly non-minimum phase) zero dynamics. One is based on receding horizon point to point steering, the other allows additional minimization of a cost function. Both algorithms explicitly address the tradeoff between stability and performance and we prove convergence of the algorithms for a reasonable class of output trajectories. To illustrate the application of these techniques to physical systems, we present experimental results using a vectored thrust flight control experiment built at Caltech. A brief introduction to differentially flat systems and its relationship with feedback linearization is also included

Additive-Decomposition-Based Output Feedback Tracking Control for Systems with Measurable Nonlinearities and Unknown Disturbances

In this paper, a new control scheme, called as additive-decomposition-based tracking control, is proposed to solve the output feedback tracking problem for a class of systems with measurable nonlinearities and unknown disturbances. By the additive decomposition, the output feedback tracking task for the considered nonlinear system is decomposed into three independent subtasks: a pure tracking subtask for a linear time invariant (LTI) system, a pure rejection subtask for another LTI system and a stabilization subtask for a nonlinear system. By benefiting from the decomposition, the proposed additive-decomposition-based tracking control scheme i) can give a potential way to avoid conflict among tracking performance, rejection performance and robustness, and ii) can mix both design in time domain and frequency domain for one controller design. To demonstrate the effectiveness, the output feedback tracking problem for a single-link robot arm subject to a sinusoidal or a general disturbance is solved respectively, where the transfer function method for tracking and rejection and backstepping method for stabilization are applied together to the design.Comment: 23 pages, 6 figure

Dynamic state feedback decoupling of a DX A/C system

A temperature and humidity controller is designed for a direct expansion air conditioning (DX A/C) system making use of a state feedback decoupling approach of nonlinear control systems. It is shown that the nonlinear dynamics of a DX A/C system can be input-output decoupled by dynamic state feedback. The resulting decoupled system is of minimum phase. Thereafter, the decoupled model is used to design a pole placement controller with guaranteed stability. Unlike controllers based on approximate local linearization of the DX A/C model, the controller proposed is global in the sense that it can track temperature and humidity setpoints in the complete operating range of the DX A/C system. Effectiveness of the controller designed is demonstrated by simulation results.https://www.journals.elsevier.com/ifac-papersonlineam2020Electrical, Electronic and Computer Engineerin

Design of generalized minimum variance controllers for nonlinear multivariable systems

The design and implementation of Generalized Minimum Variance control laws for nonlinear multivariable systems that can include severe nonlinearities is considered. The quadratic cost index minimised involves dynamically weighted error and nonlinear control signal costing terms. The aim here is to show the controller obtained is simple to design and implement. The features of the control law are explored. The controller obtained includes an internal model of the process and in one form is a nonlinear version of the Smith Predictor