Nonlinear Control Khalil Solution S Zip
Nichole Wernett
In this paper, parabolic type differential inclusions with time dependent are considered and this problem is related to the study of the nonlinear distributed parameter control systems. An existence theorem of mild-solutions is proved, and a property of the solution set is given. The directions and the results by J. P. Aubin et al are generalized and improved.
This paper addresses the issue of controller design for a
class of multi-input multi-output (MIMO) uncertain underactuated
systems with saturating inputs. A systematic controller framework,
composed of a hierarchically generated control term, meant to
ensure the stabilization of a particular portion of system dynamics
and some dedicated control terms designed to solve the tracking
problem of the remaining system dynamics is presented. Wavelet
neural networks are used as adaptive tuners to approximate the
system uncertainties also to reshape the control terms so as to deal
with the saturation nonlinearity in an antiwindup paradigm.
Gradient based tuning laws are developed for the online tuning of
adjustable parameters of the wavelet network. A Lyapunov based
stability analysis is carried out to ensure the uniformly ultimately
bounded (UUB) stability of the closed loop system. Finally, a
simulation is carried out which supports the theoretical
development.
The aims of the course in relation to knowledge and understanding are:
- Understanding of the phenomena of nonlinear dynamical systems: multiple equilibria, stability/instability, limit cycles.
- Knowledge of the stability theory and its extensions.
- Knowledge of the main methods of nonlinear control.
In relation to the capability of applying knowledge and understanding, the aims are:
- Skill to analyze nonlinear systems.
- Skil to simulate nonlinear systems on a computer.
- Skill to design nonlinear control systems in the scalar case.
1) Introduction. Nonlinear phenomena and mathematical models, applications to automation and robotics. Examples. Nonlinear state models: existence and uniqueness of solutions. Second-order dynamical systems: qualitative behavior of linear systems, phase diagrams, multiple equilibria, limit cycles. Useful mathematics for nonlinear systems. Modeling examples: kinematics of wheeled vehicles, magnetic levitators, overhead cranes. [11 hours]
2) Autonomous systems. Stability theory: the direct method of Lyapunov, Lyapunov functions and the variable gradient method. The region of attraction of an equilibrium state. Global asymptotic stability: Barbashin-Krasovkii theorem. Instability: Chetaev theorem. The algebraic Lyapunov equation and the indirect method. The invariance principle: LaSalle theorem. Stability and attractiveness of state sets. Limit cycles in feedback systems: method of the describing function. [14 hours]
3) Nonautonomous systems. Stability of state motions. Class K and class KL (comparison) functions. The direct method for the uniform asymptotic stability. Input-to-state stability. The direct and indirect method for exponential stability. Converse theorems in stability theory. [7 hours]
4) Nonlinear control. The stabilization problem. State-input feedback methods: control Lyapunov functions, integrator backstepping. Relative degree and normal form of a scalar affine control system. Input-output linearization by state-input feedback (feedback linearization). Zero dynamics and minimum-phase systems. Application to stabilization. Regulation of nonlinear scalar systems: integral control. Input-output inversion-based feedforward control. Stable inversion for nonminimum-phase systems: closed-form solutions for linear systems and iterative method for nonlinear systems. Feedforward-feedback control schemes. [16 hours]
Classroom lessons with the alternate use of slides and explanations at the blackboard. Analysis and synthesis exercises with the aid of the MATLAB software in the Informatics Laboratory. The slides used to support lessons are available on the course website. They are the main didactical material of the course.
Assessment of learning is carried out by a written test followed a week later by an oral exam.
To enroll in the written tests, it is mandatory the registration on the ESSE3 website of the University. During the written test, it is not permitted to read notes, manuals, books, etc. Some parts of the written test require the use of a basic scientific calculator.
Two-three days after the written test, the results are published on the course website. To proceed to the oral exam, the score in the written test must be 16 points or greater on a scale from 0 to 30.
The final vote is expressed in the 0-30 scale and is obtained as a weighted average of the scores in the written and oral tests.