On the relation between state feedback and full information regulators in nonlinear singular H/sub ∞/ control

In this note the relationship between state feedback control laws and full information control laws, i.e. control laws which make explicit use of the disturbance signals, is discussed. In particular it is shown that any (polynomial) full information control law can be always approximated by a state feedback control law, provided that a certain (arbitrarily small) amount of performance is sacrificed. Moreover, the obtained result is used to give alternative proof and generalization to some existing results in the area of global disturbance attenuation for nonlinear systems and to establish some new and interesting results regarding the problem of approximate model matching.

H∞ Tracking with Preview for Linear Systems with Impulsive Effects -State Feedback and Full Information Cases-

This paper presents a two-Riccati inequality approach for the design of fixed-order H/sub /spl infin// suboptimal controllers with an observer-based structure. The two Riccati inequalities are only one-way coupled and can be solved consecutively. The fixed-order controller has the structure of a fixed-order estimator of the state feedback control law in the presence of the worst case disturbances. It retains the observer-based compensator structure of the full-order central controller of the standard H/sub /spl infin// design, but adds a fixed-order dynamic and mappings between the full-order and the fixed-order state spaces. In the full-order special case, this controller recovers to the minimal entropy central controller of the standard H/sub /spl infin// design.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Presents an H/sub /spl infin// design approach for a neural net-based control scheme. In this scheme, a class of nonlinear systems is approximated by two multilayer perceptrons. The neural networks are piecewisely interpolated to generate a linear differential inclusion model. Based on this model, a state feedback control law is designed. The H/sub /spl infin// control is specified to eliminate the effect of approximation errors and external disturbances to achieve the desired performance. It is shown that finding the permissible control gain matrices can be transformed to a standard linear matrix inequality problem and solved using the convex optimization method.

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A nonlinear feedback control design for the adaptive robust H/sub /spl infin// control problem for nonlinear systems with gain bounded uncertainty is presented. An existing control scheme developed for nonlinear systems with relative degree of one is extended to the case where nonlinear systems have general relative degree. A Lyapunov function is constructed that ensures not only the stability of the closed-loop system but also satisfies the dissipation inequality ensuring L/sub 2/-gain performance. Then the controller can be obtained by the recursive use of the existing control scheme. A closed-form solution for the nonlinear H/sub /spl infin// control problem is provided without using a Hamilton-Jacobi inequality in the general relative degree case. Sufficient conditions which nonlinear systems should satisfy for solvability of the problem are provided.

Presents techniques for controlling the motion of an underactuated vehicle when disturbances are present and only imperfect state measurements are available for feedback. A state feedback controller is developed and then it is converted to an imperfect state measurement feedback controller. The state feedback tracking control law uses an H/sup /spl infin//-optimal design and produces a locally exponentially stable closed-loop system. The imperfect state measurement feedback controller combines the state feedback control law with an H/sup /spl infin//-filter to estimate the states and achieves a modified form of disturbance attenuation. The state estimator exploits a unique structure in the nonlinear equations of motion to develop a direct solution. MATLAB simulations illustrate both control algorithms for an underactuated ship model.

This paper investigates three polynomial strategies in damping oscillations in a horizontal axis turbine plant power systems, to demonstrate the influence of the introduction of the STATCOM in the power system, a comparative study is implemented using various polynomial algorithm control approaches to a horizontal wind axis turbine power system incooperating a static synchronous compensator (STATCOM). The proposed controllers' designs are based on a linear time invariant model of the plant and state feedback scheme. First, the linearized mathematical model of STATCOM is derived. Then, using polynomial algorithms as a state feedback algorithm, a state feedback control law is derived. The proposed control strategy is tested on SMIB power system with wind turbine by digital computer simulations using matlab/simulink and a power analysis toolbox. Comparison of the polynomial matching results of the controllers establishes the superb nature of polynomial approximation approach.

This chapter presents full information state feedback H∞ optimal control. This control synthesis method uses state space methods to achieve stability, performance, and robustness and allows for the direct loop shaping in the frequency domain. This chapter begins with an introduction of various norms used in control system design and analysis, followed by methods of specifying stability and performance specifications in the frequency domain. This logically leads into loop shaping using frequency-dependent weights. The state feedback control law is then synthesized using an algebraic Riccati equation approach called γ-iteration. This method is applied to a UAV design example. This control synthesis method is an excellent approach that teaches design engineers important properties in both the time domain and frequency domain and more importantly how to achieve these properties in a closed-loop design.KeywordsState FeedbackStability MarginLoop GainState Feedback ControllerAlgebraic Riccati EquationThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

A bifurcation approach is adopted to analyze and control the surge model for axial flow compressors. An explicit expression is obtained for the first nonzero coefficient of the characteristic exponents of the periodic solutions born from the Hopf bifurcation associated with surge. The sign of this coefficient determines stability of the surge model at the criticality. Local nonlinear feedback control laws are then developed to stabilize the Hopf bifurcation associated with surge. Both quadratic and cubic state feedback control laws are investigated. Feedback stabilization using output measurement such as pressure rise is also studied where stabilizing gains are characterized that can be used for synthesis of surge control laws.

Angular velocity stabilization control and attitude stabilization control for an underactuated spacecraft using only two single gimbal control moment gyros (SGCMGs) as actuators is investigated. First of all, the dynamic model of the underactuated spacecraft is established and the singularity of different configurations with the two SGCMGs is analyzed. Under the assumption that the gimbal axes of the two SGCMGs are installed in any direction, and that the total system angular momentum is not zero, a state feedback control law via Lyapunov method is designed to globally asymptotically stabilize the angular velocity of spacecraft. Under the assumption that the gimbal axes of the two SGCMGs are coaxially installed along anyone of the three principal axes of spacecraft inertia, and that the total system angular momentum is zero, a discontinuous state feedback control law is designed to stabilize three-axis attitude of spacecraft with respect to the inertial frame. Furthermore, the singularity escape of SGCMGs for the above two control problems is also studied. Simulation results demonstrate the validity of the control laws.

In this paper, the dynamic behavior of permanent magnet synchronous motors and the nonlinear output regulation of them for constant reference signals are studied. The dynamic analysis is based on previous studies and new results related to chaos phenomena are obtained. With the state feedback control law, regulation of motor velocity and direct-axis current is achieved for known and unknown load torque at constant operating points. Moreover, the control law is enhanced in the sense of robustness with respect to parameter uncertainties by utilizing an augmented system with integral operators.

Stability and performance of discrete-time switched linear systems

In this study, the authors consider the problem of frequency regulation via output feedback for a hydraulic turbine system under unknown load variations. First, to address the difficulties in estimating the unmeasurable states and the unknown load variation, they introduce a universal finite‐time observer ( UFTO ) which can estimate unmeasurable states, unknown parameters and disturbances under a unified framework. Based on the proposed UFTO , the unmeasurable wicket gate position, the flow rate and the load variation are estimated in a finite time for the hydraulic turbine system. Then by introducing a coordinate transformation, the state‐space model of hydraulic turbine system is converted into a simple form for which a state feedback control law is constructed using the adding a power integrator approach. Combining the UFTO with the finite‐time control law, an output feedback controller is designed to regulate the frequency of the hydraulic turbine system. Computer simulations are also given to validate the proposed finite‐time output feedback controller.

The problem of Earth-pointing attitude control for a spacecraft with magnetic actuators is addressed and a novel approach to the problem is proposed, which guarantees almost global closed loop stability of the desired relative attitude equilibrium for the spacecraft. Precisely, a proportional derivative (PD)-like state feedback control law is employed together with a suitable adaptation mechanism for the controller gain. Simulation results are presented, which illustrate the performance of the proposed control law