Nonsmooth stabilizability and feedback linearization of discrete-time nonlinear systems

We consider the problem of stabilizing a discrete-time nonlinear system using a feedback which is not necessarily smooth. A sufficient condition for global dynamical stabilizability of single-input triangular systems is given. We obtain conditions expressed in terms of distributions for the nonsmooth feedback triangularization and linearization of discrete-time systems. Relations between stabilization and linearization of discrete-time systems are given

State-Space Feedback Linearization for Depth Positioning of a Spherical URV

Variable ballast, a common mechanism in underwater vehichle, is utilized as vertical motion actuator of a spherical URV in order to control its depth positiong. Since the model of this system is nonlinear and controllable therefore state-space feedback linearization is utilized in this depth positioning. The idea of state-space feedback linearization is to algebraically transform all state variable of nonlinear systems dynamics into (fully or partly) linear ones, so that linear control techniques can be applied. This method can stabilize the equilibrium point of this system which is unstable in open loop system. From the control analysis and simulation results, it can be observed that the asymptotical stabilization is achieved by tracking the error. Hence, state-space feedback linearization can also be applied for tracking a trajectory of desired depth position. Keyword: variable ballast, spherical URV, feedback linearizatio

Nonlinear compensation techniques for magnetic suspension systems

In aerospace applications, magnetic suspension systems may be required to operate over large variations in air-gap. Thus the nonlinearities inherent in most types of suspensions have a significant effect. Specifically, large variations in operating point may make it difficult to design a linear controller which gives satisfactory stability and performance over a large range of operating points. One way to address this problem is through the use of nonlinear compensation techniques such as feedback linearization. Nonlinear compensators have received limited attention in the magnetic suspension literature. In recent years, progress has been made in the theory of nonlinear control systems, and in the sub-area of feedback linearization. The idea is demonstrated of feedback linearization using a second order suspension system. In the context of the second order suspension, sampling rate issues in the implementation of feedback linearization are examined through simulation

Optimality of nonlinear design techniques: A converse HJB approach

The issue of optimality in nonlinear controller design is confronted by using the converse HJB approach to classify dynamics under which certain design schemes are optimal. In particular, the techniques of Jacobian linearization, pseudo-Jacobian linearization, and feedback linearization are analyzed. Finally, the conditions for optimality are applied to the 2-D nonlinear oscillator, where simple, nontrivial examples are produced in which the various design techniques are optimal

Input-output linearization and fractional robust control of a non-linear system

This article deals with the association of a linear robust controller and an input-output linearization feedback for the control of a perturbed and non-linear system. This technique is applied to the control of a hydraulic system whose actuator is non-linear and whose load is time-variant. The piston velocity of the actuator needs to be controlled and a pressure-difference inner-loop is used to improve the performance. To remove the effect of the non-linearity, an input-output linearization under diffeomorphism and feedback is achieved. CRONE control, based on complex fractional differentiation, is applied to design a controller for piston-velocity loop even when parametric variations occu

Crone control of a nonlinear hydraulic actuator

The CRONE control (fractional robust control) of a hydraulic actuator whose dynamic model is nonlinear is presented. An input-output linearization under diffeomorphism and feedback is first achieved for the nominal plant. The relevance of this linearization when the parameters of the plant vary is then analyzed using the Volterra input-output representation in the frequency domain. CRONE control based on complex fractional differentiation is finally applied to control the velocity of the input-output linearized model when parametric variations occur