The Hybrid Motor Prototype: Design Details and Demonstration Results

A novel hybrid rotary motor incorporating piezoelectric and magnetostrictive actuators has been designed and demonstrated. The novelty of this motor was the creation of an electrical resonant circuit, whereby reactive power requirement on the power source is reduced. It was envisioned that the motor would be suitable for low output speed, high torque applications because of its design. This report presents the constructional details of this motor and the results of the demonstration

Asymptotic Stability of Nonlinear Systems with Holomorphic Structure

We consider the local asymptotic stability of a system dx/dt = F(z), z = C sup n , F : C sup n - C sup n is holomorphic, t R, and show that if the system is locally asymptotically stable at some equilibrium point in the N sup th approximation for some N , then necessarily its linear part is asymptotically stable also

Stabilization of Globally Noninteractive Nonlinear Systems via Dynamic State-Feedback

We consider the problem of semiglobal asymptotic stabilization and noninteracting control via dynamic state-feedback for a class of nonlinear control systems. It is assumed that the plant has been already rendered noninteractive. A sufficient condition for the stabilization of the overall system, without destroying the noninteraction property, is given in terms of stabilizability of certain subsystems

Asymptotic Stabilization of Low Dimensional Systems

This paper studies the asymptotic stabilization of two and three dimensional nonlinear control systems. In the two dimensional case we review some of our recent work and in the three dimensional case we give some new sufficient conditions and necessary conditions

Noninteracting Control with Stability for a Class of Nonlinear Systems

In this paper we address the problem of noninteracting control with stability for the class of nonlinear square systems for which noninteraction can be achieved (without stability) by means of invertible static state-feedback. The use of both static state-feedback and dynamic state-feedback is investigated. We prove that in both cases the asymptotic stabilizability of certain subsystems is necessary to achieve noninteraction and stability. We use this and some recent results to state a complete set of necessary and sufficient conditions in order to solve the problem

Global Tracking Problem for Minimum Phase Nonlinear Systems

We consider the tracking problem for a globally minimum phase nonlinear system. It is assumed that the signal to be tracked is slowly varying and a priori bounds on its magnitude are known. We show that if the system has bounded derivatives and exponentially stable zero dynamics then the system admits an output feedback controller which solves the tracking problem

Non-Smooth Simultaneous Stabilization of Nonlinear Systems: Interpolation of Feedback Laws

In this paper, we introduce a method that enables us to construct a continuous simultaneous stabilizer for pairs of systems in the plane that cannot be simultaneously stabilized by smooth feedback. We extend this method to higher dimensional systems and prove that any pair of asymptotically stabilizable nonlinear systems can be simultaneously stabilized (not asymptotically) by means of continuous feedback. The resulting simultaneous stabilizer depends on a partition of unity and we show how to circumvent the computation of this partition of unity by constructing an explicit simultaneous stabilizer

Time-Varying simultaneous stabilization, Part II. Finite families of nonlinear systems

In this paper, we derive sufficient conditions for the existence of a continuous time-varying feedback law that simultaneously locally or globally asymptotically stabilizes a finite family of nonlinear systems. We then focus on a class of pairs of nonlinear homogeneous systems, and by using the previous sufficient conditions, we establish their asymptotic stabilizability by means of time-varying feedback

Optimal Control of a Rigid Body with Two Oscillators

This paper is concerned with the exploration of reduction and explicit solvability of optimal control problems on principal bundles with connections from a Hamiltonian point of view. The particular mechanical system we consider is a rigid body with two driven oscillators, for which the bundle structure is (SO (3) x 者, 者, SO (3)). The optimal control problem is posed by considering a special nonholonomic variational problem, in which the nonholonomic distribution is defined via a connection. The necessary conditions for the optimal control problem are determined intrinsically by a Hamiltonian formulation. The necessary conditions admit the structure group of the principal bundle as a symmetry group of the system. Thus the problem is amendable to Poisson reduction. Under suitable hypotheses and approximations, we find that the reduced system possesses additional symmetry which is isomorphic to S1. Applying Poisson reduction again, we obtain a further reduced system and corresponding first integral. These reductions imply explicit solvability for suitable values of parameters

Non-Smooth Robust Stabilization of a Family of Linear Systems in the Plane

In this paper, we use merely continuous feedback to robustly stabilize a class of parameterized family of linear systems in the plane. We introduce a new interpolation method that enables us to construct a robust stabilizer for the entire family of systems, by using two feedback laws that robustly stabilize two particular sub-families