From Nonlinear to Hamiltonian via Feedback

Mechanical control systems are a very important class of nonlinear control systems. They possess a rich mathematical structure which can be extremely important for the solution of various control problems. In this paper, we expand the applicability of design methodologies developed for mechanical control systems by locally rendering nonlinear control systems, mechanical by a proper choice of feedback. In particular, we characterize control systems which can be transformed to Hamiltonian control systems by a local feedback transformation

Feedback control of quantum state reduction

Feedback control of quantum mechanical systems must take into account the probabilistic nature of quantum measurement. We formulate quantum feedback control as a problem of stochastic nonlinear control by considering separately a quantum filtering problem and a state feedback control problem for the filter. We explore the use of stochastic Lyapunov techniques for the design of feedback controllers for quantum spin systems and demonstrate the possibility of stabilizing one outcome of a quantum measurement with unit probability

Motion control - A SMC approach

Motion control involves many diversified control problems of complex nonlinear systems. In this paper we will be addressing the SMC approach for multi-body mechanical systems control. The main feature of the SMC is constraint of the system motion into manifold in system state space. It will be shown that usage of the SMC methods is a natural way of addressing problems in motion control including constrained systems, redundant systems and functionally related systems to name some. The consistent application of the SMC methods leads to natural decomposition of system motion for redundant tasks and allows simple, straight forward dynamical decoupling of the multiple tasks

A power-based perspective of mechanical systems

This paper is concerned with the construction of a power-based modeling framework for a large class of mechanical systems. Mathematically this is formalized by proving that every standard mechanical system (with or without dissipation) can be written as a gradient vector field with respect to an indefinite metric. The form and existence of the corresponding potential function is shown to be the mechanical analogue of Brayton and Moser's mixed-potential function as originally derived for nonlinear electrical networks in the early sixties. In this way, several recently proposed analysis and control methods that use the mixed-potential function as a starting point can also be applied to mechanical systems.

Magnetic gear dynamics for servo control

This paper considers the analysis and application of magnetic gearbox and magnetic coupling technologies and issues surrounding their use for motion control servo systems. Analysis of a prototype magnetic gear is used as a basis for demonstrating the underlying nonlinear torque transfer characteristic, nonlinear damping, and `pole-slipping' when subject to over-torque (overload) conditions. It is also shown how `pole-slipping' results in consequential loss of control. A theoretical investigation into the suppression of mechanical torsional resonances in transmission systems encompassing these highly-compliant magnetically-coupled components is included, along with experimental results, from a demonstrator drive-train. The automatic detection of pole-slipping, and recovery scenarios, is also presented

Nonlinear Feedback Control of Underactuated Mechanical Systems

This chapter presents control of a class of mechanical underactuated system using feedback linearization technique. The MIMO mechanical system is modeled by a set of nonlinear differential equations in which mathematical model is divided into two subsystems: one for actuated outputs and the other for unactuated outputs. The nonlinear feedback of states is used to “linearize” the closed-loop system. In other word, the control structure is constructed by linearly combining two components that are separately obtained from the nonlinear feedback of actuated and unactuated states. Lyapunov technique will be applied to investigate the system stability. As illustration example, nonlinear feedback control of a three-dimensional (3D) overhead crane is presented to investigate the proposed theory

Normal forms for underactuated mechanical systems with symmetry

We introduce cascade normal forms for underactuated mechanical systems that are convenient for control design. These normal forms include three classes of cascade systems, namely, nonlinear systems in strict feedback form, feedforward form, and nontriangular quadratic form (to be defined). In each case, the transformation to cascade systems is provided in closed-form. We apply our results to the Acrobot, the rotating pendulum, and the cart-pole system