Nonlinear Servomechanism Problem Research Articles

On the discrete-time robust nonlinear servomechanism problem

The paper addresses the robust servomechanism problem for nonlinear discrete-time systems. The solvability conditions for the discrete-time k th -order robust servomechanism prob- lem is first established by using the internal model principle. Then it is further shown that, under an additional assumption on the solution of the discrete regulator equations, the solvability of the discrete-time k th -order robust servomechanism problem leads to the solvability of the discrete-time robust servomechanism problem. The results of this paper give a discrete-time counterpart of the results on the continuous-time robust servomechanism problem.

A neural network-based approximation method for discrete-time nonlinear servomechanism problem

A feedback controller that solves the discrete-time nonlinear servomechanism problem relies on the solution of a set of nonlinear functional equations known as the discrete regulator equations. The exact solution of the discrete regulator equations is usually unavailable due to the nonlinearity of the system. The paper proposes to approximately solve the discrete regulator equations using a feedforward neural network. This approach leads to an effective way to practically solve the discrete nonlinear servomechanism problem. The approach has been illustrated using the well-known inverted pendulum on a cart system. The simulation shows that the control law designed by the proposed approach performs much better than the conventional linear control law.

A neural-network method for the nonlinear servomechanism problem

The solution of the nonlinear servomechanism problem relies on the solvability of a set of mixed nonlinear partial differential and algebraic equations known as the regulator equations. Due to the nonlinear nature, it is difficult to obtain the exact solution of the regulator equations. This paper proposes to solve the regulator equations based on a class of recurrent neural network, which has the features of a cellular neural network. This research not only represents a novel application of the neural networks to numerical mathematics, but also leads to an effective approach to approximately solving the nonlinear servomechanism problem. The resulting design method is illustrated by application to the well-known ball and beam system.

Solving the nonlinear regulator equations by a single layer feedforward neural network

This paper proposes to solve the nonlinear regulator equations based on a single hidden layer feedforward neural network, leading to an effective approach to approximately solve the nonlinear servomechanism problem. The resulting design method is illustrated by application to the well-known ball and beam system.

Robust control for a nonlinear servomechanism problem

This paper deals with the design of output feedback control to achieve asymptotic tracking and disturbance rejection for a class of nonlinear systems when the exogenous signals are generated by a known linear exosystem. The system under consideration is single-input single-output, input-output linearizable, minimum phase, and modelled by an input-output model of the form of an nth-order differential equation. We assume that, at steady state, the nonlinearities of the system can only introduce a finite number of harmonics of the original exosystem modes. This assumption enables us to identify a linear servo-compensator which is augmented with the original system. Moreover, we augment a series of m integrators at the input side, where m is the highest derivative of the input, and then represent the augmented system by a state model. The augmented system is stabilized via a separation approach in which a robust state feedback controller is designed first to ensure boundedness of all state variables and tracking error convergence; then, a high gain observer and control saturation are used to recover the asymptotic properties achieved under state feedback.

On the minimal robust servo-regulator for nonlinear systems

It is shown in (Huang and Lin, 1991) that the kth-order robust nonlinear servomechanism problem can be solved by a class of linear controllers called kth-order robust servo-regulator. It is further shown in (Huang, 1995) that the kth-order robust servo-regulator, under one additional condition, also solves the (exact) robust nonlinear servomechanism problem. This paper further shows that the minimal dimension of this class of linear controllers is equal to the degree of the minimal polynomial of the k-fold exosystem multiplied by p, where p is the dimension of the regulated output. This result, coupled with a characterization of the minimal polynomial of the k-fold exosystem leads to a straightforward and efficient procedure to synthesize a minimal dimension linear robust servo-regulator.

On a robust nonlinear servomechanism problem

A notion of kth-order robust control for the nonlinear servomechanism problem is introduced. A transmission zeros condition is given for the existence of a kth-order robust control law such that, regardless of small parameter perturbations of the plant and control law, the closed-loop system will induce a stable invariant manifold with the error map zero up to kth-order at each point of the manifold. Such a control law incorporates an internal model of up to k subsystems determined by the exosystem. A special case of the result of this paper recovers the well-known linear robust servomechanism result. >

Stabilization on zero-error manifolds and the nonlinear servomechanism problem

The extended-linearization methodology is applied to the nonlinear servomechanism problem for the case of time-varying exogenous signals. This yields a novel approach to establishing exponential manifold, known as the zero-error manifold. Advantages of the approach are that the underlying theory is relatively simple, and that a requirement of small derivatives for the exogenous signals is used rather than a requirement that the exogenous signals remain small. Thus certain cases of unbounded exogenous signals can be treated. A transmission zero condition for existence of the requisite zero-error manifold is given.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

An approximation method for the nonlinear servomechanism problem

An analysis of the nonlinear servomechanism problem by the authors (1992) is shown to lead naturally to a straightforward and practical method for solving the problem in an approximate sense. The results are based on a kth-order approximate solution for the plant zero-error manifold, and corresponding control law constructions are shown to yield kth-order asymptotic tracking and disturbance rejection properties for the closed-loop system. The approach is illustrated by application to the ball and beam system. >

Robust control of a class of nonlinear servomechanism problem

Robust control of a class of nonlinear servomechanism problem

The robust non-linear servomechanism problem

We study the asymptotic tracking and disturbance rejection property of a general non-linear multi-input multi-output distributed servomechanism which consists of input as well as output channel non...