Servomechanism Problem Research Articles

Robust Synthesis With Antiwindup Compensation for Electrohydraulic Servomechanism

The robust control of a general servomechanism problem is applied in the case of electrohydraulic servo actuating primary flight controls. The servocompensator structure is proved to be close to the one designed for step signals. The stabilizing compensator is ensured by the way of a linear quadratic optimal procedure. An antiwindup compensation is added to deal with the adverse effects caused by control saturation. The proof is made involving the form of a feedback compensation matrix. Numerical simulations are presented to validate the proposed procedure.

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.

Optimal tracking under decoupling constraints

In this paper, a servomechanism problem is considered in which a stabilizing controller is to be chosen as the solution of a H 2-optimization problem with asymptotic tracking and (exact or approximate) decoupling constraints. The cost functional is made-up of terms which penalize the tracking error and control effort associated with a class of persistent reference signals. To solve the optimization problem with asymptotic tracking and exact decoupling constraints, an explicit parametrization is presented of all stabilizing controllers which satisfy these constraints. On the basis of this parametrization the problem in question is recast as an unconstrained H 2 problem and conditions on problem data are then stated under which there exists a unique solution. To handle the case of asymptotic tracking and approximate decoupling constraints, a parametrization of all stabilizing controllers which achieve asymptotic tracking is used to eliminate the tracking constraint; this leads to an H 2 optimization problem with several non-definite H 2 constraints. Approximate solutions to such a problem are obtained by means of a sequence of H 2 problems with a single non-definite H 2 constraint which, in turn, are solved by line search and spectral factorization. A numerical example is presented to illustrate the effect of the exact and approximate decoupling constraints on the attained optimal cost value and time responses.

Decentralized control of descriptor systems

The decentralized stabilization and decentralized servomechanism problem for descriptor systems is considered. A descriptor system is one characterized by the existence of algebraic constraints on the plant state variables. Such constraints may translate into undesirable impulsive behavior, a property not found in conventional, proper, state space systems. Conditions are therefore investigated to determine if a system can be made impulse-free by suitable feedback action, and in this case the conditions are expressed in terms of the so-called decentralized impulsive fixed modes of the system. The notions of transmission zeros and decentralized fixed modes are defined for the class of descriptor systems and it is shown that they play a central role in determining the solvability of the decentralized robust servomechanism problem for descriptor systems. Two applications, tuning regulator design and sequential synthesis, are also addressed.

The Robust and Reliable Servo System

The paper studies the robustness and the reliability (sensor and actuator failures) of the servomechanism problem - asymptotic tracking and disturbance rejection - using the factorizatioi approach. The plant is a two-output and the compensator is a two-degree-of-freedom. Necessary and sufficient conditions for the solutions and solvability are obtained.

Performance limitations in the robust servomechanism problem for proper sampled LTI systems

Fundamental limitations for error tracking/regulation are obtained for the robust servomechanism problem (RSP) for a sampled proper system. In studying this problem, the cheap control problem for a multi-input /multi-output discrete time system is considered, and explicit expressions are obtained for the limiting steady state solution of its associated algebraic Riccati equation (ARE), as the weight on the control energy tends to zero. Application of these results is then made to the “sampled system cheap robust servomechanism problem”, and explicit expressions for the limiting costs for error tracking regulation are obtained. These limitations can be characterized completely by the number and location of the unstable transmission zeros.

On the Robust Regulator for Linear Systems With Limited Parameter Uncertainty

The linear servomechanism problem has been studied for two extreme cases. On one extreme, the problem has been studied without considering the plant parameter uncertainty. On the other extreme, the problem has been studied for the worst parameter uncertainty in the sense that all the plant parameters are allowed to vary arbitrarily in the neighborhoods of their nominal values. Between these two extreme cases is what will be called limited uncertainty case where the entries of the plant matrices vary functionally with respect to some variables. This case will be studied in this paper. The main result is that, in the limited uncertainty case, the order of the robust regulator can be strictly less than the minimal order of the robust regulator with respect to the worst parameter uncertainty.

Performance limitations in the robust servomechanism problem for sampled LTI systems

Fundamental limitations for error tracking/regulation are obtained for the robust servomechanism problem (RSP) for a sampled system. In studying this problem, the cheap control problem for a multi-input/multi-output discrete time system is considered, and explicit expressions are obtained for the limiting steady state solution of its associated algebraic Riccati equation (ARE), as the weight on the control energy tends to zero. Application of these results is then made to the “sampled system cheap robust servomechanism problem”, and explicit expressions for the limiting costs for error tracking regulation are obtained. These limitations can he characterized completely by the number and location of the unstable transmission zeros.

Adaptive switching control of LTI MIMO systems using a family of controllers approach

During the past several years, switching control from the viewpoint of both theory and practical implementation has been applied successfully to multivariable systems to accomplish a wide variety of tasks. The motivation for using this type of controller is that, often in practice, no single mathematical model of the system to be controlled is either suitable or available, since the plant is described by a family of plant models. Conventional methods of adaptive controller design generally require that certain types of specific a priori plant information be known and that certain assumptions hold, and thus cannot necessarily be implemented when the plant is described by a family of plant models. In this paper, a new class of simple robust multivariable switching control algorithms is presented to solve the servomechanism problem, which differs from previous works in this area, in that it is not necessary to know the actual family of plant models. The switching controller requires less a priori system information than previously assumed, and only requires that the plant have a satisfactory controller contained in a specified family of controllers. Simulation results obtained when using such a switching controller indicate that a reasonable system transient response generally can be achieved; moreover, experimental application studies using one such class of controllers (with almost no a priori plant information) when applied to a real-time multivariable industrial system additionally are encouraging, in the sense that certain desirable integrity features have been observed to occur.

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.

From robust control to antiwindup compensation of electrohydraulic servo actuators

A method of designing the controller to solve the robust servomechanism problem is applied in the case of an electrohydraulic servo actuating primary flight control. This method is based on the well‐known solution consisting of two separate devices: a servocompensator, in fact an internal model of the exogenous dynamics, including the reference commands and disturbance signals; and a stabilizing compensator. The proof is made involving the servocompensator structure which is close to the one designed for step signals. The stabilizing compensator is assured by way of a linear quadratic optimal procedure. An antiwindup compensation is added to deal with the adverse effects caused by actuator saturation.

H8 control synthesis via reduced-order LMIs

Linear matrix inequality-based approaches for H8 control synthesis for systems with weighting functions possibly face numerical ill-conditioning and heavy computation. In this paper, by exploiting the potential pole/zero cancellation (mostly modes of weighting functions) in the closed-loop system, a new formulation is presented to find a full-order controller via reduced-order LMIs (linear matrix inequalities) and fewer decision variables. As a result, both numerical conditioning and numerical efficiency are improved. In addition, the new formulation is directly applicable to servomechanism problems where unstable disturbance dynamics are appended for robust regulation.

A New Approach for Designing Robust Controllers for the Servomechanism Problem

In this paper, we provide an alternative method for solving the more general servomechanism problem. The new approach based on designing a simple structure of a dynamic output feedback controller to achieve asymptotic tracking, disturbance rejection and pole assignment in linear time-invariant multivariable control systems. In addition, the resulting dynamic compensator is robust in the sense that asymptotic regulation take place for some or all disturbances and reference signals independent of any nondestabilizing perturbations in the system parameters. The main results of this paper are illustrated by an example.

Regulation as an interpolation problem

The design of a controller such that the closed-loop system will track reference signals or reject disturbance signals from a specified class is known as the “servomechanism problem” or the “regulator problem.” We show here that the regulator problem can be looked at as an interpolation problem for a subspace-valued function that can be viewed as a multivariable version of the Nyquist curve. The result is applied to obtain a simple parametrization of all solutions.

Adaptive servomechanism controller with an implicit reference model

In this paper the classical servomechanism problem is resolved for the case of an unknown single-input single-output plant and an a priori uncertain command signal. Namely, it is assumed that the command signal is modelled as an output of a homogeneous dynamic system (exosystem ) of known order, but with unknown parameters. In order to provide asymptotic tracking for signals of that kind, a new closed-loop adaptive system, with an implicit reference model and original adaptive observer of the time derivatives of the command signal, is designed.

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.

A universal servomechanism for a class of nonlinear planar systems

A servomechanism problem of controlling a scalar output variable to track any given reference signal of Sobolev class W 3,∞( R ) ≕ R , while maintaining state boundedness, is addressed for a class S δ of uncertain, single-input, single-output, nonlinear planar systems (encompassing, for example, various uncertain, single-degree-of-freedom, mechanical models with extraneous disturbances and a damping effect quantified by the parameter δ, and with position y(t) , but not velocity y ̇ (t), available for feedback). The instantaneous values of the reference signal and scalar output only are available for feedback. An ( R, S δ )-universal servomechanism is presented. Specifically, an adaptive discontinuous feedback control is constructed which is ( R, S δ ) universal in the sense that, for any given reference signal of class R and every system (unknown to the controller) of class S δ , the strategy ensures that the tracking error is asymptotic to zero.

CAD of Controllers for the Servomechanism Problem Subject to Control Signal Saturation Constraints

A fundamental limitation in achieving high performance control for multivariable plants is associated with the operating range of the control input signals associated with the plant, i.e. in order to design realistic controllers for a plant, it is essential to take into account control signal saturation effects. This paper describes various classes of controllers for a LTI plant, which have the property that they solve the robust, servomechanism problem for constant tracking/disturbance signals, and maximize the operating range of the controllers for the plant. Some application studies re the control of a distillation column with pressure variation are included to illustrate the behaviour of the controllers.

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.