Control Of Linear Time-invariant Plants Research Articles

Self-Triggered Output Feedback Control of Linear Plants in the Presence of Unknown Disturbances

This note addresses the control of linear time-invariant plants in the presence of unknown, bounded disturbances when the output of the plant is only measured at sampling instants determined by a self-triggered strategy. In a self-triggered scenario, the controller is allowed to choose when the next sampling time should occur and does so based on available measurements and on a priori knowledge about the plant. The proposed solution is a cascade interconnection of a state observer and a self-triggered state feedback controller. We focus our attention on state observers that are only updated at sampling times and that are input-to-state stable (ISS) with respect to disturbances. Due to the cascade structure of the closed-loop system and the fact that self-triggered control strategies presented in the literature are ISS with respect to observation errors and exogenous disturbances, we conclude that the closed-loop is rendered ISS with respect to exogenous disturbances.

Application of Neural Network on Flight Control

Over the last three decades, adaptive control has evolved as a powerful methodology for designing feedback controller of nonlinear systems. Most of the studies assume that the system nonlinearities are known a prior, which is generally not applicable in the real world. To overcome this drawback, from twenty years ago, there has been a tremendous amount of activity in applying Neural Networks for adaptive control. With their powerful ability to approximate nonlinear functions, neuro-controllers can implement the expected objectives by canceling or learning the unknown nonlinearities of the system to be cancelled. Neural Networks are specially suitable for the adaptive flight control applications where system dynamics are dominated by the unknown nonlinearities. In the past decades, major advances have been made in adaptive control of linear time-invariant plants with unknown parameters. The choice of the controller structure is based on well established results in linear systems theory and stable adaptive laws which assure the global stability of the overall system are derived based on properties of those system. In recent years, Artificial Neural Network based control strategies have attracted much attention because of their powerful ability to approximate continuous nonlinear functions .(1) In fact, a neural controller with on-line learning can adapt to the change in a system dynamics and hence is an ideal choice for controlling highly nonlinear system with uncertainty. For adaptive control purposes neural networks are used as approximation models of unknown nonlinearities. The input / output response of neural network models is modified by adjusting the values of its adjusting the values of its parameters. Although it is true that polynomials, trigonometric series and orthogonal functions can also be used as function approximator, neural networks have been found to be particularly useful for controlling highly uncertain, nonlinear and complex systems. Neural control strategies can be broadly classified into off-line and on-line schemes based on how the parameters of the network are tuned. When the neural controller operates in an on-line mode, it has no a priori knowledge of the system to be controlled and the parameters of the network are updated while the input - output data is received. In the off-line control, the network's parameters are determined from the unknown training pairs and then those parameters are fixed for control purposes. (2)

Control of LTI plants over erasure channels

This paper studies linear time-invariant (LTI) control architectures for LTI plants when communication takes place over a scalar erasure channel. Assuming i.i.d. data dropouts, we first show that such a channel is equivalent, in a second order moment sense, to an additive white noise channel subject to an instantaneous signal-to-noise ratio constraint. This key result is then exploited in two ways: First, we use it to characterize the set of all LTI controllers that achieve mean square stability in control architectures closed over scalar erasure channels. Second, we use it to show that the optimal design of LTI controllers over scalar erasure channels can be carried out by using tools from standard quadratic optimal control theory. We finally apply our results to the dynamic output feedback control of LTI single-input single-output (SISO) plants subject to data dropouts. In this case, we are able to establish closed form necessary and sufficient conditions on the minimal successful transmission probability that allows one to design mean square stabilizing controllers.

Uncertainty remodeling for robust control of linear time-invariant plants^1

The paper proposes a measure of robust performance based on frequency domain experimental data that allows non-conservative modeling of uncertainty. Given the nominal model of the plant and closed-loop performance specifications the iterative control design and remodeling of model uncertainty based on that measure leads to a controller with improved robust performance. The structured dynamic uncertainty is allowed to act on the nominal model in a linear fractional transformation (LFT) form. The proposed method is a modification of the structured singular value with implicit constraints on model consistency. The usefulness of the method is demonstrated on a vehicle control simulation example.

Decentralised two-time-scale motions control based on generalised sampling

A design method for the decentralised time-varying discrete-time output-feedback control of linear time-invariant plants with unstable unstructured decentralised fixed modes (UDFM) is introduced. The design method uses generalised sampled-data hold functions to eliminate the UDFMs and to decouple the discrete-time equivalent model of the plant into independent input–output channels. Through this structural change, the plant becomes suitable for a stabilising high-sampling-rate controller that induces two-time-scale motions (TTSM) in the closed-loop system. As a result, the discrete-time controller is likewise decoupled into distinct local agents and the TTSM closed-loop system is decentralised.

On lp disturbance rejection using periodic feedback control

In this paper, the performance of discrete time periodically time-varying controllers for rejection of l p specific and uniform disturbances is analyzed. For control of linear time-invariant plants, this paper distinguishes linear time-invariant controllers from linear non-time-invariant periodic controllers in the performance analysis. For a given linear non-time-invariant periodic controller, a linear time-invariant controller is constructed and necessary and sufficient conditions are presented under which the linear time-invariant controller gives strictly better l p control than the non-time-invariant periodic controller.

Analysis of H2 and H∞ performance of discrete periodically time-varying controllers

This paper presents analysis of the H 2 and H ∞ performance of discrete linear periodically time-varying controllers for control of linear time-invariant plants. Using a frequency-domain lifting approach, the analysis distinguishes periodically time-varying control from time-invariant control to show that the multiple transfer channels of the system time-varying dynamics amplify the overall system gain. Such a result can provide deeper insights into the system time-varying mechanism and clarify how the time-varying dynamics acts and degrades the system performance. Quantitatively, the paper presents necessary and sufficient conditions under which a linear time-invariant controller can be found to provide strictly better control than periodically time-varying controllers.

Systematic Techniques for Determining Modeling Requirements for SISO and MIMO Feedback Control Problems

This paper presents a methodology by which the issue of modeling requirements for SISO and MIMO control of linear time-invariant plants is analyzed in a fundamental manner. The main result is the formulation of a Control-Relevant Parameter Estimation Problem (CRPEP) which explictly incorporates control considerations such as set point /disturbance directions and desired closed-loop transfer functions. The CRPEP is solved via prefiltered estimation of MIMO ARX models (model reduction case) and a state-space frequency-weighted estimation method (system identification case). Reduced-order and model predictive controllers obtained from these estimation techniques are demonstrated on a subset of the Shell Heavy Oil Fractionator problem.

Robustness of linear feedback control systems to unmodelled high-frequency dynamics

A basic issue in the control of linear time-invariant plants is the effect of neglected high-frequency dynamics on the performance, in particular on the closed-loop stability, of the control system. In this paper, the robustness of various output feedback control designs, based on a reduced-order model with neglected high-frequency dynamics, is investigated using singular perturbation techniques. A general robust design rule is to avoid static output feedback for systems with unmodelled high-frequency dynamics. From a frequency-domain standpoint, the robust design rule is to avoid closing high-frequency plant loops by using strictly proper controllers or controllers with a low-pass filtering property.

Uniformly optimal control of linear time-invariant plants: Nonlinear time-varying controllers

It is shown that in the problems of uniformly (or H ∞−) optimal control of linear time-invariant plants, arbitrary nonlinear, time-varying controllers offer no advantage over linear, time-invariant controllers.

Optimal control for linear time-invariant plants with time, fuel, and energy constraints

The structure of optimum control systems and the form of the optimal control signals are discussed for minimum time, minimum fuel, and minimum energy control of linear time-invariant plants. If the control variables are bounded by 1 in magnitude, then the control signals must have the values +1 or ?1 for minimum time response; +1, 0, or ?1 for minimum fuel operation; +1, ?1 or be linearly related to the state of the plant, between these limits, for minimum energy operation.