Robust eigenvalue assignment for time-delay systems

In this article, the problem of control of the kinematic model of an omnidirectional robot with time delay in the control input is tackled through an Active Disturbance Rejection Control (ADRC) with a disturbance predictor-based scheme, which consists in predicting the generalized forward disturbance input in order to cancel it and then using a feedforward linearization approach to control the system in trajectory tracking tasks. The novelties of the scheme are to demonstrate that using the proposed extended state disturbance estimation leads to a forward estimation following the Taylor series approximation, and, to avoid using additional pose predictions, a feedforward input as an exact linearization approach is used, in which the remaining dynamics can be lumped into the generalized disturbance input. Thus, the use of extended states in prediction improves the robustness of the predictor while increasing the prediction horizon for larger time delays. The stability of the proposal is demonstrated using the second method of Lyapunov, which shows the closed-loop estimation/tracking ultimate bound behavior. Additionally, numerical simulations and experimental tests validate the robustness of the approach in trajectory-tracking tasks.

Robust pole assignment in systems subject to structured perturbations

The stabilization problem of a 1D Schrödinger equation subject to boundary control is concerned in this paper. The control input is suffered from time delay. A “partial state” predictor is designed for the system and undelayed system is deduced. Based on the undelayed system, a feedback control strategy is designed to stabilize the original system. The exact observability of the dual one of the undelayed system is checked. Then it is shown that the system can be stabilized exponentially under the feedback control.

This paper addresses the robust fault detection (RFD) problem for a class of neutral systems with time delays in states and unknown input. The objective is to minimize the difference between the residual and the fault, and to enhance the robustness to unknown inputs and control inputs. The key idea is to formulate the design of robust fault detection filter (RFDF) as H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> filtering problem. The sufficient condition for the existence of the RFDF is proposed by means of linear matrix inequalities (LMI). Finally, a numerical example is given to demonstrate the effectiveness of the proposed method.

This paper investigates the stability analysis and state feedback controller design of linear time-invariant (LTI) systems with input time delay. By investigating the real part and the imaginary part of the transcendental equation, the characteristic equation can be transformed into an equation with two vectors related to the system parameters and the feedback gain. The characteristic roots can be determined exactly and concisely that the feedback gain can be designed directly under a given time delay condition. Based on this approach and the pole placement method, preservation of the closed-loop control performance, the state feedback gain and the maximum allowable value of input time delay can be derived by solving an optimization equation. Numerical examples are provided to illustrate the proposed algorithm.

Forecasting the level of reservoir has been a significant subject in the management of reservoirs and water resource. For many years, estimation of reservoir water level was primary based on operator’s experience, curves and mathematical models. Recently, Artificial Intelligence (AI) methods are developed in several hydrological aspects, such as classification and forecasting parameters. The major advantage of AI modeling is the considerable ability to map input-output pattern without requiring prior knowledge about the factors that affect the forecasting parameters. This study attempts to forecast the daily level of Klang Gate dam using adaptive neuro fuzzy interface system (ANFIS) in two different scenarios and various time delays in inputs. In the first scenario, daily rainfall is used solely as an input in different time delays from the time (t) to the time (t-4) that is illustrated in spite of the reasonable performance of error, less than 10% of solely rainfall data could not have reasonable response in fluctuations to forecast accurately. Increasing the level of reservoir beside precipitation as inputs in both sets of models could enhance the fitness of the estimated and observed data dramatically. Due to the fact that the distance of gauges of stations are unknown, using various models in different time delays of inputs could demonstrate the distance between gauges; moreover, it shows the reasonable duration in inputs and outputs to have accurate prediction. Key words: Klang Gate, adaptive neuro fuzzy interface system (ANFIS), forecasting model.

Control of nonlinear systems with actuator delay is a challenging problem because of the need to develop some form of prediction of the nonlinear dynamics. The problem becomes more difficult for systems with uncertain dynamics. In this paper, tracking controllers are developed for an Euler-Lagrange system with time-delayed actuation, parametric uncertainty, and additive bounded disturbances. One controller is developed under the assumption that the inertia is known, and a second controller is developed when the inertia is unknown. For each case a predictor-like method is developed to address the time delay in the control input. Lyapunov-Krasovskii functionals are used within a Lyapunov-based stability analysis to prove semi-global uniformly ultimately bounded tracking.

Predictor-based control for an uncertain Euler–Lagrange system with input delay

This study considers a novel application of electric vehicles (EVs) to quickly help reheated thermal turbine units to provide the stability fluctuated by load demands. A mathematical model of a power system with EVs is first derived. This model contains the dynamic interactions of EVs and multiple network‐induced time delays. Then, a dynamic output feedback H∞ controller for load frequency control of power systems with multiple time delays in the control input is proposed. To address the multiple time delays issue, a refined Jensen‐based inequality, which encompasses the Jensen inequality, is used to derive less conservative synthesis conditions in terms of tractable linear matrix inequalities. A procedure is given to parameterise an output feedback controller to guarantee stability and H∞ performance of the closed‐loop system. Extensive simulations are conducted to validate the proposed control method.

Consider a linear system with multiple time delays in control input $$ \dot{x}(t) = a_0(t) + a(t)x(t) + \sum \limits _{i=0}^{p} B_i(t)u(t-h_i), ~~ (4.1) $$ with the initial condition x(t0) = x0. Here, x(t) ∈ R n is the system state, u(t) ∈ R m is the control variable, h i > 0, i = 1,...,p, are positive time delays, h0 = 0, h = max{h1,...,h p } is the maximum delay shift, and a0(t), a(t), and B i (t), i = 0,...,p, are piecewise continuous matrix functions of appropriate dimensions. Existence of the unique solution of the equation (4.1) is thus assured by the Caratheodory theorem (see, for example, [29]).

This paper focuses on the problem of robust active control algorithm for the flexible air-breathing hypersonic flight vehicle in the presence of state, actuator constraints and input delays. Constraints in the model, as well as input time delays, are the highly challenging problem in the design of flight control system. Based on linear parameter varying (LPV) model obtained by Tensor-Product model transformation technology, a novel parameter dependent robust model predictive control (PD-RMPC) algorithm with explicit time-delay compensation is presented. Since developing the robust tracking controller with delay compensation, the proposed method is much less conservative and better performance. Finally, the numerical simulation results prove availability of the proposed method.

In this paper, a dynamic decoupling approach is proposed to improve the robust Takagi-Sugeno (T-S) fuzzy model-based control to cope with system uncertainty, input actuator nonlinearity, and input time delay. First, the basic dynamic decoupling concept is introduced by involving virtual input dynamics, such that the system uncertainty and control input are decoupled in each fuzzy rule. This leads to simplified linear matrix inequality (LMI) conditions. Next, the dynamic decoupling approach is extended to controlling uncertain systems with input actuator nonlinearity (e.g., saturation, quantization, dead-zone, etc.) or time-varying input delay. Due to the decoupling between uncertainty, actuator nonlinearity, and input delay, more relaxed stability conditions are obtained for the asymptotic stability and H ∞ control performance. Furthermore, the limit on the initial condition is removed when considering input saturation. Larger and faster time-varying state and input delays are allowed under fewer LMIs. Finally, to show the advantages of the developed control method, numerical simulations are carried out on an inverted pendulum (subject to either the saturation, quantization, or delay input), a delay mass-spring-damper system, and a delay truck-trailer system.

The recent decades have witnessed active studies in fault detection and isolation (FDD) of the small satellites subject to actuator failures and attitude coordination control of spacecraft formation flying (SFF) which plays a significant role in missions such as synthetic-aperture radar imaging. However, because of the time delay in communication links, the performance of coordination control is not always satisfactory. In this paper we propose a method to estimate the actuator fault as well as the input time delay at the same time. First of all, the model of the altitude control system of the small satellite with actuator fault and the model of the altitude control system with actuator fault and the input time delay are presented respectively. Based on the Two-Stage Kalman Filter algorithm, the fault and input time delay of the altitude control system of the small satellite can be estimated. At last, the simulation of the algorithm in a satellite attitude control system with actuator fault and input time delay will illustrate the effectiveness of the proposed approach.

For systems with both state and input time delays, a novel state and sensor fault observer is proposed in this paper to estimate system states and sensor faults simultaneously. In this design, a descriptor system approach and a linear matrix inequality technique are adopted, where the considered sensor fault may be in any form, even unbounded. Unbounded sensor faults will make the system fail unavoidably; it is indispensable to derive a reliable control scheme against sensor failures. Using the estimated state and sensor fault, a reliable observer-based controller is proposed, which makes the system work well no matter whether sensor faults occur or not. The present approaches are next extended to the case for systems with multiple time delays. Finally, a simulation example of the network of three cascaded reactors is used to illustrate the design procedure and demonstrate the efficiency of the present techniques.

In this paper a robust dynamic controller design algorithm for nonlinear systems with unmatched uncertainties and an input time delay is provided. For many practical systems, the existence of time delay is common in control practice. Therefore the problem of controlling such systems becomes more complex and sometimes degrades the control performance. We will propose a feasible method to deal with the problem of unmatched uncertainties and an input time delay. Based on the Lyapunov theory and the concept of functional analysis, the conditions of the robust stability of the overall closed-loop system with unmatched uncertainties and an input time delay will be derived. Finally, some examples and simulation results are provided to illustrate the versatility and performance of the proposed method.