Disturbance Attenuation Problem Research Articles

Applying Cognitive Methodology in Designing On-Line Auto-Tuning Robust PID Controller for the Real Heating System

A novel design and implementation of a cognitive methodology for the on-line auto-tuning robust PID controller in a real heating system is presented in this paper. The aim of the proposed work is to construct a cognitive control methodology that gives optimal control signal to the heating system, which achieve the following objectives: fast and precise search efficiency in finding the on- line optimal PID controller parameters in order to find the optimal output temperature response for the heating system. The cognitive methodology (CM) consists of three engines: breeding engine based Routh-Hurwitz criterion stability, search engine based particle swarm optimization (PSO) and aggregation knowledge engine based cultural algorithm (CA). Matlab simulation package is used to carry out the proposed methodology that finds and tunes the optimal values of the robust PID parameters on-line. In real-time, the LabVIEW package is guided to design the on-line robust PID controller for the heating system. Numerical simulations and experimental results are compared with each other and showed the effectiveness of the proposed control methodology in terms of fast and smooth dynamic response for the heating system, especially when the control methodology considers the external disturbance attenuation problem.

State observer‐based predictive proportional‐integral tracking control for fuzzy input time‐delay systems

SummaryThis study emphasis on the problem of state tracking and disturbance attenuation for Takagi‐Sugeno fuzzy based model with input time‐delay via improved extended state observer based predictive proportional‐integral tracking control. To be precise, a predictive proportional‐integral tracking controller is formulated by implementing the Smith‐Predictor strategy to restrain the influence of input time‐delay. Then, with the aid of improved extended state observer, the lumped disturbance is estimated and it is combined with the predictive proportional‐integral tracking control for disturbance attenuation. Further, closed‐loop control‐system is considered to ensure the satisfactory state tracking results for the considered system regardless of time‐delay in the control input and lumped disturbances. Meanwhile, based on the Lyapunov theory approach, the stability criteria for the proposed system are formulated in terms of linear matrix inequalities following which the gain matrices are derived. Finally, in order to evident the supremacy of the proffered control system, two numerical simulation results are provided.

Robust observer-based output-feedback control for epidemic models: Positive fuzzy model and separation principle approach

A feedback-type vaccination and treatment policy for a nonlinear susceptible–infected–recovered (SIR) epidemic model involving uncertainties and disturbances is designed by considering only the number of infected individuals. Specifically, an observer-based output-feedback (OBOF) controller design methodology in the Takagi–Sugeno fuzzy model framework is established. The designed controller exhibits L∞–L∞ disturbance attenuation performance, is robust against norm-bounded parametric uncertainties, and can preserve the closed-loop positivity. The primary contributions of the proposed design condition can be characterized as follows: (i) a novel structure of a fuzzy OBOF controller to ensure the closed-loop positivity; (ii) separate disturbance attenuation performances for the independent design of the controller and observer; (iii) The independent design conditions formulated as convex optimization problems in the presence of parametric uncertainties; (iv) the demonstration of the separation principle in the positive L∞–L∞ disturbance attenuation problem. Results of the case study pertaining to the SIR model demonstrate the efficacy of the proposed methodology.

Distributed H∞ Robust Control of Multiagent Systems With Uncertain Parameters: Performance-Region-Based Approach

This article deals with the distributed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {H}_{\infty }$ </tex-math></inline-formula> robust control problem for linear multiagent systems perturbed by external disturbances and norm-bounded uncertain parameters over the Markovian randomly switching communication topologies. To tackle this problem, the distributed observer-based controller is proposed, which requires the relative information between neighbors and the absolute information of a subset of the nodes, and thus is intrinsically distributed. It is of great interest to see that the distributed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {H}_{\infty }$ </tex-math></inline-formula> robust control problem governed by such a controller can be converted to the stabilization with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {H}_{\infty }$ </tex-math></inline-formula> disturbance attenuation problems of some decoupled linear systems, whose dimensions equal those of a single node. Then, the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {H}_{\infty }$ </tex-math></inline-formula> stochastic robust performance region is defined to indicate the robustness of this controller against the variation of communication topologies. It is theoretically shown that the distributed observer-based controller yields bounded and connected robust performance region. Finally, the theoretical results are verified by conducting numerical simulations and experiments.

Sliding Mode Controller with Generalized Extended State Observer for Single Link Flexible Manipulator

This paper presents an enhanced generalized extended state observer (EGESO) based sliding mode control (SMC) technique for dealing with the disturbance attenuation problem for a class of non-integral chain systems with mismatched uncertainty. In the proposed control law, the robust SMC with reaching phase elimination is applied in the proposed control law, which uses the estimated states of a system. The stability analysis is thoroughly examined for both EGESO and SMC. The efficacy of the proposed controller is verified using specific examples, and later it is applied on a single-link flexible manipulator. Through simulation and experimentation analysis, it is observed that the proposed controller is giving a robust transient response as compared to existing GESO based controllers.

Active vibration control: Design towards performance limit

Active vibration control has been conventionally treated as a disturbance attenuation problem in control-theoretic communities. Such a treatment is not satisfactory, particularly with handling finite-frequency band, tackling performance limit, and analyzing performance compromise issues etc. In this paper, a new framework is proposed where the performance is represented through geometric expressions; the important problems of performance limit and compromise are then tackled based on visual inspections; furthermore, the optimal constrained solutions are also obtained by handling the constraints within the same framework. Consequently, a performance-limit-oriented approach is established providing a new design methodology for active vibration control. A vehicle suspension structure is considered for illustration and validation of the claims.

New observer-based boundary control approaches to vibration reduction and disturbance attenuation of a flexible arm

This paper addresses the vibration reduction and disturbance attenuation problems of a flexible arm, which is modelled as a fourth-order partial differential equation. The main control objectives lie in reducing the influence of the disturbance, steering the flexible arm to the desired angular position and suppressing the vibration, simultaneously. To achieve the objectives, firstly, two different disturbance observers are designed. Secondly, we construct boundary controllers based on the two designed disturbance observers and boundary measurable signals. Then, with the two disturbance observers, the boundary disturbance compensation is achieved, and with the designed boundary controllers, the uniform boundedness of the flexible arm is guaranteed. Moreover, the well-posedness of the closed-loop system under the designed boundary controllers is discussed by means of the operator semigroup theory. Finally, the effectiveness and advantages of the proposed controllers are demonstrated through simulations and physical experiments.

Relaxed Stabilization and Disturbance Attenuation Control Synthesis Conditions for Polynomial Fuzzy Systems.

This article presents both stabilization and disturbance attenuation control synthesis conditions for a class of polynomial fuzzy systems. The sum of squares conditions is relaxed by restricting the domain of the polynomial variables that represent the membership functions as well as by using the line integral polynomial fuzzy Lyapunov function. For the disturbance attenuation problem, we consider the transformation of the Hamilton-Jacobi-Isaacs equation into a set of inequalities and a policy iteration algorithm to approximate its value function. Furthermore, we propose an alternative path following to find the initial L2 gain stabilizing control policy. Five examples are provided to demonstrate the effectiveness of the proposed conditions.

High-order fully-actuated system approaches: Part VI. Disturbance attenuation and decoupling

Two types of high-order fully actuated (HOFA) system models subject to external disturbances are firstly introduced. For the type of HOFA systems with deterministic disturbances, the problem of disturbance attenuation via state feedback is treated. While for the type of HOFA systems with dynamical disturbances, the problem of asymptotic disturbance decoupling via output feedback is considered. Utilising the full-actuation feature of the HOFA systems, disturbance attenuation and decoupling controllers for the corresponding systems are conveniently designed such that constant linear closed-loop systems with designed disturbance rejection properties are resulted in. Parametric designs for both controllers are provided, and disturbance attenuation is achieved by establishing a parametric form of the closed-loop transfer function from the disturbance to the output, while the parametric form of the disturbance decoupling controller is derived based on a complete parametric solution to a type of generalised Sylvester equations (GSEs). As a consequence of the parameter approaches, additional performance requirements on the closed-loop systems can be also easily handled. An illustrative example demonstrates the effect of the proposed approach.

Flexible control of nuclear cogeneration plants for balancing intermittent renewables

Both intermittent renewable energy (IRE) and nuclear fission energy can provide carbon-free electric power to the grid. The electric power generation from the intermittent renewable energy (IRE) sources such as the wind and solar are strongly dependent on the climatic conditions, geographical location and large land footprint. While, nuclear plants can provide consistent and clean power supply with small land footprint. Due to the strong complementarity between the IRE and nuclear, it is attractive to interconnect them to build nuclear-renewable hybrid energy systems (NRHESs) which are defined as the integrated facilities comprised of nuclear reactors, renewable energy generation and industrial processes. The flexibility of a NRHES for grid balance can be provided by actively adjusting the electric power output of nuclear cogeneration plants (NCPs), which leads to the frequent redistribution of main steam flow to the turbine and cogeneration process. For the main steam redistribution, it is necessary to guarantee the stability of grid frequency and main steam pressure, which heavily relies on the flexible control strategy of NCPs. In this paper, a new flexible control of NCPs with saturated main steam is proposed based on the idea of actively suppressing the total disturbance to the dynamics of grid frequency and main steam pressure. The stabilization problems of pressure and frequency are transferred to the disturbance attenuation Problem of a second-order disturbed dynamical system, and an active disturbance rejection control (ADRC) is then originally proposed for system stabilization. This ADRC is applied to the flexible control of a NCP composed of a nuclear heating reactor (NHR), a turbine-generator set and a multi-effect-desalination and thermal-vapor-compression (MED-TVC) process for seawater desalination. Numerical simulation results in the cases of load stepping and maneuvering show that the flexibility of this NCP is satisfactory in balancing the grid.

Quantitative Synthesis to Tracking Error Problem Based on Nominal Sensitivity Formulation

This brief presents a simple and robust design technique based on quantitative feedback theory (QFT) to solve the tracking error specification (TES) problem. The TES problem is converted into an equivalent disturbance attenuation (EDA) problem wherein the plant uncertainties are translated into equivalent external disturbance sets. The design problem then becomes a simple nominal disturbance rejection problem. The main advantage of the proposed technique is that they are simple, computationally efficient, and require less control effort (overdesign) due to the nominal sensitivity function formulation. The computational simplicity of the proposed methods makes them potentially more suitable for handling design problems involving a large number of uncertain plant parameters. Experiments are conducted on a laboratory electro-mechanical plant emulator system to demonstrate the efficacy of the proposed design method.

Disturbance attenuation for a class of Lipschitz nonlinear systems with large input delay

AbstractThis article investigates disturbance attenuation problem for a class of Lipschitz nonlinear systems subject to unknown sensor disturbances/faults and large input delay. First, the Artstein model reduction method is applied to deal with the input delay and a descriptor observer is constructed to estimate the predicted state and sensor faults simultaneously. Then, a finite‐dimensional controller is designed, which gets rid of the distributed delays in traditional reduction controllers and is easy to be implemented. By using Lyapunov‐Krasovskii functionals, sufficient conditions are derived to guarantee the disturbance attenuation. Finally, a numerical simulation is given to demonstrate the effectiveness of the proposed method.

Combining Pontryagin's Principle and Dynamic Programming for Linear and Nonlinear Systems

To study optimal control and disturbance attenuation problems, two prominent-and somewhat alternative-strategies have emerged in the last century: dynamic programming (DP) and Pontryagin's minimum principle (PMP). The former characterizes the solution by shaping the dynamics in a closed loop (a priori unknown) via the selection of a feedback input, at the price, however, of the solution to (typically daunting) partial differential equations. The latter, instead, provides (extended) dynamics that must be satisfied by the optimal process, for which boundary conditions (a priori unknown) should be determined. The results discussed in this article combine the two approaches by matching the corresponding trajectories, i.e., combining the underlying sources of information: knowledge of the complete initial condition from DP and of the optimal dynamics from PMP. The proposed approach provides insights for linear as well as nonlinear systems. In the case of linear systems, the derived conditions lead to matrix algebraic equations, similar to the classic algebraic Riccati equations (AREs), although with coefficients defined as polynomial functions of the input gain matrix, with the property that the coefficient of the quadratic term of such equation is sign definite, even if the corresponding coefficient of the original ARE is sign indefinite, as it is typically the case in the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> control problem. This feature is particularly appealing from the computational point of view, since it permits the use of standard minimization techniques for convex functions, such as the gradient algorithm. In the presence of nonlinear dynamics, the strategy leads to algebraic equations that allow us to (locally) construct the optimal feedback by considering the behavior of the closed-loop dynamics at a single point in the state space.

Observer-based event triggering [formula omitted] LFC for multi-area power systems under DoS attacks

This paper investigates the observer-based predictive event-triggered load frequency control (LFC) for a multi-area power system in a smart grid incorporating electric vehicles (EVs) under denial-of-service (DoS) attacks. The DoS attacks were launched in control channels with long duration to block the data transmission process and interrupt the LFC command. This situation becomes even more severe with the integration of EVs in the multi-area power system. The control design formulates the LFC problem as a disturbance attenuation problem in the presence of both long-duration DoS attacks and external disturbances. First, an event-triggering scheme was developed based on the observer in the presence of DoS attacks. Second, a model-based predictive control approach was presented. Then, by using the Lyapunov theory, stability for the multi-area power system with EVs was derived under consideration of the long-duration DoS attacks. Moreover, two algorithms were provided to obtain the model predictive event-triggered control (MPETC) parameters, LFC gains, and control of DoS attacks simultaneously. Finally, a simulation of a two-area power system with EVs was studied to illustrate the effectiveness of the proposed method.

Active damping injection controller for web longitude and tensions of nonlinear roll-to-roll systems

This study presents an advanced algorithm for controlling the web longitude and tension of nonlinear roll-to-roll systems in the form of a cascade structure. Parameter variation and disturbance attenuation problems are addressed systematically. The features of this article are divided into two parts. First, active damping terms are injected to stabilize the system nonlinear dynamics so that the first-order closed-loop transfer functions are obtained for each loop via pole-zero cancelation. Second, disturbance observers are introduced to ensure the performance recovery property by attenuating the disturbances from the model-plant mismatches. The closed-loop system is numerically emulated using MATLAB/Simulink to show the effectiveness of the proposed technique.

Stabilization and disturbance attenuation control of the gyroscopic inverted pendulum

In this study, a control moment gyroscope is used as an actuator to stabilize the inverted pendulum. A control strategy is proposed to stabilize the inverted pendulum at the upright unstable equilibrium point and to maintain the gimbal angle as small as possible. Such a problem is formulated as a constrained H∞ disturbance attenuation problem and then transformed into solving linear matrix inequalities. The performance of the proposed controller is evaluated through simulation for linear and nonlinear cases. It is shown that the proposed state-feedback control strategy effectively stabilizes the inverted pendulum.

Flexible Control of Nuclear Cogeneration Plants for Balancing Intermittent Renewables

Due to the complementarity between the intermittent renewable energy (IRE) and the nuclear, it is attractive to interconnect them to supply clean energy consistently and continuously in a large-scale. The flexibility of for integrating the IRE can be provided by actively adjusting the electric power output of nuclear cogeneration plants (NCPs), which induces frequent redistribution of main steam to the turbine and cogeneration process. For the main steam redistribution, it is necessary to guarantee the stability of grid frequency and main steam pressure, which heavily relies on the flexible control of NCPs. In this paper, a new flexible control of NCPs with saturated main steam is proposed based upon the idea of actively suppressing the total disturbance in the dynamics of grid frequency and that of main steam pressure. The stabilization problems of pressure and frequency are transferred to the disturbance attenuation problem of a second-order system, and an active disturbance rejection control (ADRC) is then proposed. This ADRC is applied to the flexible control of a NCP composed of a nuclear heating reactor (NHR), a turbine-generator set and a multi-effect-desalination and thermal-vapor-compression (MED-TVC) process for seawater desalination. Numerical simulation results in the cases of load stepping show that the flexibility of this NCP is satisfactory in balancing the grid.

Online barrier-actor-critic learning for H∞ control with full-state constraints and input saturation

This paper develops a novel adaptive optimal control design method with full-state constraints and input saturation in the presence of external disturbance. First, to consider the full-state constraints, a barrier function is developed for system transformation. Moreover, it is shown that, with the barrier-function-based system transformation, the stabilization of the transformed system is equivalent to the original constrained control problem. Second, the disturbance attenuation problem is formulated within the zero-sum differential games framework. To determine the optimal control and the worst-case disturbance, a novel barrier-actor-critic algorithm is presented for adaptive optimal learning while guaranteeing the full-state constraints and input saturation. It is proven that the closed-loop signals remain bounded during the online learning phase. Finally, simulation studies are conducted to demonstrate the effectiveness of the presented barrier-actor-critic learning algorithm.

Control Synthesis for Discrete-Time T–S Fuzzy Systems Based on Membership Function-Dependent $H_{\infty }$ Performance

This article focuses on disturbance attenuation problem for discrete-time Takagi-Sugeno (T-S) fuzzy systems. First, a membership function-dependent H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance index is proposed, by which, different performance can be achieved for local subsystems. Then, the better performance may be obtained for the T-S fuzzy system that works on a particular local subsystem most of the time. It may guarantee better control effects in practical engineering applications. With the help of the newly defined performance index and fuzzy Lyapunov functions, an observer-based feedback control scheme is presented in the form of linear matrix inequalities. In simulation, the performance index obtained by this article can be improved by about 10% than that obtained by the traditional H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> control method.

Disturbance attenuation with fast global finite‐time convergence for generalized high‐order uncertain nonlinear systems

SummaryThis paper focuses on the problem of disturbance attenuation with fast global finite‐time convergence (FTC) for a class of generalized high‐order uncertain nonlinear systems. Combining the fast finite‐time stabilization technique with a delicate manipulation of sign functions, a new control approach is proposed to attenuate the serious uncertainties substantially, including time‐varying control coefficients, nonlinear parameters, and external disturbances, while achieving the performance evaluated in terms of L2‐L2p gain. A notable feature of the control strategy is the fast FTC, which greatly shortens the convergent time when the initial state is far away from the origin. A numerical example is provided to demonstrate the effectiveness of the proposed method.