Robust Performance Objective Research Articles

D-decomposition-based multi-objective robust resilient control for blade pitch of wind energy conversion system

The uncertainties due to the load variations and wind speed fluctuations represent the biggest challenges to the stabilization of the wind energy conversion systems (WECS). In this regard, this paper develops a new resilient control approach for blade pitch of WECS as well as a low computational burden to tackle the uncertainty issue instead of the metaheuristics techniques. The proposed approach is formulated via a graphical D-decomposition strategy to identify the optimal region on the stability profile of the WECS that achieves the desired damping performance as well as minimum oscillation, settling time, and overshoot. Furthermore, the proposed approach takes into account a set of segment plants to achieve the robust performance and resiliency objectives simultaneously for the controller gains. The proposed approach is designed mathematically without hypothesis or probability as well as simple structure compared with metaheuristics techniques. Various performance indices are taken into account to assert the proposed approach accomplishment. Besides, the performance of the WECS based on the designed controller via D-decomposition is compared with different techniques in the literature. The results confirm that the proposed approach demonstrates better damping performance including less overshoot around 2.2329% and settling time around 9.2626 s than metaheuristics techniques. Furthermore, the robustness and resiliency of the designed controller are emphasized in the case of different test aspects including load variations and wind speed fluctuations compared with other techniques.

Robust Control of a Central Heating System Using a Cascade Controller Based on Quantitative Feedback Theory

A central heating system comprises of an arrangement of water pipes and boilers, sole purpose of which is to adjust and maintain the room temperature of a particular enclosure. The system stability and robust performance objectives can be achieved using a cascaded control system structure where the inner loop and equivalent loop controllers are meant to control the mixed water temperature and the room temperature respectively and are designed on the basis of the Quantitative Feedback Theory (QFT). The controllers designed using this framework ensure the robustness of the system. In this paper, designing the controllers and pre-filter is carried out using the QFT toolbox. Simulation is undertaken for 300 plants within the parametric uncertainty ranges and results obtained verify the performance of the system.

A Distributed Model Predictive Control for Multiple Mobile Robots with the Model Uncertainty

In this paper, a distributed predictive control with the model uncertainty which uses the data-driven strategy and robust theory (data-driven RDMPC) is proposed for the formation control of multiple mobile robots. The robust performance objective minimization is applied to replace the quadratic performance objective minimization to establish the optimization problem, where the model uncertainty is considered in the distributed system. The control policy is derived by applying the data-driven strategy, and the future predictive value is obtained by employing the linear law in the historical data. Lyapunov theory is referred to analyze the stability of the mobile robot formation system. The effectiveness of the proposed method is proved by a set of simulation experiments.

Discrete Time-Coupled State-Dependent Riccati Equation Control of Nonlinear Mechatronic Systems

Abstract A discrete-time-coupled state-dependent Riccati equation (CSDRE) control strategy is structured in this paper for synthesizing state feedback controllers satisfying the combined nonlinear quadratic regulator (NLQR) and H∞ robust control performance objectives. Under smoothness assumptions, the nonlinear plant dynamics can be formulated into state-dependent coefficient form through direct parameterization. By solving a pair of coupled state-dependent Riccati equations, the optimal stabilizing solutions can achieve inherent stability, nonlinear quadratic optimality, and H∞ disturbance attenuation performance. The established two-player Nash's game theory is utilized for developing both of the finite and infinite time optimal control laws. Furuta swing-up pendulum, a representative nonholonomic underactuated nonlinear system, is stabilized in real-time for validating the robustness and potential of proposed approach in mechatronics applications.

Robust distributed MPC for load frequency control of uncertain power systems

Reliable Load frequency control (LFC) is crucial to the operation and design of modern electric power systems. However, the power systems are always subject to uncertainties and external disturbances. Considering the LFC problem of a multi-area interconnected power system, this paper presents a robust distributed model predictive control (RDMPC) based on linear matrix inequalities. The proposed algorithm solves a series of local convex optimization problems to minimize an attractive range for a robust performance objective by using a time-varying state-feedback controller for each control area. The scheme incorporates the two critical nonlinear constraints, e.g., the generation rate constraint (GRC) and the valve limit, into convex optimization problems. Furthermore, the algorithm explores the use of an expanded group of adjustable parameters in LMI to transform an upper bound into an attractive range for reducing conservativeness. Good performance and robustness are obtained in the presence of power system dynamic uncertainties.

Fault estimation for discrete time LPV systems under noisy scheduling measurements

Developed in the paper, is a systematic design framework for parameter-dependent fault diagnosis, with noise corrupted measurements of the scheduling parameter. A stochastic fault estimation filter design method is addressed for a class of discrete-time Linear Parameter Varying (LPV) systems. First, the average valued filter stability is ensured by means of a quadratic dissipativity condition. Apart stability, within the same mean square framework a robust performance objective is defined. Conditions to satisfy robust stability requirements are translated to an optimization problem subject to Bilinear Matrix Inequality (BMI) constraints. A comparative numerical example is given to illustrate and validate the proposed methodology.

Robust distributed model predictive control for uncertain networked control systems

In this study, an approach to design robust distributed model predictive control (MPC) is proposed for polytopic uncertain networked control systems with time delays. To reduce the computational complexity and improve the flexibility, the entire system is decomposed into multiple smaller dimensional subsystems. For each subsystem, the proposed robust distributed MPC algorithm requires solving multiple linear matrix inequality optimisation problems to minimise an upper bound on a robust performance objective. An augmented polytopic uncertainty description is invoked to handle the input delays. The conservativeness of distributed MPC algorithm is reduced by utilising a sequence of feedback control laws. An iterative on-line algorithm for robust distributed MPC is developed to coordinate the distributed MPC controllers. Convergence and robust stability of the proposed distributed MPC are investigated. A numerical example is carried out to demonstrate the effectiveness of the proposed algorithm.

Constrained distributed model predictive control for state-delayed systems with polytopic uncertainty description

Although distributed model predictive control (MPC) has received significant attention in the literature, the robustness of distributed MPC with respect to model uncertainties and state delays has not been explicitly addressed. In this paper, a novel approach to design robust distributed MPC is proposed for polytopic uncertain systems with state delays. The algorithm requires decomposing the entire system into M subsystems and solving M linear matrix inequality optimization problems to minimize an upper bound on a robust performance objective for each subsystem. An iterative on-line algorithm for robust distributed MPC is developed to coordinate the distributed controllers. The algorithm is a flexible structure of robust control, which allows the independent computation of the state feedback laws for the subsystems. Convergence and robust stability of the proposed distributed MPC are analysed. Two numerical examples are carried out to demonstrate the effectiveness of the proposed algorithm.

Robust Model Predictive Control of Networked Control Systems under Input Constraints and Packet Dropouts

This paper deals with the problem of robust model predictive control (RMPC) for a class of linear time-varying systems with constraints and data losses. We take the polytopic uncertainties into account to describe the uncertain systems. First, we design a robust state observer by using the linear matrix inequality (LMI) constraints so that the original system state can be tracked. Second, the MPC gain is calculated by minimizing the upper bound of infinite horizon robust performance objective in terms of linear matrix inequality conditions. The method of robust MPC and state observer design is illustrated by a numerical example.

Evolutionary optimization of interval mathematics-based design of a TSK fuzzy controller for anti-sway crane control

Abstract A hybrid method combining an evolutionary search strategy, interval mathematics and pole assignment-based closed-loop control synthesis is proposed to design a robust TSK fuzzy controller. The design objective is to minimize the number of linear controllers associated with rule conclusions and tune the triangular-shaped membership function parameters of a fuzzy controller to satisfy stability and desired dynamic performances in the presence of system parameter variation. The robust performance objective function is derived based on an interval Diophantine equation. Thus, the objective of a fuzzy logic-based control scheme is to place all the closed-loop control system characteristic polynomial coefficients within desired intervals. The reproduction process in the proposed Evolutionary Algorithm (EA) is based on the arithmetical crossover, uniform and non-uniform mutation along with gene deletion/insertion mutation ensuring a diversity of genomes sizes, as well as a diversity in the parameter space of membership functions. The proposed algorithm was implemented to design a fuzzy logic-based anti-sway crane control system taking into consideration the rope length and the mass of a payload variation. The results of experiments conducted using the EA for different conditions assumed for system parameter intervals and desired closed-loop system performances are compared with results achieved using the iterative procedure which is also described in the paper.

Robust Distributed Model Predictive Load Frequency Control of Interconnected Power System

Considering the load frequency control (LFC) of large-scale power system, a robust distributed model predictive control (RDMPC) is presented. The system uncertainty according to power system parameter variation alone with the generation rate constraints (GRC) is included in the synthesis procedure. The entire power system is composed of several control areas, and the problem is formulated as convex optimization problem with linear matrix inequalities (LMI) that can be solved efficiently. It minimizes an upper bound on a robust performance objective for each subsystem. Simulation results show good dynamic response and robustness in the presence of power system dynamic uncertainties.

A robust distributed model predictive control algorithm

Although distributed model predictive control (DMPC) has received significant attention in the literature, the robustness of DMPC with respect to model errors has not been explicitly addressed. In this paper, a novel online algorithm that deals explicitly with model errors for DMPC is proposed. The algorithm requires decomposing the entire system into N subsystems and solving N convex optimization problems to minimize an upper bound on a robust performance objective by using a time-varying state-feedback controller for each subsystem. Simulations examples were considered to illustrate the application of the proposed method.

A robust anti-windup design procedure for SISO systems

A model-based anti-windup (AW) controller design approach for constrained uncertain linear single-input–single-output (SISO) systems is proposed based on quantitative feedback theory (QFT) loopshaping. The design approach explicitly incorporates uncertainty, is suitable for the solution of both the magnitude and rate saturation problems, and provides for the design of low-order AW controllers satisfying robust stability and robust performance objectives. Robust stability is enforced using absolute stability theory and generic multipliers (i.e. circle, Popov, Zames–Falb), and robust performance is enforced using linear lower-bounds on the input–output maps capturing the effects of saturation as a metric. Two detailed design examples are presented. These show that even for simple systems, certain popular AW techniques lead to compensators that may fail to ensure robust stability and performance when saturation is encountered, but that the proposed QFT design approach is able to handle both saturation and uncertainty effectively.

Multiple robust H∞ controller design using the nonsmooth optimization method

AbstractThis paper proposes a systematic technique to design multiple robust H∞ controllers. The proposed technique achieves a desired robust performance objective, which is impossible to achieve with a single robust controller, by dividing the uncertainty set into several subsets and by designing a robust controller to each subset. To achieve this goal with a small number of divisions of the uncertainty set, an optimization problem is formulated. Since the cost function of this optimization problem is not a smooth function, a numerical nonsmooth optimization algorithm is proposed to solve this problem. This method avoids the use of Lyapunov variables, and therefore it leads to a moderate size optimization problem. A numerical example shows that the proposed multiple robust control method can improve the closed‐loop performance when a single robust controller cannot achieve satisfactory performance. Copyright © 2009 John Wiley & Sons, Ltd.

An Online Algorithm for Robust Distributed Model Predictive Control

Distributed Model Predictive Control (DMPC) has received significant attention in the literature. However, the robustness of DMPC with respect to model errors has not been explicitly addressed. In this paper, an online algorithm that deals explicitly with model errors for DMPC is proposed. The algorithm requires decomposing the entire system into N subsystems and solving N convex optimization problems to minimize an upper bound on a robust performance objective by using a time-varying state-feedback controller for each subsystem. Simulations on two typical examples were considered to illustrate the application of the proposed method.

Stabilisation using a stable controller and robust stability and performance

A class of strictly proper multi-input multi-output (MIMO) causal linear time invariant (LTI) systems with a detectable and stabilisable realisation in a proposed observer-controller scheme, is considered. This class is characterised by the rank of the observability matrix in closed loop. The considered scheme is based on an ℋ∞ pre-compensator and on an ℋ∞ dual post-compensator stabilising a full actuation full information plant and on pseudo inverses of the input and of the output matrices. The pre-compensator and post-compensator are of reduced complexity and belong to the family of all stabilising controllers. The separation principle is satisfied and necessary and sufficient stability conditions are presented for the overall system getting a stable ℋ∞ controller. An algebraic approach and a state space approach are used to find this stability condition. The estimated error is zero in stationary state. Also, the control parameters allow the stationary state error and the complementary sensitivity function in high frequencies to approach zero asymptotically. So, robust stability and performance are achieved. A compromise exists between the stability of the compensators and the robust performance objective. The results are illustrated on a mechanical system.

INTEGRATION OF H∞ AND TIME DOMAIN SPECIFICATIONS USING THE CONVEX COMBINATION METHOD

Aircraft flight control systems often require the satisfaction of multiple simultaneous specifications to fulfil different robust stability and performance objectives along with good handling qualities. Many specifications such as H∞-norm, overshoot, undershoot, etc are convex with respect to the closed loop transfer matrix. In this paper it is suggested to use the convex combination method to integrate H∞ frequency domain specifications with additional time domain constraints. For this purpose, existing techniques are used to design an H∞ controller which is then modified in a new structure using Q-parametrization which makes the problem convex in the new design parameter Q. At this stage, if different controllers are obtained for each convex specification, they can be combined into a single controller using convex combination which could satisfy all specifications.

Robust continuous‐time controller design via structural Youla–Kučera parameterization with application to predictive control

AbstractThis paper addresses the continuous‐time control of uncertain linear SISO plants and its nominal and robust stability and nominal and robust performance objectives. A specific application of the Youla–Kučera (Q) parameterization concept leads to a new development of observer‐like controller structures. This method is combined with a nominal design of continuous‐time generalized predictive control suitable for both minimum‐phase and non‐minimum‐phase plants. The subsequent design procedure consists of two steps. Firstly, the nominal stability and nominal performance of the control system are established by using an analytical design methodology, based on a collection of closed‐loop prototype characteristics with definite time‐domain specifications. And secondly, a generic structure of the controller is enhanced by suitable Q‐parameters guaranteeing that the control system has the required robustness properties. The proposed structural (reduced‐order) Q‐parameterization relies on an observer structure of controllers, which can be easily enhanced with certain filters necessary for control robustification. To reduce the complexity of the resulting robust controllers, we suggest using a structural factorization, which allows for simple forms of robustifying (phase‐lag) correctors of low order, easy for implementation, and convenient for optimization and tuning. Two numerical examples are given to illustrate the composed technique and its practical consequences. Copyright © 2004 John Wiley & Sons, Ltd.

Multi-Objective Robust Control of an Evaporation Process

In this paper, a new multi-objective robust control design approach is applied to an evaporation process. The new approach, proposed in (Yan and Cao, 2002) extends the standard generalized-12 (G12) control problem based on a new Lyaponov stability condition to a set of new linear matrix inequality (LMI) constraints such that the multi-objective robust control problem associated with robust stability and robust performance objectives can be less conservatively solved using computationally tractable algorithms. A comparison of simulation results with controllers designed by different techniques demonstrates the superiority of the new method.

Open-loop and closed-loop robust optimal control of batch processes using distributional and worst-case analysis

Abstract The recognition that optimal control trajectories for batch processes can be highly sensitive to model uncertainties has motivated the development of methods for explicitly addressing robustness during batch processes. This study explores the incorporation of robust performance analysis into open-loop and closed-loop optimal control design. Several types of robust performance objectives are investigated that incorporate worst-case or distributional robustness metrics for improving the robustness of batch control laws, where the distributional approach computes the distribution of the performance index caused by parameter uncertainty. The techniques are demonstrated on a batch crystallization process. A comprehensive comparison of the robust performance of the open-loop and closed-loop system is provided.