Norm-bounded Model Uncertainties Research Articles

Adaptive Threshold-based Fault Detection for Systems Exposed to Model Uncertainty and Deterministic Disturbance

The fault detection problem is investigated for discrete-time linear uncertain systems. Instead of designing a fault detection system from the viewpoint of observer design for robust residual generation, an adaptive threshold approach is proposed to attain robustness against disturbance and norm-bounded model uncertainty. The main goal of the research is to develop a threshold design method that could establish an appropriate trade-off between false alarms and missed fault detection in the presence of model uncertainty. For this purpose, the H∞ optimization technique is adopted in the linear matrix inequality framework to compute the unknown parameters of an adaptive threshold. It is shown that the proposed fault detection system based on an adaptive threshold depends only on the system parameters and the control input of the monitored system. It is independent of robust residual generator designs in traditional observer-based fault detection systems. The effectiveness of the proposed approach is verified on two well-known benchmark systems: a direct-current motor and three tank systems. Several types of faults are successfully detected in both applications.

Distributed fault detection and isolation for uncertain linear discrete time-varying heterogeneous multi-agent systems

The distributed fault detection and isolation of linear discrete time-varying multi-agent systems subject to heterogeneous dynamics and norm bounded model uncertainties is investigated. By combining the model uncertainties and external disturbances into a new generalized disturbance, a distributed closed-loop residual generator is constructed based on the estimate of the generalized disturbance. Then, the concerned fault detection is transformed into an indefinite quadratic minimum problem by using the finite-horizon robust H∞ filtering method, for which necessary and sufficient minimum conditions are provided by the Krein-space theory. Afterwards, a computationally efficient recursive algorithm is further developed to determine the residual for individual agent. Based on the resulting residuals, the fault occurrence can be alerted by devising a novel distributed fault detection scheme, which is then applied for the fault isolation by some appropriate transformation of the output measurements. Finally, both numerical and practical simulations are proposed to verify the effectiveness of the proposed algorithm.

Output feedback robust MPC for linear systems with norm-bounded model uncertainty and disturbance

This paper presents an output feedback robust model predictive control strategy for linear systems with norm-bounded model parametric uncertainty and disturbance. In order to reduce the computational burden and enhance the control performance, in the optimization problem we optimize the estimator state matrix instead of the state estimator gain. The infinite horizon control moves and estimated states are parameterized by a dynamic output feedback control law, where its state feedback gain and estimator state matrix are optimized at each sampling instant. By appropriately refreshing the estimation error set, the optimization problem is shown to be recursively feasible and the convergence of the augmented state is guaranteed. A numerical example is given to show the effectiveness of the proposed approach.

Robust H∞ Computed Torque Control of Flexible Joint TVC Systems

Abstract Flexible Joint Thrust Vector Control (FJ-TVC) is often used to control the orientation of spacecraft and aircraft since there is no thrust loss in the nozzle and a longer lifespan is possible due to the absence of moving parts. However, the structure of the flexible material and some parameters in the system introduce uncertainties, such as misalignment of the pivot point on the nozzle and nonlinear behavior in the elastomer material, that impact negatively on high precision and tracking control. In this paper a computed torque control law together with a PD controller is first designed but the results are not sufficiently robust and stability problems could arise in the resulting control loop. To counter such effects, an H∞ based computed torque controller is designed based on norm bounded model uncertainty, where Monte Carlo based simulations have been used to model the effect of the uncertainties. Finally, the effectiveness of the new design is demonstrated by a simulation study.

A Novel Robust Sparse-Grid Quadrature Kalman Filter Design for HCV Transfer Alignment Against Model Parameter Uncertainty

A novel robust scheme for Transfer Alignment (TA) is proposed for improving the accuracy of the navigation of a Hypersonic Cruise Vehicle (HCV). The main goal is to instil robustness in the safety and accuracy of the attitude determination, despite mode uncertainties. This article focuses on Robust Sparse-Grid Quadrature Filtering (R-SGQF) using two given robust factors for norm-bounded model uncertainties in non-linear systems. Missile dynamic and measurement model uncertainties are established to validate TA technologies. The nominal stability of the R-SGQF is defined by estimating error dynamics. The technique gives sufficient conditions for the R-SGQF in terms of two parameterised Riccati equations. Robust stability is analysed using Lyapunov theory and the accuracy level of the Sparse-Grid Quadrature (SGQ) algorithm. Embedding the SGQ technique into the robust filter structure, R-SGQF is not only of robust stability against uncertainty but also of higher accuracy. The simulation results of the TA algorithm demonstrate that attitude determinations validate the effectiveness of the R-SGQF algorithm.

Multirate Vibration Attenuation Beyond Nyquist Frequency with Performance, Stability and Robustness Analysis

In digital/sampled-data motion control systems, the system outputs are only available at certain rates. This sets a great challenge to high-precision motion control systems that subject to high-frequency disturbances, since the feedback regulator cannot directly observe the inter-sample outputs. To handle such situations, a robust multirate control approach is proposed in this paper to enhance disturbance attenuation at high frequencies, including those, under certain conditions, near and beyond the Nyquist Frequency. First, based on the Youla parameterization of all stabilizing controllers, an add-on compensator based on multirate observer is constructed using the a priori nominal model of the disturbance dynamics. Then robust design of a proper Q filter is formulated via the theory of multiple-input-multiple-output (MIMO) robust control, which guarantees the closed-loop stability in the presence of norm-bounded model uncertainties. Effectiveness of the proposed algorithm is evaluated by simulations on a hard disk drive (HDD) benchmark problem, where the inter-sample position errors are approximately recovered and high-frequency disturbance is greatly attenuated with guaranteed closed-loop stability.

Fault Detection for a Class of Uncertain Linear Discrete-time Systems with Intermittent Measurements and Probabilistic Actuator Failures

This paper deals with fault detection (FD) problem for linear discrete-time systems subject to random intermittent measurements, probabilistic actuator failures, norm-bounded model uncertainty, and stochastic model uncertainty. By taking into account the probabilistic actuator failures, a new reference residual model is proposed to formulate the FD issue as an H∞, model-matching problem. The corresponding reference residual is generated through maximizing a stochastic H–/H∞ or H∞/H∞ performance index via solving an algebraic Riccati equation (ARE). By the aid of the linear matrix inequality (LMI) techniques, a fault detection filter (FDF) is constructed such that the residual is sensitive to fault but insensitive to unknown inputs, mixed model uncertainties, random intermittent measurements and stochastic actuator failures. An illustrative example is given to demonstrate the effectiveness of the proposed method.

A Norm-Bounded robust MPC strategy with partial state measurements

In this paper a robust MPC scheme based on a partial-state availability is developed for uncertain discrete-time linear systems described by structured norm-bounded model uncertainties and subject to saturation and rate of variation constraints. The algorithm is based on the minimization, at each time instant, of a semi-definite convex optimization problem subject to Linear Matrix Inequalities (LMI) feasibility constraints which are derived by a judicious use of S-Procedure arguments. Numerical comparisons with competitor algorithms are finally reported by dealing with the control augmentation problem of an High Altitude Performance Demonstrator (HAPD) unmanned aircraft with redundant control surfaces.

Robust Positively Invariant Sets for Linear Systems subject to model-uncertainty and disturbances

In this paper, we propose an algorithm for the computation of Robust Positively Invariant sets for linear discrete-time systems subject to norm-bounded model-uncertainty, additive disturbances and polytopic constraints on the input and state. The invariant set (optimized with respect to a measure of size) and the corresponding controller are computed simultaneously by solving a single LMI optimization problem. The novelty lies in the fact that the proposed scheme explicitly takes account of (norm-bounded) model-uncertainty and does not require any iterative computations or initial estimates of the invariant set or controller. A numerical example, taken from literature, demonstrates the applicability of proposed algorithm.

Norm-bounded robust MPC strategies for constrained control of nonlinear systems

This paper considers nonlinear predictive control via embedding strategies. A novel robust MPC algorithm for input-saturated uncertain discrete-time linear systems subject to norm-bounded (LFR) model uncertainties is presented and contrasted with direct nonlinear and robust polytopic MPC methods in two final nonlinear examples: a mildly nonlinear two-tanks hydraulic system and a highly nonlinear CSTR plant. From the examples it results that the embedding strategies compare favourably with direct nonlinear MPC in the mildly nonlinear system whereas their performance may degrade, often considerably though exceptions are not rare, in highly nonlinear plants. However, the numerical savings achievable by adopting embedding approaches are remarkable, especially for the proposed solution.

Robust constrained predictive control of uncertain norm-bounded linear systems

A novel robust predictive control algorithm is presented for uncertain discrete-time input-saturated linear systems described by structured norm-bounded model uncertainties. The solution is based on the minimization, at each time instant, of a semi-definite convex optimization problem subject to a number of LMI feasibility constraints which grows up only linearly with the control horizon length N . The general case of arbitrary N is considered. Closed-loop stability and feasibility retention over the time are proved and comparisons with robust multi-model (polytopic) MPC algorithms are reported.

Robust stability constraints for fuzzy model predictive control

This paper addresses the synthesis of a predictive controller for a nonlinear process based on a fuzzy model of the Takagi-Sugeno (T-S) type, resulting in a stable closed-loop control system. Conditions are given that guarantee closed-loop robust asymptotic stability for open-loop bounded-input-bounded-output (BIBO) stable processes with an additive l/sub 1/-norm bounded model uncertainty. The idea is closely related to (small-gain-based) l/sub 1/-control theory, but due to the time-varying approach, the resulting robust stability constraints are less conservative. Therefore the fuzzy model is viewed as a linear time-varying system rather than a nonlinear one. The goal is to obtain constraints on the control signal and its increment that guarantee robust stability. Robust global asymptotic stability and offset-free reference tracking are guaranteed for asymptotically constant reference trajectories and disturbances.

Robustness of multivariable linear controllers to process nonlinearities

Many nonlinear processes have highly structured model mismatches which make a controller, based on an inverse of a linear nominal model, more robust than is predicted from the theories that assume unstructured, norm-bounded model uncertainty. The structure of model mismatch due to process nonlinearities is analyzed via singular value decomposition of the locally linearized steady-state models at different operating conditions. It is shown that certain constraints on the decomposition matrices, for example one of the decomposition matrices being unaffected by the nonlinearities, have important consequences on robust stability. The implications of this analysis for the identification of ill-conditioned processes for robust controller designs are also discussed. Binary distillation columns and catalytic reactors are treated as examples of processes with such structured model mismatch

System Identification for H ∞ -Robust Control Design

Conventional identification techniques are based on stochastic assumptions and yield minimum variance estimates. A major drawback of these techniques is that disturbances as well as model- uncertainties are treated as additive noise and are thus minimized together. Consequently hardly any indication of model-error bounds can be given, whereas robust control theory is based upon a nominal model together with both norm-bounded model-uncertainties and noise characterised in the frequency domain. It is our goal to present a new identification method using H ∞ -norms which yields a nominal model and information about the model-uncertainties applicable to H ∞ -robust control design. In the proposed method disturbances and noise signals at the input and output of the system are characterized as norm-bounded. The first step in the identification method is to compute uncertainty regions for the process dynamics in the complex plane. The a priori knowledge about the norm-bounds on the disturbances and properties of conformal mappings are used to compute these regions. The second step is to find a model in a model-set that minimizes the H ∞ -norm of the model errors, given the uncertainty regions. The first elementary implementation of the method is presented with two simulation studies.