Design Conservatism Research Articles

Design of Distributed Interval Observers for Multiple Euler–Lagrange Systems

This paper investigates the problem of distributed interval estimation for multiple Euler–Lagrange systems. An interconnection topology is supposed to be strongly connected. To design distributed interval observers, the coordinate transformation method is employed. The construction of the distributed interval observer is given by the monotone system theory, and the stability is analyzed by the Lyapunov stability theory. Unlike the current works, each sub-interval observer has its own gain; in addition to this, additional observer gains are used to reduce the conservatism of design. The gains of all sub-interval observers are determined by both the monotone system theory and the Lyapunov stability theory. Finally, a simulation example verifies the feasibility of the presented distributed interval observers.

A control-theoretic approach for input saturated linear systems: Integration of phase-shaping and gain-scheduling

Saturation is mainly characterized by its passivity and magnitude bound. But most of the saturation control methods only make use of either of these features. To enhance the performance of saturated systems, this paper develops a novel method capable of fully using both of these two features. This method is a two-stage design scheme which integrates the phase-shaping technique with the gain-scheduled control. The phase-shaping fully uses the passivity of saturation while the gain-scheduling actively utilizes the magnitude bound of saturation. In this way, the design conservatism associated with existing methods is reduced substantially. Specifically, a matrix-type phase-shaping method is developed through the placement of systems’ frequency loci, and a meta-heuristic method is devised for the design of the phase-shaping function. Furthermore, the gain-scheduled control is transformed into the robust performance problem of a passive uncertain system, and designed by the passivity-based robust control method of the authors. Application to two practical control systems validates the effectiveness of the proposed method. The superiority is demonstrated via comparisons with typical saturation control methods.

Vehicle Actuator Fault Detection With Finite-Frequency Specifications via Takagi-Sugeno Fuzzy Observers: Theory and Experiments

This article presents a new nonlinear observer-based method to detect the faults of both steering and torque actuators of autonomous ground vehicles. To this end, the nonlinear vehicle system is reformulated in a Takagi-Sugeno (TS) fuzzy model with both measured and unmeasured nonlinear consequents, called N-TS fuzzy model. Differently from the classical TS fuzzy technique with linear consequents, this N-TS fuzzy reformulation enables an effective use of differential mean value theorem to deal with unmeasured nonlinearities, which is known as a major challenge in TS fuzzy observer design. Moreover, the N-TS fuzzy form also allows reducing not only the design conservatism but also the numerical complexity of the design conditions as well as the observer structure, which is crucial for real-time vehicle application. To minimize the disturbance effect with an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathscr {H}_\infty$</tex-math></inline-formula> performance and maximize the fault sensibility with an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathscr {H}_-$</tex-math></inline-formula> performance, the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> information on the disturbance/fault frequency ranges is taken into account in the N-TS fuzzy observer design via the generalized Kalman–Yakubovich–Popov (KYP) lemma. Based on Lyapunov stability theory, the design of the proposed multiobjective <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathscr {H}_-/\mathscr {H}_\infty$</tex-math></inline-formula> N-TS fuzzy fault detector is recast as an optimization problem with strict linear matrix inequality (LMI) constraints, which can be effectively solved with numerical solvers. Both numerical and experiments are performed under realistic driving conditions to demonstrate the theoretical and practical interests of the new finite-frequency fuzzy fault detection method.

Further Stability Criteria for Sampled-Data-Based Interval Type-2 Fuzzy Systems via a Refined Two-Side Looped-Functional Method

This article investigates the stability and stabilization problem of aperiodic sampled-data nonlinear systems in the framework of interval type-2 (IT-2) fuzzy models. First, by introducing two adjustable parameters and splitting the sampling intervals into four nonuniform intervals, a refined two-side looped-functional method is constructed to fully utilize inner state information during the whole aperiodic sampling interval. Simultaneously, the positive definiteness constraint for the individual matrix in Lyapunov–Krasovskii functional can be further relaxed. Then, via constructing a novel fuzzy Lyapunov–Krasovskii functional (FLKF) together with a fuzzy-dependent-switching scheme, the available features of fuzzy membership functions (FMFs) can be further taken into consideration to increase the design flexibility. Consequently, the stability condition and corresponding controller design approach for aperiodic sampled-data IT-2 fuzzy systems can be obtained with less design conservatism and larger sampling intervals. Finally, two simulation examples are employed to demonstrate the validity and superiority of the proposed method.

Uncertainty modeling methods capable of capturing phase and gain information

In practice, the plant model is usually built from its frequency responses obtained from identification experiments. In this sense, it is desirable to build an uncertainty model from the frequency responses. Up to date, there are mainly two kinds of uncertainty models: norm-bounded and passive. For general systems, the range of uncertainty is inevitably enlarged by these two uncertainty models, thus leading to design conservatism. This paper proposes two novel uncertainty models, together with sophisticated modeling algorithms. These models are able to reduce the enlargement of uncertainty's range to the utmost, and can be easily combined with existing robust design methods. It can be interpreted as a fine capture of uncertainty's gain and phase ranges. A case study demonstrates the superiority of the proposed models.

Experiment and evaluation model of liner design for renewal of deteriorated reinforced concrete pipes utilizing cured-in-place-pipe technology

Cured-In-Place-Pipe (CIPP) is an emerging trenchless rehabilitation technology for repairing urban drainage pipes growing significantly in China. However, overestimated external loads due to a completely deteriorated-pipe assumption may increase conservatism in the CIPP liner structure design. In this study, ring stiffness test machine was employed to quantify the bearing characteristics of pipe-liner system. The concrete and reinforced concrete pipes with an inner diameter of 200 mm, which deteriorated to several states, were renewed with CIPP. Digital Image Correlation (DIC) was employed to reveal the contact characteristics between the host pipe and CIPP liner under external loads and the mechanism of loads transferred from the pipe to the liner. An evaluation model for load-bearing performance of reinforced pipe was established. Parametric studies were carried out including lateral load distribution angle, concentrated load dispersed angle, and lateral interactions. Furthermore, a case study was conducted in conjunction with the indirect design method for buried pipes, and then the improved model was compared with experiment results. An average value of 20 % reduction in CIPP liner thickness was achieved by employing the modified model than the ASTM standard. This study can serve as a database for engineers designing CIPP rehabilitation projects for concrete pipes whose structure has not been completely damaged.

Dissipative-based sampled-data control for T-S fuzzy wind turbine system via fragmented-delayed state looped functional approach

This study investigates thedissipative-based fuzzy sampled-data control scheme for variable-speed wind turbine system (WTS) by fragmented-delayed state looped functional framework. The main objective of this study is to stabilize the nonlinear variable-speed WTS and enhance its dynamic performance. To do this, initially, the proposed nonlinear variable-speed WTS is transformed into linear subsystems based on the Takagi–Sugeno (T-S) fuzzy approach. Then, the concept of coupling leakage time-varying delay is proposed to construct a more generalized T-S fuzzy model. After that, to minimize design conservatism, an improved fragmented- delayed state looped-Lyapunov functional is developed to fully utilize the advantages of the variable characteristics related to the actual sampling pattern. Besides, by applying the proposed new integral inequalities, some sufficient conditions are derived to ensure the addressed system is asymptotically stable under an optimizing performance index. Finally, numerical simulations are given to verify the effectiveness and feasibility of the proposed control scheme. The essential outcome of the proposed approach is that it can provide a superior dissipative performance index under the maximal sampling period.

A difference-algebraic interval observer design for perturbed discrete-time descriptor systems

This paper investigates a difference-algebraic (DA) interval observer (IO) design technique for perturbed discrete-time descriptor systems. The existence condition of the IO with a DA structure is first established, along with the canonical implementation of descriptor systems and its non-negativity criterion. Then, combined with such an IO, a triangular block transformation (TBT) is further introduced to reduce the universal IO design conservatism on cooperativity construction. Besides, the general and particular solutions to the TBT&DA-based IO are successively proposed not only to clearly show the available design parameters but also to achieve a convenient construction process. Three simulation results demonstrate the validity and superiority of the proposed methods.

Linear Parameter Varying Models-Based Gain-Scheduling Control for Lane Keeping System With Parameter Reduction

In this paper, a robust <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {H}_{2}$ </tex-math></inline-formula> controller based on Linear Parameter Varying (LPV) model with scheduling variable reduction is applied for a lane-keeping system. On a curved road section, varying longitudinal speed and roll motion lead to multiple parameter variations in the lateral vehicle dynamics. To trade-off between the complexity of the multiple scheduling variables and the accuracy of the LPV model, an order reducing method by Autoencoder (AE) is performed to obtain a reduced model and diminishes the conservatism of LPV-based controller design. Further, to ensure the continuous convex set membership of the reduced scheduling variables in online test scenarios, the Lipschitz constant of the offline trained neural network (NN) is tightly estimated by solving a Semidefinite Program (SDP). The convex set of local Linear Time-Invariant (LTI) controllers is designed according to the estimated Lipschitz bound of the trained NN. The LPV-based robust <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {H}_{2}$ </tex-math></inline-formula> feedback controller is then designed by solving a set of Linear Matrix Inequalities (LMIs). Numerical simulations with full vehicle dynamics from CarSim are given to demonstrate the performance of the proposed system on various test roads. The continuous finding of the reduced scheduling variable membership is guaranteed in the online tests, and the effectiveness of the proposed method is confirmed with the mean value of lateral offset error reduced by about 50% compared with LTI-based <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {H}_{2}$ </tex-math></inline-formula> controllers.

Admissible edge-dependent finite-time ℋ∞ filtering for discrete-time switched systems with average dwell time

Considering that the property of finite-time convergence is of great significance for practical filters, this article is focused on the finite-time ℋ∞ filtering for discrete-time switched systems with average dwell time. Different from the case of the general mode-dependent switching, the information of the admissible switching edge is fully exploited to derive more preferable filtering scheme. In order to further reduce the design conservatism, the multiple discontinuous Lyapunov function approach, which incorporates the concept of admissible edge-dependent average dwell time, is used to analyze the finite-time stability and ℋ∞ performance of the filtering error system. This approach assigns each subsystem of the error system with a discontinuous function rather than a continuous one, so it is less conservative compared to the conventional multiple Lyapunov function approach. First, the finite-time boundedness and ℋ∞ performance is analyzed for general switched nonlinear systems with admissible edge-dependent average dwell time. Then, a sufficient condition of the finite-time boundedness and ℋ∞ performance is derived for the filtering error system based on the obtained criterion. Subsequently, an admissible edge-dependent finite-time filtering scheme is proposed for the underlying system in terms of linear matrix inequalities. Finally, the proposed filter design scheme is applied to a DC–DC power converter circuit, and its effectiveness and superiority are verified by the simulation results.

Model-scale tests to examine water pressures acting on potentially buoyant underground structures in clay strata

Throughout the service life, underground structures are subjected to transient and sustained hydrostatic pressures. The reservoir impoundment results in an increase in water level, as well as hydraulic gradient, which can endanger the uplift performance of infrastructure. In uplift design, a reduction factor is often suggested for buoyant force acting on underground structures in clays due to the time lag effect. However, the mechanism of pore pressure generation in clays is not fully understood. This investigation presents a novel U-shaped test chamber to assess the pore pressure generation with time in the horizontal branch subjected to an increase in reservoir level in the left vertical branch. A mathematical model is developed to explain the time lag effect of pore pressure generation. The test program also involves the evaluation of uplift pressure acting on foundation model in the right vertical branch due to adjacent reservoir impoundment. It is found that the time lag effect of pore pressure generation in clays can be observed irrespective of hydraulic gradient, but a higher hydraulic gradient can lead to a faster response in pore pressure sensors. A reduction factor of 0.84–0.87 should be considered to reduce the conservatism of uplift design.

Robust H∞$H_\infty$ dynamic output feedback control of the DC–AC converter with a neutral leg

This paper investigates the problem of robust H ∞ $H_\infty$ dynamic output feedback control of 3-phase 4-wire converter with neutral bridge arm in the application of smart grid and distributed generation. Based on Lyapunov functions, a novel sufficient Linear Matrix Inequality condition analysis was performed on the dynamic output feedback stabilisation controllers. Meanwhile, some auxiliary slack variables with special structure and well-established performance conditions are employed to reduce design conservatism. This topology along with the H ∞ $H_\infty$ controller can solve the DC link balancing problem and maintain the deviation between the neutral point and the midpoint of DC supply very small. The achievable performance is analysed quantitatively and the controller design method was conducted and verified both in MATLAB simulation and the real-time simulation platform built by StarSim and MT, respectively.

Hybrid-triggered H∞ Fault Detection for Distributed Time-delay Systems with Communication Quantization Based on T-S Fuzzy Model

In the network environment, the time-triggered mechanism wastes limited bandwidth resources due to the transmission of all sampled data to the network. The event-triggered mechanism may increase system errors due to ignoring factors such as changes in network utilization. In order to reduce the design conservatism, this paper studies the design of a hybrid-triggered H∞ fault detection filter for a class of nonlinear networked control systems described by Takagi-Sugeno (T-S) fuzzy model, and applies quantization techniques in the communication channel. Using the Lyapunov-Krasovskii functional and integral inequality methods, new results on the stability and H∞ performance of fuzzy fault detection systems are presented. In particular, the designed fault detection filter has a specific H∞ noise attenuation level γ. The final simulation results verify the effectiveness of the design.

A refinement approach to the multivariable tracking error problem

This article presents a new refinement design routine aimed at solving the robust multivariable tracking error problem with reduced conservatism. The prevailing multivariable quantitative feedback theory (QFT) approach is to implicitly overbound the model-error tracking set frequency response in magnitude using the triangle inequality, with the intention of arriving at a set of univariate design constraints that independently describe the feedback controller solution space. While this method is effective in the low-frequency range (where the loop gain tends to be large), the mid- to high-frequency design regions (where diagonal dominance is not possible in general) suffers from arbitrarily large design conservatism. This inhibits minimum gain-phase solutions and necessitates undesirable over-design in the frequency band that can contribute to large, expensive control action. The proposed method follows a refinement approach that makes use of information from an a priori feedback control design. In this way, the tracking error problem is reposed as a differential design, and gain-phase information from the previous iteration can be captured to reduce the conservatism imposed when applying the triangle inequality. Additionally, a constrained optimization routine is used to select a prototype feedforward filter that can relax the constraint set, thereby increasing the accessible solution space of the diagonal feedback controller. Finally, a nondiagonal, multivariable feedforward filter bound generation routine is defined that relies on existence conditions and is free of induced design conservatism. The viability of this design methodology is demonstrated on two benchmark problems of varying complexity, in order to demonstrate the widespread efficacy.

Peak-to-peak fuzzy filtering of nonlinear discrete-time systems with markov communication protocol

This study deals with the peak-to-peak fuzzy filtering problem for a class of nonlinear discrete-time systems with analog fading channels and communication protocol, in which the nonlinear system is modeled by the Takagi-Sugeno fuzzy model. In analog fading channels, a homogeneous Markov chain is forwarded to model the random time-varying amplitude attenuation. Aiming at alleviating the utilization of energy consumption and preventing data collision/congestion in constraint networks, a Markov communication protocol is exploited to orchestrate the data transmission, in which only one sensor can get permission to release the measurement during each time interval. In virtue of the merging strategy, a new joint Markov chain is presented to incorporate the fading channels and the communication protocol. Differently, in order to eliminate the obstacle of design conservatism, a novel peak-to-peak filter design methodology is developed, whose asynchronization is described by a nonhomogeneous hidden Markov model. Under the aforementioned framework, the resulting system is stochastically stable with a desired peak-to-peak performance index. To this end, a practical example is addressed to indicate the validity and applicability of the presented peak-to-peak filter design strategy.

Semi-Markov jump linear systems with bi-boundary sojourn time: Anti-modal-asynchrony control

This paper investigates the problem of control synthesis for a class of discrete-time semi-Markov jump linear systems, in which the sojourn time of each mode is bi-boundary (with upper and lower bounds). The system is subject to modal asynchrony, which means that the switchings of the mode-dependent controller to be designed lag behind the ones of the controlled plant, and the lag is mode-dependent. In contrast with the traditional mode-independent lag commonly assumed in the existing studies, not only is the modal lag more practical and general, but also it yields less conservatism of the controller design. By virtue of the semi-Markov kernel approach, the conditions on the existence of the anticipated stabilizing controllers capable of overcoming the modal asynchrony are derived. Illustrative examples including a class of vertical take-off and landing (VTOL) helicopter models are presented to demonstrate the necessity and the validity of the designed anti-modal-asynchrony controllers.

A probabilistic Q-system using the Markov chain to predict rock mass quality in tunneling

Uncertainty in rock mass conditions is mainly caused by the inherently inhomogeneous nature of rock masses. Assessment of rock mass quality without accounting for inherent uncertainty often leads to unnecessary conservatism in design and construction, resulting in excessive cost and schedule overrun. In this study, to advance rock mass quality assessment, a rock mass classification Q-based prediction model to assess probabilistic rock mass quality has been proposed using the Markov chain framework with Monte Carlo simulation. In addition, an analytical approximation approach has also been developed to derive the statistics (mean, standard deviation, and coefficient of variation) of the Q value given statistics of Q parameters in the Markov chain model. The proposed prediction model and analytical calculation approach were applied to a water tunnel. The probabilistic prediction results have been validated by the field recorded Q data during tunnel construction in a probabilistic framework with the use of the accuracy plot where uncertainties are explicitly quantified in the predicted probabilistic model. The proposed Q-based prediction model can assess the rock mass quality in unexcavated tunnel sections using a probabilistic approach to serve as a preliminary site condition indicator.

Damping identification of offshore wind turbines using operational modal analysis: a review

Abstract. To increase the contribution of offshore wind energy to the global energy mix in an economically sustainable manner, it is required to reduce the costs associated with the production and operation of offshore wind turbines (OWTs). One of the largest uncertainties and sources of conservatism in design and lifetime prediction for OWTs is the determination of the global damping level of the OWT. Estimation of OWT damping based on field measurement data has hence been subject to considerable research attention and is based on the use of (preferably operational) vibration data obtained from sensors mounted on the structure. As such, it is an output-only problem and can be addressed using state-of-the-art operational modal analysis (OMA) techniques, reviewed in this paper. The evolution of classical time- and frequency-domain OMA techniques has been reviewed; however, the literature shows that the OWT vibration data are often contaminated by rotor speed harmonics of significantly high energy located close to structural modes, which impede classical damping identification. Recent advances in OMA algorithms for known or unknown harmonic frequencies can be used to improve identification in such cases. Further, the transmissibility family of OMA algorithms is purported to be insensitive to harmonics. Based on this review, a classification of OMA algorithms is made according to a set of novel suitability criteria, such that the OMA technique appropriate to the specific OWT vibration measurement setup may be selected. Finally, based on this literature review, it has been identified that the most attractive future path for OWT damping estimation lies in the combination of uncertain non-stationary harmonic frequency measurements with statistical harmonic isolation to enhance classical OMA techniques, orthogonal removal of harmonics from measured vibration signals, and in the robustification of transmissibility-based techniques.

Membership-function-dependent model predictive control for nonlinear systems in a piecewise-fuzzy framework

This paper is concerned with the membership-function-dependent model predictive control (MPC) problem for a class of Takagi-Sugeno (T-S) fuzzy systems with hard constraints. In order to design a set of membership-function-dependent controllers in the framework of MPC, the original T-S fuzzy systems are equivalently converted into a piecewise-fuzzy model by means of the partition method of the premise variable space. Then, instead of calculating vertices to construct the fuzzy MPC controller as adopted in the traditional T-S fuzzy control strategies, some staircase membership functions are employed to approximate the continuous membership functions, such that the information of membership functions can be adequately considered in the control synthesis to reduce the conservatism of the controller design. Furthermore, associated with the piecewise-fuzzy model, an online optimization problem based on the membership-function-dependent terminal constraint set is formulated in terms of the piecewise-Lyapunov-function-based MPC to calculate the feedback gains. Besides, by employing polynomial constraints based on the shape information of the membership functions, errors between the staircase membership functions and the original continuous membership functions are taken into account for facilitating the feasibility investigation and the stability analysis. Finally, two illustrative examples are used to illustrate the validity of the proposed membership-function-dependent MPC strategy.

Robust predictive control of a supercavitating vehicle based on time-delay characteristics and parameter uncertainty

Supercavitating vehicle can realize high-speed underwater sailing. However, the nonlinear force and time-delay characteristics caused by the tail flapping the cavity wall become the main challenge of the vehicle controller design. Aiming at time-delay characteristics, the nonlinear of planing force, cavity radius perturbation and parameter uncertainty, the paper establishes a time-delay linear-parameter-varying (LPV) model and designs a robust predictive controller with anti-interference performance. In the process of predictive controller design, the variable quadratic function is used to achieve the robustness of the vehicle and reduce the conservatism of the controller design. Meanwhile, the memory state feedback is used to solve the problems of cavitation radius perturbation, control constraints, vehicle parameter uncertainty and external disturbance. The simulation results show that the controller has strong robustness against the disturbance of external parameters, and can guarantee the stability of the system.