Robust Stability Analysis of Fuzzy Feedback Linearization Control Systems

In this paper, the Takagi-Sugeno (TS) fuzzy modelling and the fuzzy regulation theory are considered in order to design a fuzzy controller capable of taking the output of a fuzzy plant to the reference signal generated by an external system. It is well-known that TS fuzzy modelling allows the stabilizer to be obtained by means of numerical techniques. As a result, stability region defined by the fuzzy stabilizer is larger than the one obtained when a simple linear stabilizer is considered. On the other hand, a fuzzy regulator constructed from linear controllers does not solve the exact regulation problem in general [6], [12], [13], [15]. Therefore, a fully nonlinear regulator, defined on the overall TS fuzzy model, is considered in this work. The results are applied on a simple fuzzy model in order to illustrate the improvement achieved with the proposed approach.

Using Takagi-Sugeno fuzzy model, feedback linearisation which is widely used in nonlinear control theory can be applied to fuzzy control. If perfect linearization can be obtained, the stability can be analysed by linear system theory. However, since modeling uncertainty and disturbance affect the stability, the robust stability analysis is needed to deal with uncertainty. In this paper, the sufficient L/sub 2/ robust stability condition is derived from the multivariable circle criterion. A simple example illustrates the proposed method.

The author presents a robust technique for designing compensators for a certain class of nonlinear systems following the philosophy behind input-output linearization and sliding mode control. The technique takes advantage of a robust equivalent feedback linearization using sliding mode theory and then superimposes linear design algorithms in order to shape the loop operator (loop transfer function) of the feedback linearized system. Robustness issues are addressed; when the external disturbances to the system and modeling parameter uncertainties are bounded and satisfy the matching conditions, the nonlinear system can be robustly linearized. The proposed scheme has enough parameters to give flexibility in the choice of the desired closed-loop characteristics. At the same time, it leaves the designer with the responsibility of selecting the following parameters: boundary layer, strength of attraction to the sliding surface, and bandwidth.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Strain rockburst is a severe failure phenomenon caused by the release of elastic strain energy in intact rocks under high-stress conditions. They frequently occur in deep tunnels, causing significant economic losses, casualties, and construction delays. Understanding the factors influencing this disaster is of significance for tunnel construction. This paper first proposes a novel three-dimensional (3D) discrete element numerical analysis method for rockburst numerical analysis considering the full stress state energy based on the bonded block model and the mechanics, brittleness, integrity, and energy storage of the surrounding rock. This numerical method is first validated via laboratory tests and engineering-scale applications and then is applied to study the effects of compressive and tensile strengths of rock mass, tunnel depth, and lateral pressure coefficient on strain rockburst. Meanwhile, sensitivity analyses of these influencing factors are conducted using numerical results and systematic analysis methods, and the influence degree of each factor on the rockburst tendency is explored and ranked. The results reveal that laboratory tests and actual engineering conditions are consistent with numerical simulation results, which validates the rationality and applicability of the novel rockburst analysis method proposed in this paper. With the increase in compressive strength, the stress concentration degree, energy accumulation level, maximum stress difference, and maximum elastic strain energy within the rock mass all increase, leading to a stronger rockburst tendency. Tunnel depth and the lateral stress coefficient are positively correlated with rockburst tendency. As the lateral pressure coefficient and tunnel depth increase, rockburst tendency exponentially increases, while the maximum stress difference and maximum elastic strain energy within the rock mass also increase. The influence degree of each factor is ranked from highest to lowest as follows: tensile strength, lateral pressure coefficient, compressive strength, and tunnel depth. The research results provide theoretical support and technical guidance for the effective prediction, prevention, and control of rock burst disasters in deep tunnels.

The robust stability and stabilization, and H-infinity control problems for discrete-time Markovian jump singular systems with parameter uncertainties are discussed. Based on the restricted system equivalent (r.s.e.) transformation and by introducing new state vectors, the singular system is transformed into a discrete-time Markovian jump standard linear system, and the linear matrix inequality (LMI) conditions for the discrete-time Markovian jump singular systems to be regular, causal, stochastically stable, and stochastically stable with γ-disturbance attenuation are obtained, respectively. With these conditions, the robust state feedback stochastic stabilization problem and H-infinity control problem are solved, and the LMI conditions are obtained. A numerical example illustrates the effectiveness of the method given in the paper.

The primary objective of this study is to investigate the rolling noises made by passenger car radial (PCR) tires with special pitch angles using the numerical analysis method, and compare the numerical analysis results with those of physical tire experiments. By using the numerical simulation features, we can understand the noise performances of the different designs through the numerical analysis results before creating the actual molds and thereby reduce the development costs. In this study, the researcher adopted the finite volume (FV) numerical simulation method because the rapid solving speed feature of the FV method enabled it to be widely adopted by the various major fields such as automotive, aerospace, or shipbuilding where the simulation results are time-sensitive and analytically correct. To achieve the experimental results, the researcher of this study commissioned Kenda Rubber Ind., Co., Ltd. to design the tire pitches and manufacture the tires, and deliver the tires to the Automotive Research & Testing Center (ARTC) for the experiments. When the numerical simulation and experiment results are compared, the characteristic frequency positions are consistent with the error rate of only 3.98%. As such, the analysis method proposed in this study can serve as references for tire manufacturing designs as well as mobile object noise analyses in the future.

Seepage-stress coupling in fractured rock mass is a hot and difficult issue in the field of rock mechanics and engineering research. Firstly, the research status of the experiments and mathematical models of the coupling of fractured rock mass were described systematically. Meanwhile, some common numerical analysis methods and their applications were summed up. Then the hotspots and engineering applications of coupling were summarized. According to the analysis of the research status of seepage-stress coupling, some suggestions were put forward:(1)In most of past researches, the relationship between permeability and normal stress were focused, and the effects study of shear stress or three dimensional stress on permeability were less. So the latter should be carried out. (2)In view of the difficulty of simulating the expansion of fractures by traditional numerical methods, new numerical methods that can consider the generation and expansion of fissures, such as meshless method, numerical manifold method and coupling analysis of FEM/DEM,should be developed. (3)Considering the mechanism and application study of multifield coupling of fractured rock mass in special environment, such as high or low temperature, chemical corrosion, et al. And the characteristics of rock such as heterogeneity, rheological properties should also be taken into account. (4)Although there were disparity between the existing models and the actual situations, the theories should also be fully utilized to make the design and analysis of the project more reasonable.

In this paper, the problem of forcing a nonlinear system to track a desired reference signal is addressed by combining the theory of output regulation and the Takagi-Sugeno fuzzy modelling. The designing of the fuzzy regulator is based on LMI techniques.

This article is concerned with robust stability of uncertain discrete-time linear systems. The matrix defining the linear system (system matrix) is assumed to depend affinely on a set of time-invariant unknown parameters lying on a known polytope. Robust stability is investigated by checking whether a certain integer power κ of the uncertain system matrix has spectral norm less than one. This peculiar stability test is shown to be equivalent to the positivity analysis of a homogeneous symmetric matrix polynomial with precisely known coefficients and degree indexed by κ. A unique feature is that no extra variables need to be added to the problems being solved. Numerical experiments reveal that the value of κ needed to test robust stability is mostly independent of the system dimension but grows sharply as the eigenvalues of the uncertain system approach the unit circle. By identifying the proposed stability test with a particular choice of a parameter-dependent Lyapunov function, extra variables can be introduced, yielding linear matrix inequalities optimisation problems of improved convergence.

This paper addresses the robust stability and stabilization of continuous-time linear systems with Markov jump parameters taking values in a finite set. It is shown how each of the robust analysis and synthesis problems can be expressed in terms of two alternative linear matrix inequalities, in which the scaling parameters appear as decision variables. As a by-product, new contributions to the theory of stability radii of Markov jump linear systems are provided. Some numerical examples illustrate the main results presented here.

This paper deals with the problem of robust tracking and disturbance rejection for a linear time-invariant system where the uncertainty of the system is represented in a structured form and the output to be controlled may be different from the measurement output. First, the problem is considered in a rather classical setting in that the required property of tracking and disturbance rejection can be attained as long as the resulting closed-loop system remains stable. Conditions for solvability of the problem are given and two algorithms are presented for designing controllers having the robust tracking and disturbance rejection property. Second, the problem of robust output regulation with robust stability is formulated as one of finding a controller such that the resulting closed-loop system satisfies an additional requirement of robust stability and thus the output regulation property can be maintained for all perturbations of uncertain parameters within a prescribed set. A procedure based on a high gain observer approach is proposed to solve this problem.

The flow field in a wall attachment amplifier was visualized and analyzed numerically, and the flow pattern was made clear in the former studies (1) (2) (3). Also, the field-diving method using the k-εturbulent flow model was developed, and its effectiveness has been confirmed by the experiment of flow visualization and velocity measurement. In this study, the variations of the input and output static characteristics of a wall attachment device were made clear by numerical analysis and experiments changing the splitter distance, supply and control flow rate. In this case, a FLIP-FLOP-type logical device was used as the wall attachment device. The numerical method used was the flow-field diving method using the k-εturbulent model, as in the former reports. The input and output static characteristics were determined from the velocity and pressure distributions obtained by using this numerical analysis method. The experiments were performed by changing the Reynolds number, control flow rate and splitter distance. The results were compared with analytical values with which they were in good agreement. From these results, the effects that the variation of splitter distance, control flow rate and supply flow rate exerted on the characteristics of the device were made clear, and the effectiveness of the flow-field dividing method for the calculation of the characteristics was confirmed.

Robust state feedback controllers for linear time-invariant systems with uncertain parameters are considered. Both matched and unmatched uncertainty structures are studied. A basic tool of analysis is a special auxiliary LQR problem without uncertainties. The solution to this problem guarantees unconditionally robust stabilization in the matched case. In the unmatched case, if some testable sufficient conditions are satisfied, the solution of the LQR problem is robustly stabilizing as well. Moreover, robust pole placement into an arbitrary left halfplane is constructively proved to be achievable in the matched case. In the unmatched case, our sufficient conditions for robust stabilization can be modified for the robust pole placement problem but they become void if the required set, into which the eigenvalues ought to be placed, is too far away from the imaginary axis.

This paper addresses the problems of the robust stability and stabilization for fractional order systems based on the uncertain Takagi-Sugeno fuzzy model. A sufficient and necessary condition of asymptotical stability for fractional order uncertain T-S fuzzy model is given, and a parallel distributed compensate fuzzy controller is designed to asymptotically stabilize the model. The results are obtained in terms of linear matrix inequalities. Finally, a numerical example and fractional order Van der Pol system are given to show the effectiveness of our results.

Delay-dependent criteria for robust stability and stabilization of fractional-order time-varying delay systems