Showing papers in "International Journal of Systems Science in 1993"

Grey linear programming, its solving approach, and its application

Abstract: In systems analysis, uncertainties may exist in model parameters and input data. Those uncertainties can propagate through the analysis and generate uncertainty in the results. Grey systems theory offers a method for incorporating uncertainties into systems analysis. In this paper, a new method of solution for a grey linear programming (GLP) model is advanced. The GLP model allows grey messages concerning the model parameters and input data to be communicated into optimization processes and solutions. A new application field—grey systems analysis of water resource planning and decision making under uncertainty—is introduced, and a case study is reported of water quantity allocation and quality planning in a drainage basin area connected to a water delivery canal in Xiamen, China. The results indicate that the solutions derived are feasible for the study area. Sensitivity tests of the effects of grey inputs on grey outputs are reported. It is indicated that the grey degrees of the solutions increa...

A state-space description for GPC controllers

Abstract: Generalized predictive control (GPC)-type control algorithms traditionally derived in the polynomial domain are derived in this paper in the state-space domain, but following the polynomial approach due to Clarke et al. (1987). Relations between the polynomial and state-space parameters are presented. Some possible state-space representations which were used earlier in different publications are discussed. The problem of deriving the GPC algorithm in the state-space domain is solved for the unrestricted case as well as for the case of restricted control and output horizons. Some properties of the state estimate for this problem are presented; in particular, two methods of Kalman filtering—optimal and asymptotic—are proposed. The solution is valid for any possible (minimal or non-minimal) state-space representation. Another approach to this problem is by the ‘dynamic programming method’ and solving the Riccati equation (Bitmead et al. 1990). This approach is also presented in this paper but the me...

State estimation of stochastic singular linear systems

Abstract: This simple algorithm for the state estimation of stochastic singular linear systems is based on the least squares method.

Stochastic differential equations with fractional Brownian motion input

Abstract: Kolmogorov-Levy-Mandelbrot (t − s)2a -fractional Brownian motion (FBM) appears to be quite relevant for modelling long range memory stochastic systems, and the problem of defining stochastic differential equations subject to such a noise is considered. The Liouville fractional derivative and the self-similarity property of FBM are recalled and then, via detailed calculation, the main statistical characteristics of FBM are derived. First-order stochastic differential equations with FBM are considered via path integrals and a corresponding mean squares approach to non-linear filtering is described. Lastly, a new modelling via stochastic differential equations of fractional order is suggested.

Observer design for discrete and continuous non-linear stochastic systems

Abstract: An observer design methodology that is applicable to a general class of non-linear stochastic system and measurement models is given. It is proved that, under the conditions given, discrete- and continuous-time state estimation is possible with guaranteed exponential rate of convergence. The superior performance of the observer is illustrated with two examples.

Fuzzy supervision and application to lean production

Abstract: A novel philosophy of process supervision based on functional redundancy, i.e., analytical or knowledge based redundancy which may specifically be used for lean production, is suggested. The key idea is to replace the conventional residual evaluator of the fault diagnosis system based on crisp logic, by both a decision maker with fuzzy logic for residual pre-evaluation and the human operator to make the final decisions using his natural intelligence, experience and common sense. The purpose of the employment of fuzzy logic for residual pre-evaluation is to release only weighted alarms instead of yes-no decisions, so that (by definition) no false alarms can be produced; besides this, the man-machine interaction becomes much easier. In contrast to the conventional expert system approach, the proposed concept leaves the final yes-no decisions to the natural intelligence, capability and responsibility of the human operator which are still superior to the artificial intelligence and decision making ca...

Robust stabilization of uncertain linear dynamical systems

Abstract: Based on the stabilizability of a nominal system (i.e. a system in the absence of uncertainty), by making use of the Lyapunov stability criterion and combining with the algebraic Riccati equation, a new approach for designing a robust linear state feedback controller for uncertain linear dynamical systems is presented. Using this approach, the BIBO stability of uncertain linear dynamical systems is also discussed, Some analytical methods and the Bellman-Gronwall inequality are employed to investigate the robust stabilization conditions on the feedback controller. The main features of this approach are that no matching condition about uncertainty is needed and the uncertain systems can be asymptotically stabilized. An example is given to demonstrate the validity of our results.

Receding-horizon predictive control with exponential weighting

Abstract: Exponential weighting of future tracking errors and control increments is employed for receding-horizon predictive control and seen to improve the dynamic behaviour of the closed-loop system. A sufficient condition for the asymptotic stability of generalized predictive control (GPC) with these weightings is derived. The condition can be easily satisfied whereas the corresponding condition for GPC with constant weighting is highly restrictive. In the case of constrained receding-horizon predictive control (CRHPC), a prescribed degree of stability is obtained just as with infinite-horizon optimal control using the same type of weighting. This makes it possible to use a simplified CRHPC law with no weighting on the tracking error but which guarantees convergence to the set-point faster than a bounding exponential

Decentralized iterative learning control methods for large scale linear dynamic systems

Abstract: Decentralized iterative learning control methods are presented for a class of large scale interconnected linear dynamic systems, in which an iterative learning controller in each subsystem operates on its local subsystem exclusively with no exchange of information between subsystems. Sufficient conditions for convergence of the algorithms are given and numerical examples are illustrated to show the validity of the algorithms. In particular, the algorithms are useful for systems having large uncertainty of interconnected terms.

Eigenvalue clustering in subregions of the complex plane for interval dynamic systems

Abstract: Various sufficient conditions of eigenvalue clustering for interval matrices are presented. The proposed sufficient conditions guarantee that all eigenvalues of the interval matrices lie inside various specified regions in the complex plane. The derived theorems can be applied to both continuous- and discrete-time dynamic interval systems. The dynamical characteristics of a linear system are influenced by the eigenvalue locations of the system. Therefore, by the analysis of eigenvalue clustering, we can understand more properties about interval dynamic systems such as stability margin, performance robustness and so on. Three examples are given to illustrate the applicability of the results.

Fault diagnosis and reconfiguration of systems using fuzzy logic: application to a thermal plant†

Abstract: A fault evaluation and reconfiguration method using fuzzy logic is proposed. The motivation for this study is the desire to ensure good degraded performances for systems that cannot afford an immediate stop when failures occur as, for example, planes, the cooling circuit of nuclear plants and so on. In the case of actuator failures occurring in a plant, it is often possible to use remaining functional control elements to substitute the impaired actuators automatically (Morse and Ossman 1990). But, the degraded modes that are acceptable with regard to the required performances are supposed to be defined precisely. The proposed approach is based on the failure detection and isolation scheme combined with a control reconfiguration algorithm (FDIR). Once the failure is isolated, the control energy is redistributed among the remaining effective actuators. For illustration, the FDIR method is applied to a thermal plant. Some justifications of the importance of fuzzy logic in FDIR systems are given and ...

Discrete variable structure control systems

Abstract: We discretize n-th order linear systems with variable structure control under a particular discretisation scheme and analyse these systems in detail The occurrence and structure of pseudo-sliding modes give insight into the corresponding sliding modes for continuous systems, and enable the relation between the system parameters and the stepsize to be explored By means of constructing asymptote hyperplanes on which the system trajectories diverge, an algorithm is developed that calculates an upper bound of stepsize, within which the system will remain in a neighbourhood of switching hyperplanes A sufficient condition for the existence of pseudo-sliding mode is derived This discretisation helps one to understand the inherent properties of computer controlled variable structure control systems The analysis is illustrated with simulation studies of second and third-order systems

Microbial specific growth rate control via MRAC method

Abstract: A problematic feature in most fermentation processes is that on-line measurement of the most important biological process variables, the concentration of the bio-mass and its specific growth rate, cannot be directly measured. An approach for estimating these biological variables and for controlling the specific growth rate in a continuous flow bioprocess of a stirred tank reactor is presented and analysed. The goal in the control is to get the specific growth rate to track the rate of a given reference model, A dynamic model for the specific growth rate is obtained from the general growth and substrate consumption model. The structure of the rate model is then applied in the reference model structure. The methodology studied is based on two issues, joint state and parameter estimation and direct adaptive control. From the theoretical viewpoint, this forms a combination of indirect and direct adaptive control. The structure of the control law is justified by the structure of the law obtained for k...

Constructing rule-bases for multivariable fuzzy control by self-learning Part 1. System structure and learning algorithms

Abstract: A novel method is presented capable of constructing rule-bases via self-learning for the use of fuzzy controllers. The controlled process is assumed to be a multivariable system with strong interaction within variables and with pure time delays in control. The objective of the proposed system is to build, in the case of two-input two-output systems, two separated and decoupled rule-bases for two control loops with some design requirements. The paper is divided into two parts. In the first part, a system structure comprising four functional modules is proposed. Then, the paper focuses on the issues concerning the learning algorithm. By introducing learning errors, three learning update laws are suggested. Furthermore, the convergence property of the learning algorithms is analysed in the sense of some defined norms. In addition, some comments and remarks about the proposed algorithms are given. The second part of the paper deals mainly with the issues of the methodology for rule-base formation and...

Model reduction of unstable systems

Abstract: A simple and powerful method for unstable model reduction has been developed in which the approach is based on the fact that translation transformations in the s-plane preserve the input-output properties of a system. Using translation transformations in the frequency domain it is possible to change the stability of the system without losing input-output information. Although balancing requires that the model be asymptotically stable, it reduces the model depending only on the information of input to state and state to output. The stability requirement comes from the computation of the controllability and observability gramians which are used for characterizing the contribution of the states to the input-output map. It has been shown in this paper that it is possible to use balancing to reduce the models of unstable systems by transforming them into the stable models, reducing the model order, and then transforming the models back. The method has been demonstrated by case studies.

Pulse width modulated control of robotic manipulators

Abstract: We propose a practical discontinuous feedback control scheme for the regulation of joint positions of robotic manipulators. A robust on-off switching control strategy based on a pulse-width-modulation (PWM) feedback scheme is proposed for the joint torques. The discontinuous PWM controller design is carried out on the basis of a suitable controller designed for an average model which is of continuous nature. Simulations of the closed-loop performance of the proposed control scheme are presented for a two-link robotic manipulator.

Fuzzy control of an inverted pendulum with fuzzy compensation of friction forces

Abstract: The purpose of this paper is to compare the stabilization, with friction compensation, of an unstable mechanical system, an inverted pendulum, by two methods: the state feedback method, which belongs to the mathematical model-based approach, and fuzzy control. In both cases, the friction forces are compensated either by a simple method, the switching of a constant threshold, or a more sophisticated one: a disturbance observer in the model-based approach and a fuzzy compensator in the fuzzy control situation. The results obtained with the latter are comparable with or even better than those obtained with the former.

Echelon stock formulation for multi-stage lot-sizing with component lead times

Abstract: Material requirements planning of batch production in multi-stage manufacturing systems is discussed where component parts may have significant non-zero production or purchasing lead time. The presence of such lead time poses a synchronization problem for the rolling horizon planning of component part production in the system. The synchronization problem is analysed, discussed and modelled first for the case of assembly product structures where a component has a unique successor component. The analysis is then extended to the more complex case of general product structures where a component may have multiple successor components. The associated general structure multi-stage lot-sizing problem is then formulated as a mixed integer linear program first in terms of conventional stock, and then reformulated in terms of echelon stock. The echelon stock quantity of a component is its lead-time adjusted total system stock, counted both as a stand-alone component and as part of successor components. The ...

Fuzzy control in process automation

Abstract: Fuzzy logic provides an extremely practical method of incorporating empirical process knowledge and linguistically formulated control strategies appropriately into process automation applications. This potential makes fuzzy logic controllers attractive for a wide range of industrial processes. In view of its significant appeal, the obvious way of implementing practical fuzzy control solutions quickly and successfully is by integrating the fuzzy functions into existing systems and providing software tools for support. A universal fuzzy function block concept is introduced which gives process control systems comfortable access to the world of fuzzy logic. The three new function blocks FUZ, RULE and DFUZ enable fuzzy logic to be integrated into existing system environments flexibly and with a high degree of acceptance. Combined with the fuzzy tool SIFLOC TM, these software blocks form a powerful enhancement to conventional control systems for a large number of tasks that have hitherto evaded satisfa...

Robust implementation of sliding mode control schemes

Abstract: The choice of smoothing structure for practical implementation of a sliding mode control scheme is considered. Previous results considering the effect upon nominal system performance are reviewed. The effect of the smoothed control on an uncertain system is considered. A simple method of analysing and prescribing the smoothing parameter to ensure robust stability of the sliding mode is presented and illustrated using a numerical example.

Fuzzy and Quantitative Model-based Control-systems for Robotic Manipulators

Abstract: Generally fuzzy control systems use simple controllers with a few inputs and one output. Here more complex control systems, based explicitly on a model of the controlled process and primarily developed in the frame of quantitative control, are adapted to fuzzy control. Three model-based control schemes are proposed for position control of a robotic manipulator. The feasibility of such control systems and the ability of their quantitative and fuzzy implementations to cope with disturbances, parameter variations and unmodelled dynamics, are evaluated and compared by simulation analysis. The extension of the model-based control paradigm to fuzzy control pinpoints a concept unknown in the usual fuzzy controllers, i.e. intrinsically fuzzy variables that may be a source of problems in fuzzy feedback loops.

Portfolio efficiency tests based on stochastic dominance and co-integration

Abstract: The theory of dynamic portfolio behaviour is evaluated by estimating and comparing the relative efficiency of alternative mutual fund portfolios by means of stochastic dominance and co-integration tests. Varying market conditions such as bullish and bearish markets and volatility of temporal return variances are found to play a major role in the return generating process. Thus the risk-return relationship is found to be highly asymmetrical and some groups of mutual funds tend to outperform the others.

Positively invariant sets for singular discrete-time systems

Abstract: The aim of this paper is to present some results allowing positively invariant and asymptotically stable polyhedral sets to be determined for the linear singular discrete-time system ExK+1 = AxK; the regular and singular cases of pencil (E, A) are considered. Necessary and sufficient algebraic conditions guaranteeing that some sets are positively invariant and asymptotically stable are given. Also discussed are some issues relating to the positive invariance of some domains and consistent initial conditions. Finally, as an application, the proposed results are used to determine a stability domain for a state feedback regulator with constraints on controls

Improving delay estimates derived from least-square algorithms and Padé approximations

Abstract: It is shown that an on-line estimate of the unknown delay using the Pade approximation can be improved substantially. Based on an initial on-line estimate, a sequence of the estimates of delay is then constructed, which converges to the true delay.

State estimation schemes for fault detection and diagnosis in dynamic systems

Abstract: The state estimation problem for dynamic systems is one of the fundamental problems in the fields of modelling, optimal control, and fault detection and diagnosis. Linear and non-linear state estimation has been a very active research field during the last 30 years. The purpose of this paper is to give a brief review of the basic fault detection and diagnosis methods based upon the analytical and knowledge-based redundancy. The main emphasis is placed upon estimation methods that are widely applied for fault detection. The advantages and disadvantages of these methods also are discussed both in general and in diagnostic applications.

Decentralized variable-structure adaptive controller synthesis of large-scale systems subjected to bounded disturbances

Abstract: The regulation control problem is considered for a large-scale system in the presence of interconnected terms, system parameter variations and external disturbances. Based on the technique of parameter estimations and the theory of variable-structure systems, this paper presents a new and feasible design algorithm for the synthesis of a decentralized variable-structure adaptive controller which can easily tackle the control problem of large-scale systems subjected to interconnected terms, system parameter variations and bounded disturbances. In contrast to previous results, the restrictive condition that the exact value of the parameter describing the input gain must be known can be relaxed. A series of computer simulations are also included to illustrate the proposed design algorithm.

Fault detection in linear discrete dynamic systems by a reduced order generalized-likelihood-ratio method

Abstract: The detectability by conventional step-hypothesized generalized-likelihood-ratio (SHGLR) method for detection of a parameter change (fault detection) in a linear discrete dynamic system is analysed and it is shown that a weakly-diagnosable-space (WDS) exists for dynamics and sensor faults. Based on the fault detectability, a reduced order SHGLR method is then developed which highly improves the detection rate and speed. In the same framework of the GLR method, another reduced order detection scheme is given, which makes the most use of the information about the input and the state of the system to raise the detectability for faults for the case where the step hypothesis cannot be applied effectively.

Fuzzy logic control

Abstract: In recent years, fuzzy control has been proposed as an alternative approach to traditional process control techniques. The construction and use of fuzzy logic controllers for dynamic processes is explored. Many references to fundamental works on this subject are given but the paper is restricted to a presentation of practical results. The design, implementation and calibration of fuzzy logic controllers are reviewed with specific examples.

On identification of block orientated systems by non-parametric techniques

Abstract: The identification of block orientated systems is discussed. Particular attention is devoted to memoryless and dynamic systems with cascade structure. An optimal model of a memoryless cascade system is derived and estimated by kernel regression. Nonlinear dynamic systems of the Hammerstein and Wiener type are identified by means of non-parametric techniques. Convergence of the identification procedures is investigated.

State estimation of stochastic singular linear systems: convergence and stability

Abstract: In this paper we present necessary and sufficient conditions of convergence of the generalized Riccati equation and stability for the state estimator developed by Darouach et al. (1993).