Search

This paper presents a fault detection methodology based on the Fisher discriminant analysis (FDA) and individuals control charts (XmR control charts). As the first step, FDA is used to find the optimal discriminant direction between the normal operation data and the fault data. In the next step, XmR control charts on the discriminant direction are used to monitor the process. To reduce the amount of false alarms, we also used a variable selection technique based on the contribution plot of FDA. The performance of the proposed technique is demonstrated through application to the monitoring of the Tennessee Eastman challenge process.

A novel decentralized temperature controller is designed for a tubular packed bed reactor. The method estimates the concentration distribution of each component in the reactor as well as the temperature distribution. The estimated distributions of concentrations are integrated in a feedback control of temperature distribution in the reactor. The method was evaluated by experiments and showed good performance in the control of temperature distribution. Excellent agreement between estimated and measured outlet concentrations are also observed.

A rigorous numerical model is developed to simulate the dynamic performance of a stacked molten carbonate fuel cell with commercially realistic dimensions. The model takes account of gas stream utilization due to electrochemical reaction, conductive heat transfer between cell hardware and gas streams, energy transfer accompanying mass addition to the bulk streams, and in-plane heat conduction through the cell hardware. The over-potential is calculated using the resistance as a function of temperature and composition of chemical species from literature. It is shown that for a step increase in the current load the output voltage falls at once to a considerable degree and then gradually recovers to the steady state level. The sluggishness of the response is mainly due to the slow dynamics of cell temperature. Therefore, control of cell temperature is necessary to stabilize the response of output voltage under varying current-load situations.

In recent years robust control theory has met wide acceptance and made significant advances especially in terms of development of tools for analysis and design. However, the application of those tools, like the H∞ optimal theory and μ-synthesis in MATLAB, to real-time control of chemical processes has not been very successful. Among the factors hindering widespread application is lack of systematic way to model uncertainty that occurs at different locations in the feedback structure. In this work, time series data is used to model additive plant uncertainty through power spectral methods by performing least-squares regression in frequency domain. The concept is illustrated for real-time control of axial temperature distribution in a packed-bed column, which is modelled by partial differential equations and Fourier transforms to obtain an eigen-mode plant for controller design and robust analysis. Spectral uncertainty description is obtained from error analysis of smooth signals from the nominal and the perturbed plant and robustness is evaluated using the structured singular value (SSV). It is shown that through a proper choice of parameters, the spectral method gives better uncertainty description for robustness analysis than parametric methods.

The objectives of this study are two-fold; to apply robust control tools hitherto used mostly for lumped parameter systems (LPS) to distributed parameter systems (DPS); and to investigate robustness of decentralized distributed controllers when operated under a full MIMO plant in the presence of unmeasured disturbance. The energy balance model of the packed-bed reactor is discretized using orthogonal collocation with the heat of reaction regarded as unmeasured disturbance. The resulting MIMO state space model is used for designing a decentralized temperature controller. Employing the IMC tuning rules as baseline, a decentralized PI controller is designed using only the diagonal elements of MIMO model treating off-diagonal terms as uncertainty. The off-diagonal interactions are used to design bounds called “μ-interaction measures” which are imposed on nominal closed-loop transfer functions. Satisfaction of these bounds guarantees that the designed decentralized controller will yield robustness over the full MIMO plant.

This work details an IMC-based pole placement controller tuning procedure for a multi-loop SISO system in the presence of model uncertainty. For a given uncertainty level, selection of the IMC low-pass filter parameter is done using Kalman filter poles and open-loop poles as respective lower and upper limits. Tuning is facilitated using a convex tuning parameter, which depends on both the structured singular value as a quantitative performance measure and closed-loop behaviour like overshoots and manipulated variable move sizes as qualitative measures. The method is applied to a distributed parameter system using modal control, but can be generally applied for any multi-loop SISO system using a state estimator. Using simulation studies it is shown that the ambiguity encountered during selection of the IMC filter constant is significantly reduced.

Control of temperature profiles of a tubular packed-bed reactor with our proposed design method for a parabolic distributed parameter system is investigated. The oxidation reactor of carbon monoxide over a platinum-catalyst is used as a controlled process. The reactor dynamics are modeled by a simple parabolic partial differential equation in one-dimensional space, on the assumption that temperature distribution in the radial direction of the reactor is negligible. A state feedback controller was designed by use of a reduced order lumped parameter system, which was obtained by applying the finite integral transform technique to the phenomenological model of the process. It is demonstrated that hot-spot temperatures can be eliminated and the axial temperature profile of the reactor can be made to agree well with a specified target profile.

A parameter identification method is presented for the cases where unknown parameters appear in both the state equation and the boundary condition of DPS model. For example, this method will be applicable to heat conduction processes where the heat flux from the surroundings to the boundaries of the materials to be heated is unknown or uncertain in addition to the thermal properties of the materials. The basic feature of the method is that the parameters are estimated based on the lumped parameter system (LPS) model derived by using the finite integral transform (FIT) technique. The Marquardt method, which is one of the nonlinear least square methods, is employed in the estimation algorithm

Two mathematical models are proposed to represent gas temperature distributions in suspension flows heated at the tube wall. These models are quite different from each other in the turbulent mixing mode of solid particles. Two parameters in these models were determined from experimental measurement of temperature distribution by using a parameter estimation technique. These models express observed temperature distributions well, especially when the loading ratio is smaller than unity. Mean gas eddy diffusivity and Nusselt number were calculated from these two parameters, which could be correlated well with a single nondimensional parameter that represents the operating conditions. By using this correlation and the models, temperature distributions can be easily predicted in the usual practical operating conditions of industrial suspension flows.

An ellipsoid bouncing model, previously presented to express the irregular bounce of particles on a duct wall, was extended to simulation of gas-solid suspension flow in a circular pipe. Simulated results were compared with experiments in terms of concentration distribution, particle velocity, additional pressure drop and frequency of particle collisions with the pipe wall. If the mean observed deformation, ηob, was taken as the value of the parameter, the mechanism of particle motion was explained for the most part by the simulation.

It is difficult to control the start-up of a packed-bed catalytic reactor with exothermic reaction by conventional controller. In this paper, a controller based on the fuzzy set theory is applied to such a system. The controller treats heuristic rules by fuzzy interpretation, and it is also equipped with adaptive scaling factors. The performance of the controller is experimentally examined with a reactor for the catalytic oxidation of hydrogen.

The minimum air velocities required to keep particles from depositing on the bottom of a pipe are measured experimentally for 19 groups of spherical particles ranging from 20 to 1600 microns in three pipes of 20, 26 and 49 mm I.D. It is found that there is a substantial difference in the effect of particle size between fine- and coarse-particle suspensions. This difference is explained theoretically by means of numerical simulation on a digital computer based on the previously proposed ellipsoid bouncing model. A general correlation is presented to predict the minimum transport velocity over a wide range of particle size, in which an empirical equation for the distinction between the fine- and the coarse-particles system is included.

The choking velocity, at which the substantial transport of solids becomes impossible in a pneumatic conveying system, is predicted on the basis of the dynamic stability analysis of the whole conveying system including characteristics of blower and pipelines as well as gas-solid suspension. The system is expressed by a lumped parameter approximation. The results are in good agreement with experimental ones obtained by using a 20 mm-I.D., 5.6 m-long vertical glass tube with three sizes of glass beads, within an error of 10%.

The minimum transport velocity, that is, the mean air velocity required to prevent the settling of particles on the bottom of a horizontal pipe, was experimentally studied for granular particles. Two pipe sizes were used, 26 mm and 49 mm diameter, and 14 groups of solid particles ranging from 0.3 mm to 2 mm diameter were used. A general correlation for minimum transport velocity was obtained including density and size of solid particles and pipe diameter. The saltation point, at which the flow pattern changed from suspension flow to sliding flow, was also correlated on the basis of a simple theoretical consideration.

A new attempt, based on the fuzzy reasoning, is proposed for prediction of flow patterns occurring in a given situation. The prediction algorithm is implemented in a fuzzy expert system INSURE, which is provided for execution of fuzzy inference based on the fuzzy-rule base. The rule base is constructed from experimental data only in literature and/or laboratory. The prediction system is tested for horizontal flow of air-water system. It is shown that the satisfactory performance can be obtained.

On the basis of wall roughness, a simple model is presented to explain the irregular bouncing phenomena of particles in pneumatic conveying. By introducing a random factor to the model, a pneumatic transport process was simulated by Monte Carlo method. The model could fairly well account for the concentration and velocity distribution and the rate of revolution of particles. Even very small degree of roughness was found to have a great influence upon the behaviour of particles.

The mechanism of suspension of particles in horizontal pneumatic conveying was studied by experimental and numerical analyses. It was found from experiment that the particles flowing in the duct were rotating at high speeds such as 1, 000 r. p. s. or more. A model based on the ellipsoid approximation of the particle shape was constructed and was applied to account for the irregular bouncing phenomena of nonspherical particles. Moreover, the real pneumatic transport process was simulated satisfactorily by introducing a random factor into the ellipsoid model.