Plant dynamics

Mathematically speaking, a process simulation model consists of a set of variables (stream flows, stream conditions and compositions, conditions of process equipment, etc) that can be equalities and inequalities. Simulation of steady-state processes assume that the values of all the variables are independent of time a mathematical model results in a set of algebraic equations. If, on the other hand, many of the variables were to be time dependent (m the case of simulation of batch processes, shutdowns and startups of plants, dynamic response to disturbances in a plant, etc), then the mathematical model would consist of a set of differential equations or a mixed set of differential and algebraic equations. 

S. K. Shum and co-workers, "A Knowledge-Based System Framework for Diagnosis in Process Plants," in Proceedings of the Seventh Power Plant Dynamics, ControlandTestingSymposiums Knoxville, Term., 1989. 

If the plant dynamics are first-order, then Figure 4.22 can be described as shown in Figure 4.23. The plant transfer function is... 

Structured uncertainty relates to parametric variations in the plant dynamics, i.e. uncertain variations in coefficients in plant differential equations. 

With an appropriate specification of the system performance weighting and objective function, a generalized plant dynamics is established, as shown in Fig. 22.2. The feedback controller processes the measured signal y to determine the injection rate of the control fuel rhin based on a regulated relationship between variables w and z, where w is associated with disturbance and uncertainty, and 2 with the objectives of system performance and stability. 

Based on the above performance concerns, Eqs. (22.22) and (22.24), an L2-gain robust controller is designed such that the plant disturbance d and sensor noise 6 have minimum effect on the plant dynamics and control actions. In an energy sense, this can be specified by... 

A comprehensive framework of robust feedback control of combustion instabilities in propulsion systems has been established. The model appears to be the most complete of its kind to date, and accommodates various unique phenomena commonly observed in practical combustion devices. Several important aspects of distributed control process (including time delay, plant disturbance, sensor noise, model uncertainty, and performance specification) are treated systematically, with emphasis placed on the optimization of control robustness and system performance. In addition, a robust observer is established to estimate the instantaneous plant dynamics and consequently to determine control gains. Implementation of the controller in a generic dump combustor has been successfully demonstrated. 

Padulles J., Ault G.W., McDonald J.R. (2000) An integrated SOFC plant dynamic model for power systems simulation. Journal of Power Sources 86, 495-500. 

Takamatsu, K., et al. (2004), Development of Plant Dynamics Analytical Code Named Conan-GTHTR for the Gas Turbine High Temperature Gas-cooled Reactor, (I) , Journal of Atomic Energy Society of Japan, 3 (1), pp. 76-87. 

Greaves et al. (2003) proposed a framework to optimise the operation of MVC columns with substantial reduction of the computational power needed to carry out the optimisation calculations. The framework relies on the use of NN based process model. The optimisation of a pilot-plant middle-vessel batch column (MVC) was considered to test the viability of the proposed framework. The maximum product problem was considered and solved by optimising the column operating parameters, such as the reflux and reboil ratios and the batch time. The NN based model is found to be capable of reproducing the actual plant dynamics with good accuracy, and that the proposed framework allows a large number of optimisation studies to be carried out with little computational effort. 

The structure in Fig. 1 is essentially a cascade design. This structure is appropriate because of the differences in the plant dynamics and disturbance frequencies associated with the decisions at each level. Control responds to rapid disturbances and requires execution periods on the order of 1 sec. Real time optimization typically responds to disturbances occurring every few hours or slower, and it requires tens of minutes to compute. The higher levels respond to disturbances occurring every few days. While the cascade... 

The results are still relevant, given that RTO computations can take a substantial amount of time relative to the dominant plant dynamics. 

Stokes, C. J. (1999). Woody plant dynamics in a. south Texas savanna pattern and process. Ph.D. Dissertation, Texas A8cM University, College Station. 

The simple human task that we want to model is of an operator responding to an annunciator. The procedure requires that the operator compare readings on two meters. Based on the relative values of these readings, the operator must either open or close a valve until the values on the two meters are nearly the same. The task network in Figure 9 represents the operator activities for this model. Also, to allow the study of the effects of different plant dynamics (e.g., control lags), a simple one-node model of the line in which the valve is being opened is included in Figure 10. 

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