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Ficure 8: The unit responses as the load is ramped down from full- load to half-load conditions ((a) power, (b) pressure, and (c) fuel).

Figure 12 Ficure 8: The unit responses as the load is ramped down from full- load to half-load conditions ((a) power, (b) pressure, and (c) fuel).

Related Figures (15)

FiGurE 2: Boiler control system (fuel and feedwater). Figure 1: Coordinated control system configuration.
FiGurE 2: Boiler control system (fuel and feedwater). Figure 1: Coordinated control system configuration.
Figure 3: The structure of neuro-fuzzy-based Hammerstein model. fuel, steam pressure, and electrical power with respect to the desired unit load defined by operator or dispatcher. In this paper, a fuzzy Hammerstein structure is employed to develop the unit load models, which are used as the core of feedforward controllers. The structure of fuzzy Hammerstein (FHS) model is presented in Figure 3. A Hammerstein model consists of a linear function, describing the system dynamics, and a nonlinear static function, N(-), describing the steady- state relations, as given by
Figure 3: The structure of neuro-fuzzy-based Hammerstein model. fuel, steam pressure, and electrical power with respect to the desired unit load defined by operator or dispatcher. In this paper, a fuzzy Hammerstein structure is employed to develop the unit load models, which are used as the core of feedforward controllers. The structure of fuzzy Hammerstein (FHS) model is presented in Figure 3. A Hammerstein model consists of a linear function, describing the system dynamics, and a nonlinear static function, N(-), describing the steady- state relations, as given by
in which N is the number of inputs to the fuzzy system and N, is the number of fuzzy rules. The membership function L; ; is considered to be Gaussian specified by the center o and the spread C, fulfillment degrees of fuzzy rules are calculated through a five-layer feedforward network structure [23]. The weighted sum average according to fuzzy rules R; is obtained as follows:
in which N is the number of inputs to the fuzzy system and N, is the number of fuzzy rules. The membership function L; ; is considered to be Gaussian specified by the center o and the spread C, fulfillment degrees of fuzzy rules are calculated through a five-layer feedforward network structure [23]. The weighted sum average according to fuzzy rules R; is obtained as follows:
Ficure 4: Linear and nonlinear parts plus time delay in a SISO fuzzy Hammerstein model.
Ficure 4: Linear and nonlinear parts plus time delay in a SISO fuzzy Hammerstein model.
TABLE 1: The optimization parameters for genetic algorithm. The whole operating range can be divided to smaller regimes using clustering method. It is noted that the number of fuzzy rules is equal to the number of cluster centers. Thus, it is necessary to define the number of cluster centers to achieve an acceptable degree of accuracy. It is recommended that the number of cluster centers is chosen to be four to divide the operating range into four subregions [29].
TABLE 1: The optimization parameters for genetic algorithm. The whole operating range can be divided to smaller regimes using clustering method. It is noted that the number of fuzzy rules is equal to the number of cluster centers. Thus, it is necessary to define the number of cluster centers to achieve an acceptable degree of accuracy. It is recommended that the number of cluster centers is chosen to be four to divide the operating range into four subregions [29].
Therefore, the constrained least squares (CLSs) estima- tion problem can be captured by as follows [30]: with respect to (11), by some simplifications, the linear equality constraints can be considered as
Therefore, the constrained least squares (CLSs) estima- tion problem can be captured by as follows [30]: with respect to (11), by some simplifications, the linear equality constraints can be considered as
where N,, is equal to c (the number of cluster centers). Also, the parameter vector @ is as, Therefore, we define the regressor vector ® as follows:
where N,, is equal to c (the number of cluster centers). Also, the parameter vector @ is as, Therefore, we define the regressor vector ® as follows:
TABLE 2: Fuzzy rules for fuzzy controller.
TABLE 2: Fuzzy rules for fuzzy controller.
TABLE 3: The error functions for the unit’s models.
TABLE 3: The error functions for the unit’s models.
where ¥ is the average of y over the m samples and y; and yp are the ith target and the model output, respectively. The error functions for the developed models are presented in Table 3. time signals with five seconds sampling time, consisting of transient and steady-state conditions (45~65, 65~75, 75~90, and 90~100 percent). By applying the proposed modeling approach to the steady-state and transient data, the linear and non-linear part of fuzzy Hammerstein models can be developed. The accuracy of the developed models is assessed by comparing the responses of the models and the real plant performances. For this aim, the error functions are calculated by defining the error as the difference between the predicted values by the models and the experimental data. Here, the upper bound of error (Max (|e|)), lower bound of error (Min (Jel)), mean absolute error (MAE), and the coefficient of determination (R’) are calculated by the following equations:
where ¥ is the average of y over the m samples and y; and yp are the ith target and the model output, respectively. The error functions for the developed models are presented in Table 3. time signals with five seconds sampling time, consisting of transient and steady-state conditions (45~65, 65~75, 75~90, and 90~100 percent). By applying the proposed modeling approach to the steady-state and transient data, the linear and non-linear part of fuzzy Hammerstein models can be developed. The accuracy of the developed models is assessed by comparing the responses of the models and the real plant performances. For this aim, the error functions are calculated by defining the error as the difference between the predicted values by the models and the experimental data. Here, the upper bound of error (Max (|e|)), lower bound of error (Min (Jel)), mean absolute error (MAE), and the coefficient of determination (R’) are calculated by the following equations:
FiGure 6: The responses of fuzzy Hammerstein models for the unit's subsystem.
FiGure 6: The responses of fuzzy Hammerstein models for the unit's subsystem.
Ficure 5: (a) PD-fuzzy logic controller and (b) incremental fuzzy logic controller.
Ficure 5: (a) PD-fuzzy logic controller and (b) incremental fuzzy logic controller.
Ficure 7: The unit responses at high-load conditions ((a) power, (b) pressure, and (c) fuel).
Ficure 7: The unit responses at high-load conditions ((a) power, (b) pressure, and (c) fuel).
Ficure 9: The unit responses as the load is ramped up from half-load to full-load conditions ((a) power, (b) pressure, and (c) fuel).
Ficure 9: The unit responses as the load is ramped up from half-load to full-load conditions ((a) power, (b) pressure, and (c) fuel).
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