Model-based dynamic sliding mode control and adaptive Kalman filter design for boiler-turbine energy conversion system
Introduction
A boiler-turbine system (BTS) is a critical component of an electric power plant. There are two levels of energy conversion in a BTS, initially chemical energy is converted into mechanical energy, which is further converted into electrical energy, cf. [1], [2]. The primary function of a BTS is to meet the electricity demand while keeping the drum pressure, electric power and water level within the specified limits regardless of the load variations, cf. [3]. At the beginning of the BTS operation, water enters into the economizer section before getting into the steam drum. The economizer transfers the heat of boiler stack gases to the boiler feed water and raises its temperature. The main function of the steam drum is to separate water and steam coming from the economizer and water walls, respectively. The steam generated in the steam drum is provided to the inlets of high and low-pressure turbines to generate electricity. The steam is super-heated to a high temperature before entering the turbines, cf. [1], [4].
The Researchers have been extensively working on the modeling and control of BTS for the last three decades. The control system design of a BTS has a significant importance to achieve the desired performance and for the safe operation of a power plant. However, the development of a control system for a BTS is a challenging task due to the process nonlinearities, external disturbances, strong coupling between state variables and inputs, and physical limitations imposed on the control inputs, cf. [1], [5], [6].
Over the years, numerous linear and nonlinear control techniques have been designed for the BTS to achieve the desired levels of the output power, drum pressure and water by manipulating the flow rate of fuel, steam and water, respectively. In [2], [7], [8], [9], [10], various linear controllers are designed by linearizing the nonlinear BTS model reported in [11]. Tan et al. cf. [2], [9] have designed loop shaping design based and PID controllers for the BTS. The controllers exhibit good tracking performance in the presence of modeling inaccuracies. However, the conventional PID controller is not optimal for BTS due to hard nonlinearities, cf. [1]. In [7], the nonlinear BTS model proposed in [11] is transformed into the linear parameter varying (LPV) form to design the gain scheduled controller. The simulation results show that the desired performance is achieved. In [8], Dimeno and Lee have designed PI and state feedback controllers by using the genetic algorithm (GA). The external disturbances are not considered in the control design. The results of both the controllers are compared, which show the superiority of state feedback control law. In [10], authors have linearized the BTS model proposed in [11] to design the controller. The simulation results show the adequate performance of the designed controller both in the time and frequency domains.
In [6], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], the model proposed in [11] is employed to design various model-based nonlinear control techniques. In [6], the BTS model is simplified to design the disturbance rejection control (DRC) and the unknown states and external disturbances are also estimated by designing a higher order sliding mode observer (SMO). However, large control efforts and a slight deterioration in output tracking are observed due to model simplification. In [17], authors have designed the robust adaptive sliding mode control (RASMC) using the input–output feedback linearization. Moreover, the type-I servo controller is designed by linearizing the BTS model around a single operating point. Both the control schemes are implemented on the nonlinear model and the simulation results show the superiority of RASMC. Ghabraei et al. cf. [15] have designed the robust adaptive variable structure control (RAVSC) and controller for the BTS. The RAVSC is designed by employing almost similar methodology presented in [17]. Both the controllers are implemented on the nonlinear model and the results depict that RAVSC has slightly better performance than controller. In [20], [22], sliding mode control (SMC) is designed for the linear model proposed in [24], [25], respectively. The results are also compared with the controller and it is observed that the SMC outperforms . Ataei et al. cf. [18] have designed the SMC for the reduced order nonlinear model presented in [26]. The results of SMC are compared with PI controller which show the superiority of SMC.
Similarly, authors have used the feedback linearization and gain scheduling techniques to design the control laws for BTS, cf. [23]. The simulation results illustrate that the control design based on feedback linearization gives better performance as compared to gain-scheduling controller. In [21], the model proposed in [26] is used to design the decentralized control by employing the backstepping technique. The model is partitioned into two sub-systems and the control laws are designed separately for each sub-system. The desired levels of the throttle pressure and output power are maintained by manipulating the throttle valve position and firing rate. In [12], [14], [16], [19], fuzzy sliding mode control (FSMC), nonlinear predictive control (NPC), robust model predictive control (RMPC) and general active disturbance rejection control (GADRC) are designed, respectively by linearizing the BTS model presented in [11]. In [19], authors have designed the FSMC to eliminate the chattering phenomenon in the conventional SMC. Moreover, the results of PI control and SMC are compared with FSMC which show the predominancy of FSMC. In [16], the extended kalman filter (EKF) is also used to estimate the unknown states. In [12], authors have constructed a global LPV model by combining the linearized models obtained at various operating points. Zhu et al. [14] have designed the multivariable extended state observer (MESO) for the estimation of external disturbances. The results are compared with and model predictive control with integral action (MPC-integral), which shows better performance of GADRC. Lei et al. cf. [13] have linearized the BTS model presented in [27] to design the internal model robust adaptive control (IMRAC). Moreover, authors have designed the state predictor for the unmeasurable state used in the control design. The IMRAC is compared with fuzzy extended state observer based predictive control which shows the supremacy of the designed control law. To identify the gap analysis, the related work of nonlinear control techniques is summarized in Table 1.
In our previous work, cf. [28] the super-twisting based SMC is designed for the drum boiler system (DBS). The decentralized control law is designed based on the assumption that and have a significant impact on and , respectively. However, the decentralized controller is not feasible for the BTS due to its highly coupled nature. It is evident in the above-mentioned literature that mostly nonlinear control techniques are designed by assuming that the system fluid density is directly measurable. However, it is highly unrealistic to design the model-based control by using the unmeasurable states, cf. [6], [29], [30], [31], [32], [33]. Hence, the estimator design is essential to develop a control system for the BTS. It is also pertinent to mention that the mathematical expression for the water level, one of the outputs of the BTS, is highly nonlinear and complex. Moreover, the water level has an explicit dependence on the control inputs which further complicates the design of SMC. Therefore, the direct control of water level is quite cumbersome. Most of the literature focuses on the control of drum pressure, electrical power and system fluid density pertaining to a BTS. Furthermore, the BTS model is linearized through Taylor series expansion (TSE) for both the observer and controller designs. The linearization of highly nonlinear systems by TSE can cause instability [34], [35], [36]. Moreover, the control design based on the linear model always ensure adequate performance and stability for a limited operating range. Thus, the design of a centralized control law based on the nonlinear model along with a state estimator is essential for the BTS to address the aforesaid shortcomings.
As described in the gap analysis, BTS is a highly coupled nonlinear system, therefore, it is not possible to figure out which output is affected by which input. Hence, practically for such systems centralized controller is a better choice instead of a decentralized controller to achieve the desired performance. Thus, in this work, a nonlinear model-based centralized dynamic sliding mode control (DSMC) is designed to maintain the drum pressure, electric power and water level at the desired levels. The primary reason to design a DSMC is to mitigate the chattering phenomenon which inherently exists in a conventional SMC. In the literature, the design of numerous control laws are based on the assumption that the system’s fluid density is available. However, in practice, this state is not directly measurable, and it is impractical to use it directly in the model-based control. For this purpose, an adaptive Kalman filter (AKF) is designed which adapts initial biased covariances to provide an accurate estimate of the system fluid density of the BTS. The DSMC is designed in such a way that the sliding mode is established in a manifold where the system fluid density attains the desired level, which is chosen in such a way that the water level follows its reference trajectory. The time derivatives of the desired system fluid density required to synthesize the controller are computed using the uniform robust exact differentiator (URED), cf. [37]. A detailed analysis is also presented to prove the stability of the closed loop system. In order to validate the efficacy of the proposed control scheme, the designed control law is implemented on the nonlinear model with practical considerations like external disturbances, and measurement and process noises.
The rest of the paper is organized as follows. The control-oriented model of the BTS is explained in Section 2, the problem statement is described in Section 3. The DSMC design and stability analysis is presented in Section 4. The design of AKF is discussed in Section 5. The simulation results are presented in Section 6 and finally, this article is concluded in Section 7.
Section snippets
Model description
A suitable model selection has a significant role in the model-based control design. In the literature, various mathematical models of BTS have been proposed by the researchers, cf. [11], [27], [38], [39], [40]. The mathematical model of BTS developed by Astrom and Bell, cf. [11] is employed to design the model-based control system. The mathematical model of the BTS in [11] is a first principle based model, and hence it provides essential physical insight about the process. This model is simple
Problem statement
To design a model-based nonlinear controller for the BTS which drags the drum pressure, electric power and water level to the desired set points. The controller should be capable to ensure fast convergence, robustness and stability in the presence of external disturbances, and process and measurement noises. Also, the controller should meet the physical constraints imposed on the actuators.
Control design
Owing to highly coupled states and inputs, a model-based, centralized DSMC is designed for the BTS by using the nonlinear model presented in (1), (2). The step by step design procedure of DSMC is summarize as follows:
- 1.
The sliding variable vector is selected such that the sliding mode shows the desired characteristics.
- 2.
For obtaining continuous control input, a DSMC is designed by intentionally adding an integrator to enforce sliding mode in the time-derivative of the control input.
- 3.
It can
Adaptive Kalman filter design
In order to make the model-based control design possible, the unknown state of BTS, i.e., needs to be estimated. Therefore, the AKF is designed to reconstruct . The effect of process and measurement noises is also included in the system since the performance of the KF depends on sensor and process noise covariances [42]. Generally, in practical applications these covariances are partially known or completely unknown [42]. Hence, in order to improve the performance of KF, the initial biased
Results and discussions
In this section, the designed DSMC is implemented on the actual nonlinear model in the presence of external disturbances and noises. The implementation scheme is shown in Fig. 3. Moreover, the performance of DSMC is compared with PI controller. The practical scenario is presented by incorporating the following considerations.
- •
The noises given in (1), (2) are considered during the simulation study to investigate their impact on the performance of the DSMC and AKF. The process noises have zero
Conclusion
In this work, the significance of a multi-variable, model-based control system for the BTS is highlighted. A model-based DSMC control law has been designed to maintain the drum pressure, electric power and water level at the desired levels in the presence of modeling inaccuracies, external disturbances and noises. Owing to the complex mathematical expression of water level, the control problem is formulated by computing an auxiliary function and an implicit sliding manifold is designed such
CRediT authorship contribution statement
Imtiaz Ur Rehman: controller design; stability analysis; adaptive Kalman filter design; implementation of the proposed methodology; paper write-up; proofreading. Syed Bilal Javed: controller design and implementation; paper write-up; proofreading. Afraz Mehmood Chaudhry: adaptive Kalman filter design and implementation; paper write-up; proofreading. Muhammad Rizwan Azam: stability analysis; paper write-up; proofreading. Ali Arshad Uppal: idea; supervision of all the tasks; paper write-up;
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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