Identification and predictive control for a circulation fluidized bed boiler

Abstract

This paper introduces the design and presents the research findings of the identification and control application for an industrial Circulation Fluidized Bed (CFB) boiler. Linear Parameter Varying (LPV) model is used in the model identification where steam flow is selected as the operation-point (scheduling) variable. Three kinds of weighting functions, namely linear, cubic splines and Gaussian functions are compared. LPV model based Model Predictive Control (MPC) is also simulated. Test results show that LPV model is more accurate than linear model, and LPV MPC yields a better control effect than linear MPC.

Introduction

Most industrial processes are nonlinear. There are many model-based control methods being proposed to improve the efficiency of these nonlinear processes. MPC is one of such methods, which incorporates a class of computer control algorithms that utilize an explicit process model to predict the future response of a plant. At each control interval, the MPC algorithm attempts to optimize future plant behavior by computing a sequence of future manipulated variable adjustments [1]. The performance of an MPC system is inherently tied to the accuracy of prediction, namely the accuracy of the model. Although the use of nonlinear models in MPC of nonlinear processes may yield better control effect than the use of linear models, some other problems could arise. Firstly, using nonlinear models would lead to a non-convex optimization problem for which a globally optimal solution is not guaranteed. Secondly, the identification of nonlinear models is usually time-consuming and effort-demanding, especially for complex processes [2]. Therefore it is important to study simple modeling methods for nonlinear systems in order to enhance MPC with respect to its control effect. For our research purpose, we adopt a work-in-progress industrial CFB boiler as our case; put forward its modeling method based on LPV models, and present its MPC simulation results.

It is well understood that nonlinear AR(MA)X models, neural-network models [3], [4], [5] and echo state network models [6] are often used in nonlinear system identification. To our knowledge, these models are complex in structure and difficult to compute numerically. While block-oriented nonlinear models such as Hammerstein models and Wiener models are simpler, however, they can only model nonlinear process with static gains, which is often too limited for process control applications. There are also feedback nonlinearities based models like LuGre. The fact that these models can simulate the nonlinear dynamics of a static block makes them more useful than the Wiener and Hammerstein models, but they are quite hard to develop. Parameter-varying process identification has attracted great attention in both academic and industry. LPV modeling is a good example [7]. The terminology of LPV systems was first introduced by Shamma and Athans [8] in their gain-scheduling-control research. Since then, several LPV model identification and control algorithms have been developed and published. Among others, multiple-model approaches [9], subspace approaches [10], [11] and orthonormal basis functions [12] were studied. Most publications available on the subject of LPV models [13], [14], [15] are based on parameter interpolation. This kind of LPV models often have complicated, strong nonlinear dependencies on some exogenous parameters, therefore can be unstable. To overcome this problem, Zhu and Xu [16] proposed an LPV model based on blended linear models interpolation. It was followed by Zhu and Ji [17], who proposed a modified version of the LPV model based on blended linear models by adding weights to the input sides. By doing so, it is easy to guarantee the stability of this kind of LPV models, if the local linear models are all stable. LPV models in process control have several advantages: (1) they can be identified easily; (2) they can model both static and dynamic nonlinearities; and (3) they can take into account the process operation knowledge by selecting the operation-point variables. Several studies of MPC based on LPV models have been done up to now. Lu and Arkun proposed quasi-min–max MPC algorithm [18]; Lee and Won proposed a new robust MPC technique [19] and Yu et al. studied a method based on a parameter-dependent control law [20]. Other methods are also proposed, including closed-loop min–max MPC algorithm based on dynamic programming [21], off-line MPC based on ellipsoidal calculus and viability theory [22] and closed-loop subspace based predictive control [23], [24].

In Section 2 of this paper, the identification of LPV models with weights on output and on input sides are studied. Three different kinds of weighting functions are analyzed. In Section 3, LPV models for an industrial CFB boiler using steam flow as the operation-point variable are proposed. In Section 4 the effectiveness of simulation and control using LPV models are validated. Finally, conclusions are given in Section 5.