روش رگرسیون شبه خطی چند تکرار و مدل اختلال انطباقی برای MPC

This paper proposes an MPC method that uses an adaptive disturbance model to improve the accuracy of prediction. In unmeasured disturbance model identification, a novel multi-iteration pseudo-linear regression (MIPLR) method is used which is more accurate and has faster convergence than traditional recursive identification methods. The adaptive disturbance model is used in an MPC scheme for improved performance in disturbance rejection. The method is demonstrated by the simulation of a distillation column and also tested on the real process. The test results show that the proposed MPC scheme can not only increase control performance, but also increase robustness.

Model predictive control (MPC) refers to a class of control algorithms that optimize plant behavior over a finite-time horizon based on an explicit mathematical model. MPC has been applied widely in controlling multiple-input multiple-output (MIMO) processes with constraints. Finite impulse response (FIR) and step response models are adopted in primal MPC formulations such as dynamic matrix control (DMC) [1] and the quadratic DMC (QDMC) [2]. They have had an enormous impact on industrial process control and served to define the industrial MPC paradigm [3]. Clarke and colleagues [4] proposed the generalized predictive control (GPC) in which transfer functions are used. In recent years, MPC in state space form has been an area of intensive research [5] and has also been employed in industrial MPC techniques, e.g., SMOC by Shell and SSC by AspenTech [3]. MPC is a model-based technique. Therefore model accuracy plays an important role in the performance of MPC systems. Modeling error and unmeasured disturbances can lead to poor control performance. The constant state disturbance model is a standard technique in linear quadratic regulator design [6]. In DMC and QDMC, a constant output step disturbance model is used to achieve offset-free control. This method has proved to be simple to implement and robust in real practice. However, it is less effective in rejecting unmeasured disturbances which are not steps. To improve the rejection of input disturbances, a ramp model to represent the output disturbance was suggested by Morari and Lee [7]. These methods work well under the special assumption of a ramp model on the disturbance. Wellons and Edgar [8] presented a generalized analytical predictor by using a first-order or second-order transfer function to estimate the effect of disturbance. However, fixed disturbance models have limited performance when disturbance properties are time varying. Shen and Lee [9] proposed an adaptive inferential control to identify an AR model for the disturbances in real time. In order to achieve a better performance, Karra and co-workers [10] proposed an adaptive MPC scheme in which the process model and disturbance model are updated on-line by two separate recursive pseudo-linear regression schemes. The input-output data is used to identify an output error (OE) model to describe process model, while the residuals generated by the OE model are modeled by ARMA processes. This approach has practical problems: when there are no test signals applied, there is a persistent excitation problem for process model identification; when test signals are used, the process is continuously disturbed. Gerksic, Strmcnik and van den Boom [11] presented a tuning procedure for the Kalman filter, based on the sensitivity functions, in order to improve the sluggish rejection of disturbances. Although robustness is considered, it is difficult to maintain the performance as disturbances in industrial processes are diverse and time varying. Muske and Badgwell [12] proposed a disturbance model that adds step disturbances either to the state or to the process outputs for linear MPC in state space framework. Moreover corresponding conditions are derived for guaranteeing zero steady-state offset. A general disturbance model for systems in which the controlled variables and measured ones are distinct is proposed by Pannocchia and Rawlings [13]. The difference between [12] and [13] is that [12] uses a block-diagonal structure for the disturbance model; while [13] use and unstructured model. In industrial MPC applications for continuous process units working at stationary operating points, we have observed that the process dynamics from inputs to outputs do not change for a long period of time; but the character of unmeasured disturbances change frequently. For example, in the refining/petrochemical industry, unmeasured disturbances are caused by variations in feed composition, in weather conditions, and in steam pressure. These variations cannot be modeled as stationary stochastic processes. In this work, we will develop an MPC technique that uses a fixed process model and an on-line identified adaptive disturbance model. The process model is identified by some identification methods, say, the asymptotic method (ASYM) [14] and [26], using externally excited input–output data. The unmeasured disturbances at the outputs are modeled as a time varying process filtered by an integrated white noise sequence [15]; a time series ARMA model is used to describe the dynamics of the disturbances. Traditional adaptive MPC, in which both process model and disturbance models are adapted, may suffer from poor excitation conditions if no test signals are applied; whereas in the proposed method no persistent excitation problem will occur as long as the simulation errors are non zeros. The proposed method is also much simpler than traditional adaptive MPC. The idea can be used in any MPC algorithms. Due to its popularity, the DMC structure is used to illustrate the concept proposed in this paper. Like the representation given by Lundstrom, Lee, Morari and Skogestad [16], in this paper, the DMC algorithm is separated into two parts, a predictor and an optimizer; and the modification is made in the predictor part. The model prediction of MPC is improved without influencing the optimizer. In recursive (adaptive) disturbance model identification a multi-iteration pseudo-linear regression (MIPLR) method is proposed in order to obtain accurate and fast converging model parameters. The outline of the paper is as follows: in Section 2, the basis of DMC algorithm is reviewed briefly; Section 3 presents the proposed method; in Section 4, the recursive identification method is developed and a simulation is used to show its performance. An industrial case study from a chemical plant is carried out in Section 5; Section 6 contains the conclusion and discussion.

For a large number of continuous processes in process industries, the process model does not change over a long period of time, while the dynamics of process disturbances change continuously. For this class of processes, an MPC control scheme that uses an adaptive disturbance model and fixed process model is proposed and studied. A recursive identification method using multi-iteration is proposed for fast convergence and more accurate estimates. The on-line identifier is used in MPC controllers in order to achieve better disturbance rejection. The results of applying proposed DMC-A control algorithm in a real process indicate that the proposed method can indeed increase the control performance. The simulation results for testing the robustness against model errors show that the proposed method is both higher performing and much more robust, which is a pleasant surprise (a free lunch?) Work is underway to carry out a theoretical analysis of this phenomenon. The round-off errors have caused the divergence problem in the real life test which needs to be addressed for applications of the DMC-A controller.