Convex Optimization Based Performance Assessment Of Hierarchical Control Systems

With the emerging growth of the scale of industrial processes and the complexity of the plant in recent years, traditional centralized control strategies are gradually replaced by the newly devel-oped hierarchical control systems due to its advantages of flexible configuration and robustness. A Hierarchical control system including direct control layer and constraint control layer is a prospec-tive scheme in processes control practice, which could guarantee control demands in different aspects, including the safety, stability, reliability and efficiency of the plant operation. In hierarchi-cal control system, control tasks are composed of disturbances depression, set-point tracking, and economic performance optimization. And they are assigned to three individual subsystem layers to fulfill. Because there exists mutual influences between the realization degree of these tasks, and also interactions of control layers, it is not convenient for control engineers to determine how well the performance of local controllers and the plantwide system are. It is important and of practical significance to comprehensively evaluate the overall performance of a hierarchical con-trol system. To assess performance of direct control layer and constraint control layer, the most important components in a hierarchical control system, we proposed in this thesis a framework of benchmarking, assessing and optimizing the direct control and economic performance based on convex optimization technology. Especially, the non-convexity brought in by PID structure of the minimum achievable error variance problem in assessing direct control performance is refor-mulated as a new non-convex constraint with more explicit mathematical structure with respect to PID parameters.The original nonconvex optimization problem is then approximated by a convex optimization which can be easily solved with low-complexity algorithms. The main contributions of this thesis are as following:1. Minimum achievable output variance (MAOV) is a common benchmark for control per-formance assessment. Finding the MAOV of proportional-integral-derivative (PID) control systems is computationally expensive due to the inherent non-convexity of the associated optimization problem. We present a new method for computing the MAOV of PID control systems. The problem of estimating the MAOV of a PID control system is novelly for-mulated as a convex program with an additional non-convex constraint. The non-convex constraint is linearized and handled by the penalty approach. Based on this, a customized low-complexity algorithm, which relies on the iterative convex programming technique, is developed to solve the MAOV problem. The new algorithm is proved to be convergent. We show via numerical examples that the new approach yields close-to-optimal solutions that are better than (or as good as) the solutions generated by the existing methods.2. Considering the set-point of direct control layer is often affected by upper constraint control layer, a novel comprehensive performance assessment framework is proposed. Minimum achievable regulatory error variance (MAREV) is used as regulatory performance bench-mark, and minimum integrated absolute tracking error (MIATE) is established as benchmark of tracking performance. A regulatory/tracking performance trade-off curve is obtained to evaluate how balance the total control effect is. The problem of estimating the MAREV of a PID control system is formulated as a quadratic programming (QP) with a bilinear ma-trix inequality (BMI) constraint, and the problem of estimating the MIATE is formulated as a linear programming (LP) with a BMI constraint. Accordingly the problem of searching the balanced tracking/regulatory performance benchmark is formulated as a QP with BMI constraints with respect to PID parameters. These optimization problems are dealt with a standard sequential quadratic programming (SQP) algorithm. Thus facing multiple tasks in direct control layer, a flexible control performance benchmark suited for PID controllers is obtained. We show via numerical examples that compared to commercial software PENBMI which is specially designed for solving BMI problems, the approach we presented yields the same optimal solutions with less time consumption.3. Batch processes usually have strong nonlinearity or time-varying property, and are often operated in multiple phases. For those batch processes which can be described as linear time varying (LTV) systems, we suggest a new control performance benchmark which is based on the minimum achievable structured residual variance (MASRV). Firstly, for the ease of elaboration, a model called time-varying impulse response matrix is established to describe the LTV systems, which makes the LTV systems own similar formation with LTI systems. Secondly, a duration time of a batch is divided into regulatory and tracking stages according to set-point dynamics, then a structured residual is defined based on the weight matrix of the stage. The problem of estimating the MASRV of LTV system with PID controller is formulated as a non-convex optimization. The fact that the introduced structured matrix is whether invertible or not affects the choice of optimization algorithm. Iterative semidefinit programming (SDP) is selected to handle the convex optimization with a rank one constraint if structured matrix is invertible, otherwise, sequential quadratic programming (SQP) method is used to solve the QP problem with BMI constraints. Numerical simulations study prove that the reformulation of the problem improves the efficiency of optimization.4. In order to ensure multivariable industrial processes operating in a safe and economic mode, a method for control performance assessment of hierarchical control systems was proposed. The three-layer structure of a hierarchical control system:direct control layer, constraint con-trol layer and real-time optimization layer, was analyzed to formulate the control objective functions of three aspects:suppressing disturbances, keeping constraints and maximizing process profits, respectively. A control performance assessment benchmark called "best to worst performance range" was established to monitor the economic performance of industrial processes, and to evaluate how much potential would be improved. To avoid the degrada-tion of control performance due to model-plant mismatch, a method to compute generalized object model through open loop model and regulatory parameters was presented. The relia-bility and efficacy of the proposed performance assessment technique is demonstrated on a case study on Shell heavy oil fractionator control problem.