# Performance Assessment of Predictive Control--A Survey
## 1 Introduction  
Modern control systems are organized into a hierarchical structure, often presented in the form of a functional pyramid, as shown in Figure 1. The targeted plant of the control system is situated at the bottom. An instrumentation layer is atop the process layer, which enables the upper levels to communicate with the process layer. The regulatory control layer is organized into basic univariate loops that mostly utilize the PID algorithm. This algorithm constitutes a significant majority (>90% or even >95%) of the algorithms utilized [1; 2; 3]. These percentages might seem strange, but more advanced control techniques, such as Kalman filtering, optimal, robust, predictive, and adaptive algorithms, are only used in a limited number of applications, such as military, expensive processes, nuclear plants, or similar applications. This is a small fraction of the applications compared to civilian industry plants, and the selected MPC applications (even large ones) in the process industry are not comparable to the PID applications, and the applications can be measured in the billions [4]. Moreover, these applications come in the form of supervisory implementations over regulatory PID loops. In such a case, the PID loops are not replaced, but are still used. The majority of control applications are not very complex and not very demanding. Actually, most PID controllers only use the PI elements. However, the improvements achievable with the PID control rules are limited. More complicated controllers, such as multivariate, nonlinear, predictive, adaptive, or ones using soft computing, fall under the general term of Advanced Process Control (APC) [5; 6]. They go beyond the scope ofoperation of PID loops. The majority of the Model Predictive Control (MPC) implementations are situated here, although, in some cases, MPC plays the role of a regulatory control without any downstream PID loop. The supervisory level consists of Process Optimization (PO), economic planning, and long-term scheduling. A properly designed and tuned controller allows high operational performance to be achieved [7]. A poorly tuned or improperly selected control philosophy results in worse total process performance. Furthermore, real, most full-scale industrial plants are non-stationary, nonlinear, and complex. The owner of the installation is not only interested in reaching a single shot result, but it is also expected to improve sustainability. On-line performance monitoring, diagnostics, and maintenance play increasingly important roles and constitute inevitable aspects of good practices on site. These aspects appear at the PID regulatory level, but they are crucial for APC [8; 9] solutions, as advanced controls mostly operate close to the technological constraints. It is expected that the base control maintains the operation in automatic (AUTO) mode, while APC is aimed at additional financial benefits. Advanced control techniques are becoming more and more popular. MPC is the main component and is often synonymous with APC. A predictive strategy with a receding horizon computes the control signal, called the Manipulated Variable (MV), on the basis of the embedded process model. While the model supports the controller with prediction, optimization is used to calculate the control rule by minimizing a given cost function simultaneously the satisfying constraints. MPC approach is very flexible, e.g., it makes it possible to control processes described by linear [10] or nonlinear models [11], and can incorporate on-line setpoint optimization [12] or fault-tolerant approaches [13]. The implementation of APC predictive controllers is a complex task, taking more time and materials than the startup of a univariate PID loop [14]. Such an installation is always preceded by and concluded with an assessment, which is used to justify the effort and calculate the benefits. Thus, the performance assessment of MPC is required even more than for other regulatory algorithms. Control Performance Assessment (CPA) actually is as old as controllers.