ON THE STABILITY OF NONLINEAR QUADRATIC DYNAMIC MATRIX CONTROL

State estimation is incorporated in a version of Quadratic Dynamic Matrix Control (QDMC) that utilizes nonlinear process models. This formulation enables us to deal with open loop unstable systems as illustrated with simple example. The second part of the paper studies the use of this type of control algorithm for the temperature control of a semibatch polymerization reactor. A model and related control requirements for this problem were recently presented in a session on "Industrial Challenge Problems in Process Control."

A decentralized quadratic dynamic matrix control algorithm

This article presents comparative analysis between the classical PI (proportional-integral control) and MPC (model predictive control) techniques for a drying process on spouted beds. The on-line experimental setups were carried out in a laboratory-scale plant of a spouted bed dryer. The main objective was to optimize the plant operation by searching for the best control structure to be used in future scale enlargement. The major drawbacks encountered in this kind of system were high interactivity among variables, a malfunction as a result of calculated variables out of the operational window, and modeling mismatch. Despite the robustness of the operational PI, the control actions of this strategy did not overcome the variable interactions. The DMC (dynamic matrix control) and the QDMC (quadratic dynamic matrix control) algorithms performed satisfactorily over the major drawbacks. Special attention was given to the latter algorithm due to its ability to hold the variables under constrained oscillations. However, the best results were found for the adaptive GPC (generalized predictive control) algorithm whose actions prevailed over the modeling mismatch due to the strong nonlinear behavior intrinsic to the process. The main goal of the present work is to describe a procedure that can be standardized for other types of dryers and different scales. This is especially the case for the adaptive GPC, whose control structure is independent of the dryer nature and scale and whose implementation does not require previous identification procedures (self-tuning) and/or structural changes.

Sufficient conditions for robust stability of multivariable quadratic dynamic matrix controllers with an end condition (EQDMC) are developed, and the effect of these conditions on closed‐loop performance is examined. Hard and soft constraints on process inputs and outputs, and process modeling uncertainty are present Modeling uncertainty is quantified in the time domain as upper and lower bounds on the coefficients of a finite pulse response process model. The robust stability conditions that we develop involve the prediction and control horizon lengths, and a set of inequalities that the move‐suppression coefficients in the on‐line EQDMC objective function must satisfy. These conditions imply that for processes with modeling uncertainty, the move‐suppression coefficients could be quite large and quite sensitive to the control horizon length and process modeling errors. This could make the EQDMC controller conservative, thus significantly deteriorating performance. To determine the optimal control horizon length corresponding to the best robust performance of the EQDMC controller for a class of disturbances, follow the proposed EQDMC controller design methodolo∼. To illustrate this methodology simulations on an SISO example and a 2 × 2 subsystem of the Shell Standard Control Problem are presented.

Supervisory Control of High Pressure LDPE Reactors

In this chapter, methodologies are described for the plant-wide optimization and control of nonlinear modular systems for continuous-flow pharmaceutical manufacturing. First-principles models for such modular systems are formulated as partial differential-algebraic equations (PDAEs). The spatial discretization of PDAEs, to enable their numerical solution with standard solvers, usually results in a very high number of states. Quadratic dynamic matrix control (QDMC) is an implementable approach for the real-time control of systems with very high state dimension, by using a linear input-output model so that the resulting optimization does not depend on the number of states. To address the strong nonlinearities in these modular systems, linear input-output model construction methodologies are described that can provide good closed-loop performance. Additionally, dynamic optimization of dynamical plant operations such as startup is formulated as a nonlinear program. The dynamic optimization determines optimal trajectories which are used as setpoints for QDMC to control the plant. Results are presented for a computational case study for the upstream synthesis of atropine in a modular continuous-flow system. Dynamic optimization and closed-loop simulation results are presented for plant operations under various disturbance and time-invariant parametric uncertainty scenarios.

Dynamic matrix control (DMC) has been widely applied in many industrial processes due to the simple design for multivariable process control. However, lack of the adaptability restricts its application in the highly nonlinear and complex processes. The nonlinear model predictive controller for processes is needed, but, from a computational perspective, it has quite comprehensive demands. In this paper, modified quadratic dynamic matrix control (MQDMC), which integrates DMC with the neural network model, is proposed. The predictive model control strategy linearizes the model by applying instantaneous linearization to the nonlinear neural network model at each sampling time. MQDMC has two advantages. First, less computation of linear DMC is used. Second, the nonlinear characteristics of neural networks can be incorporated into predictive control design. In the simulation studies, the performance of MQDMC matches that of nonlinear neural network model predictive control.

The original MPC(Model Predictive Control) algorithm cannot be applied to open loop unstable systems, because the step responses of the open loop unstable system never reach steadystates. So when we apply MPC to the open loop unstable systems, first we have to stabilize them by state feedback or output feedback. Then the stabilized systems can be controlled by MPC. But problems such as valve saturation may occur because the manipulated input is the summation of the state feedback output and the MPC output. Therefore, we propose Quadratic Dynamic Matrix Control(QDMC) combined with state feedback as a new method to handle the constraints on manipulated variables for multivariable unstable processes. We applied this control method to a single-input-single-output unstable nonlinear system and a multi-input-multi-output unstable system. The results show that this method is robust and can handle the input constraints explicitly and also its control performance is better than that of others such as well tuned PI control. Linear Quadratic Regulator (LQR) with integral action.

A FCC model is used to compare five different Model Predictive Control (MPC) strategies. The FCC process is a complex petrochemical unit with catalyst recycling that makes its behaviour highly nonlinear. The FCC comprises a riser, a separator and a regenerator with important heat coupling due to the endothermic cracking reactions of gas oil in the riser and the exothermic combustion reactions in the regenerator. The riser and the regenerator exhibit fast and slow dynamics respectively. The temperatures at riser top and in the regenerator should be controlled by manipulation of catalyst and air flow rates. All these nonlinear and coupled characteristics render the multivariable control problem difficult and thus the FCC process constitutes a valuable benchmark for comparing control strategies. Here, the performances of Dynamic Matrix Control, Quadratic Dynamic Matrix Control, MPC control with penalty on the outputs, NonLinear MPC control, Observer Based MPC control are compared.

Mathematical modeling of a pressurizer in a pressurized water reactor for control design

ROBUSTNESS AND TUNING OF ON-LINE OPTIMIZING CONTROL ALGORITHMS

For a class of inherently nonlinear systems with uncertain parameters, the global stabilization problem via sampled-data control is investigated in this paper. First of all,based on the technique of adding a power integrator and a recursive argument, a class of sampled-data state feedback controllers are proposed. Then under the proposed controller, by using a suitable Lyapunov functional, it is shown that there is a maximum allowable sampling period which can guarantee the global asymptotical stability of the closed-loop system. Since the proposed controller is discrete-time, it can be easily implemented by computers. Finally, an example is given to verify the efficiency of the proposed method.

This paper presents dynamic modeling, controller design, and virtual reality (VR)-based human-in-the-loop real-time simulation for a wheel loader control system. In particular, a loader with electrohydraulic actuation is considered. A detailed nonlinear dynamic model is developed for the hydraulic system and the loader linkage. The hydraulic model includes a load sensing pump, valves, and cylinders. The linkage model represents a two degree of freedom loader with lift and tilt functions. A linear quadratic Gaussian based robust controller is designed for automatic bucket leveling to assist the operator by keeping the angle of the bucket leveled while the boom is in motion. The closed-loop control system design is tested with a nonlinear model in a real-time VR simulation. In the VR simulation, the operator interacts with the model using a joystick input. The loader linkage geometry is displayed to the operator in real time using a VR display. The controller performance was assessed in the VR environment. As expected, the controller was found to provide a significant improvement in the accuracy of the bucket leveling, particularly in the case of a novice operator controlling the linkage motion. While prototypes cannot be eliminated, the VR simulation combined with realistic physics and control dynamics provided a useful tool for evaluating hydraulic systems and controls with less reliance on prototype machines.

Reinforcement learning based fractional fuzzy controller for photovoltaic systems

We show how bifurcation analysis is used to detect regions of infeasible steady-state operation in a jacketed, styrene polymerization reactor. The selected operating point is close to an infeasible region rendering single input-single output control of reactor temperature impossible, once model uncertainty is considered. We apply a multivariable nonlinear quadratic dynamic matrix control (NL-QDMC) strategy to this problem. The NL-QDMC algorithm incorporates an extended Kalman filter to handle state variable and parameter estimation; also included is an integrated white noise disturbance model. The initial case study is based on the use of coolant and monomer flow rates to regulate the reactor temperature, subject to noisy measurements, disturbances and varying process parameters. We also show results for the control of number average molecular weight and reactor temperature by manipulating coolant and initiator flow rates.