Robust Controller Design for Systems with Constraints

该研究项目旨在开发过程控制算法来处理约束和不确定性。约束影响控制器的设计，因为虽然许多过程的动态行为可以用线性模型精确地描述，但系统运行总是受到非线性因素的约束。必须设计控制器来处理这些非线性。这些限制可能来自执行器饱和或加工限制（例如，不能超过某些温度和压力）。不确定性是一个因素，因为控制设计者从来没有一个完美的动态描述（模型）任何真实的工业过程。系统是近似的，模型阶数和参数总是包含一定的误差，甚至可能随运行条件的变化而变化。PI计划实施两种技术来处理这类问题，模型预测控制（MPC）和抗上发条无颠簸传输（AWBT）。MPC要求控制目标用单个二次目标函数表示，约束转化为线性不等式约束。AWBT控制器的设计分两个步骤进行，首先设计一个可接受的线性鲁棒控制器，忽略所有非线性回路元素和目标。在此基础上，提出了一种补偿方案，用于处理约束等非线性问题。本研究将分三个步骤进行：(1)设计一种新的鲁棒线性MPC控制器。它将通过优化器以非线性方式实现，该优化器旨在满足所有过程约束，同时最大限度地减少与线性行为的偏差。​(2)开发一种AWBT合成程序，在平滑开关性能、测量噪声灵敏度和鲁棒性之间取得平衡。(3)建立机制，有效地将实际目标和约束转化为MPC或AWBT的形式主义。

This research project is aimed at developing process control algorithms to handle both constraints and uncertainty. Constraints affect controller design because while the dynamic behavior of many processes can be accurately described by a linear model, system operation is always subject to constraints which are nonlinear elements. The controller has to be designed to handle these nonlinearities. Such constraints may arise from actuator saturation or processing limitations (certain temperatures and pressures may not be exceeded, for example). Uncertainty is a factor because the control designer never has a perfect dynamic description (model) of any real industrial process. The system is approximated and model order and parameters always contain some error, and may even change with operating conditions. The PI plans to implement two techniques for dealing with such problems, Model Predictive Control (MPC) and Anti-Windup Bumpless-Transfer (AWBT). MPC requires that the control objective is expressed in terms of a single quadratic objective function and the constraints are translated into linear inequality constraints. AWBT controller design proceeds in two steps where first an acceptable linear robust controller is designed neglecting all nonlinear loop elements and objectives. Then a compensation scheme is added which deals with the nonlinear issues such as constraints. This research will proceed in three steps: (1) A new robust linear MPC controller will be designed. It will be implemented in a nonlinear manner through an optimizer which aims at satisfying all process constraints while minimizing the deviation from linear behavior. (2) Development of an AWBT synthesis procedure that balances the trade-offs between smooth switching performance, measurement noise sensitivity and robustness. (3) Development of mechanisms to translate practical objectives and constraints into an MPC or AWBT formalism in an effective manner.