Research Initiation Award: A Comprehensive Controller Design Methodology for Nonlinear Processes

控制文献的主要内容涉及线性时不变系统控制器设计技术的发展。在过程模型中遇到的非线性通常被视为由于模型在稳态附近线性化而产生的不确定性。化学品制造中的大多数实际过程本质上是非线性的，这是由于例如，速率方程的指数形式依赖于温度、精馏塔中塔板的持有率、本项目的目标是为连续时间的非线性过程开发控制器设计方法。过程建模的不确定性、扰动不确定性以及对过程输入和输出的硬约束将被明确考虑。整个控制器设计问题将被描述为一个加权极小极大问题，其解不会被解释为最坏情况设计，但将被证明为自然产生的多目标优化问题的非劣解之一。极小极大问题的可解性和理论性质的研究将通过一些关于化学和生化反应器以及蒸馏塔的案例研究来进行，所有这些都是已知的呈现非线性的。非光滑变分法用于使目标函数关于闭环系统输入信号达到最大，而非线性规划将用于实现关于控制器的最小化，后者通过有限的Volterra级数建模。

The main body of control literature has dealt with the development of controller design techniques for linear time- invariant systems. Nonlinearities encountered in a process model have usually been treated as uncertainties resulting from the linearization of that model around a steady state. Most of the real processes in chemicals manufacturing are inherently nonlinear due to, for example, the exponential form of the rate equations' dependance on temperature, hold-up on trays in distillation columns, etc. The objective of this project is to develop controller design methodologies for continuous-time nonlinear processes. Process modelling uncertainty, disturbance uncertainty, and hard constraints on process inputs and outputs will be explicitly considered. The overall controller design problem will be formulated as a weighted minmax problem, whose solution will not be interpreted as "worst-case" design, but will be shown to generate one of the noninferior solutions to a naturally occurring multi-objective optimization problem. Investigation of the solvability and of theoretical properties of the minmax problem will be undertaken through a number of case studies on chemical and biochemical reactors and distillation columns, all of which are known to present nonlinearities. Nonsmooth calculus of variations will be used to perform the maximization of the objective function with respect to closed loop input signals, while nonlinear programming will be employed to carry out the minimization with respect to the controller, the latter modelled through finite Volterra series.