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

控制文献的主体已经处理了线性时不变系统的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认为是由于该模型在稳态周围线性化而产生的不确定性。化学制品生产中的大多数实际过程本质上都是非线性的，例如，速率方程的指数形式依赖于温度、蒸馏塔中托盘的阻力等。这个项目的目标是开发连续时间非线性过程的控制器设计方法。过程建模的不确定性，干扰的不确定性，以及过程输入和输出的硬约束将被明确考虑。整体控制器设计问题将被表述为一个加权最小最大问题，其解决方案将不会被解释为“最坏情况”设计，但将被显示为生成一个自然发生的多目标优化问题的非劣解之一。研究最小最大问题的可解性和理论性质将通过对化学和生化反应器和蒸馏塔的一些案例研究来进行，所有这些都已知呈现非线性。非光滑变分法将用于实现目标函数相对于闭环输入信号的最大化，而非线性规划将用于实现相对于控制器的最小化，后者通过有限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.