Linear Parameter-Varying Control - Complexity of Analysis, Synthesis and Implementation

在实践中遇到的系统往往只能准确地表示为非线性或时变微分方程组。线性变参数控制的范例是一个有吸引力的框架建模和控制这样的系统，由于控制器合成工具，保证在整个操作范围内的稳定性和性能的可用性。尽管这些工具已经使许多成功的应用，它们的使用仅限于低复杂性的系统。我们解决了不同类型的复杂性所带来的挑战：分析，综合和实施的复杂性，每个构成的障碍，在控制器设计的不同阶段要克服。这将在四个工作包中完成。第一个涉及的分析，综合和实施时遇到的问题的复杂性评估使用不同类型的LPV表示。减少调度参数的数量的方法将被提出，是基于转换成不同的等价形式或近似。由于基于近似模型的综合控制器将使稳定性和性能保证无效，第二个工作包将开发一个后验分析工具，用于检查当控制器应用于原始设备时，保证是否仍然有效。这将是一个重要的好处，离线分析可以进行减少保守性，简单的合成方法后，已被用来获得控制器的低实现复杂性。进一步采用这种方法，第三个工作包的目标是将这些分析结果转化为综合方法，从基于近似模型的初始控制器开始，并基于精确的工厂模型在分析和综合之间迭代。更复杂的方法将包括组合梯度LMI算法，以有效地解决潜在的非线性优化问题。这种综合技术也将被用来当稳定性和性能保证已经失去，需要通过优化控制器参数恢复。对于更一般的LPV表示，我们建议研究分析方法，已开发的经典增益调度技术。在第四个工作包中，开发的方法将在汉堡理工大学提供的一些具有挑战性的工厂上进行实验验证。

Systems encountered in practice can often only be accurately represented by nonlinear or time-varying sets of differential equations. The paradigm of linear parameter-varying control is an attractive framework for modelling and controlling such systems, due to the availability of controller synthesis tools that guarantee stability and performance in the whole operating range. Even though these tools have already enabled many successful applications, their use is limited to systems of low complexity. We address challenges imposed by different types of complexity: analysis, synthesis and implementation complexity, each posing obstacles to be overcome in different stages during controller design. This will be done in four work packages. The first deals with the assessment of complexity of problems encountered in analysis, synthesis and implementation when using different types of LPV representations. Methods for the reduction of the number of scheduling parameters will be proposed that are based either on a transformation into different equivalent forms or on an approximation. As synthesizing controllers based on approximated models will render stability and performance guarantees void, the second work package will develop a posteriori analysis tools for checking whether guarantees still hold when the controller is applied to the original plant. An important benefit of this will be that off-line analysis can be performed with reduced conservatism, after simple synthesis methods have been used to obtain controllers of low implementation complexity. Taking this approach further, the third work package will aim at turning these analysis results into synthesis methods, starting with initial controllers based on approximated models and iterating between analysis and synthesis based on an accurate plant model. More sophisticated approaches will include combined gradient-LMI algorithms for efficiently solving the underlying nonlinear optimization problem. Such synthesis techniques will also be used when stability and performance guarantees have been lost and need to be recovered by optimizing the controller parameters.For more general LPV representations, we propose to investigate analysis methods that have been developed for classical gain-scheduling techniques. In the fourth work package the developed methods will be validated experimentally on a number of challenging plants, which are available at the Hamburg University of Technology.