Multi-Objective Optimization Design Of Insensitive Control Systems Based On LMI Technique

With the rapid development of computer and automation technology, more and more attention is paid to digital control system which has been considered as one of the most important and active fields in the research. However, limitation in available microproces-sor memory, effects of finite word length of the digital processor, errors for truncation and quantization of the A/D and D/A converters and so on always cause the controller param-eters trivial deviations from the original design values. On the other hand, the sampling time of digital control system may be jeopardized in practice by clock error drift, jitter, measurement noise, imperfect hold circuits, synchronization or other hardware problems etc. However, the trivial controller/filter parameter variations and the small sampling time jitter may lead to a severe degradation of the closed-loop system performance and even unstable. Therefore, how to design a controller/filter to insensitive to the trivial parameter variations is a very important issue in theory and in practical engineering applications. Sensitivity theory can well characterize the impact of the trivial parameter deviations on the system performance which motivates us to design multi-objective parameter insensi-tive controller/filter in the framework of parameter sensitivity theory.This dissertation, combining sensitivity analysis method and linear matrix inequality (LMI) technique in robust control and using their advantages, presents a new insensitive optimization design method. The norms of parameter sensitivity functions of the state-space realization of controller/filter as a design objective and combined with the other design objectives of the system, the problem of designing insensitive controller/filter is converted to a convex optimization problem or computable optimization problem in terms of LMI technique. On the other hand, this dissertation also combines Fisher lemma, Projection lemma and descriptor system approach to reduce the conservativeness of multi-objective designs by introducing auxiliary variables. Parts of the developed theories are applied to the simulation studies of F-404engine model and F-18aircraft model. The main research contents are outlined as follows:Chapters1-2summarize and analyze the background and the development of insen- sitive control. Preliminaries about the considered problem are also given.Chapter3investigates the problem of designing multi-objective parameter insen-sitive H∞filters for linear continuous-time systems. Parameter sensitivity functions of transfer functions with respect to filter additive/multiplicative parameter variations are first defined, and the H∞norms of the sensitivity functions are used to measure the sen-sitivity of the transfer functions with respect to filter parameters. In addition, in order to deal with the filter design problem for the multiplicative filter coefficient variation case, new measures based on the average of the sensitivity functions are also defined. Based on the above two types of sensitivity measures, novel methods for designing insensitive H∞filters subjected to additive/multiplicative filter coefficient variations respectively are given in terms of LMI techniques. Furthermore, an indirect method for solving the mul-tiplicative variations is also proposed. In comparison with the existing method, the new proposed method has less computational burden. What’s more, it is difficult to use the existing method to obtain convex conditions for the filter design problem with respect to interval multiplicative parameter variation case, while this problem can be resolved well by using the new proposed method. The simulation examples also have shown the effectiveness of the proposed method.Based on the results in Chapter3, Chapters4-5focus on the problems of designing multi-objective parameter insensitive H∞filters and output tracking controller for Delta operator discrete-time systems, respectively. The designed filters/controllers are insen-sitive to the filter/controller parameter variations. Being different from using a common Lyapunov matrix of Chapter3, the design conservatism is reduced by introducing slack variables in these two chapters. It is worth mentioning that delta operator approach offers better parameter sensitivity than the traditional shift operator approach at high sampling rate. Finally, some numerical examples including a linearized model of an F-404engine and F-18aircraft are given to show the effectiveness and the superiority of the proposed approaches in above two chapters.Chapter6studies the problem of designing multi-objective parameter insensitive H∞dynamic output feedback controllers for linear discrete-time systems. Two different design methods with different degrees of conservativeness and computational complexity are proposed for this problem. The designed controllers are insensitive to the controller parameter variations. The first method presents a necessary and sufficient condition for the existence of the insensitive controller. The problem of designing multi-objective dy-namic output feedback controllers is a non-convex problem itself, an LMI-based proce- dure which is a sequential linear programming matrix method (SLPMM) is proposed to solve this non-convex problem. However, the search for satisfactory solutions may be very difficult when the SLPMM algorithm acts on a module of very high dimension. To overcome the above difficult, the non-fragile controller design method is adopted to ob-tain an initial solution for SLPMM algorithm for the first time. In the second method, a sufficient condition is provided for the multiplicative parameter variation case based on a new type of sensitivity measures. Finally, the effectiveness of the proposed method is validated by numerical examples.Chapter7is concerned with the problem of designing multi-objective insensitive H∞filters for Delta operator discrete-time systems with low sensitivity to sampling time jitter. Being different from the above several chapters, a new type of sensitivity function is proposed. The effects of sampling time jitter on system performance are mitigated by minimizing the H∞norms of the sensitivity functions. First, based on Projection lemma and descriptor system approach, a necessary and sufficient condition with three slack variables are presented to make the Delta operator discrete-time system be asymptotically stable and satisfy H∞performance requirement. Then, the problem of designing insen-sitive filters is converted to a multi-objective optimization problem. The corresponding design method is also proposed to realize the optimal trade-off between the standard H∞criterion and the sensitivity performance. The superiority of the proposed method over the standard design method is demonstrated by a numerical example.Based on the approaches in Chapter7, Chapter8studies the multi-objective insensi-tive.H∞control synthesis problem via dynamic output-feedback for linear delta operator discrete-time systems with insensitivity to sampling time jitter. An LMI-based two-step procedure is adopted to solve the non-convex multi-objective problem. At the same time, the controller design condition with considering the standard H∞performance and the sensitivity performance simultaneously is presented. The simulation example has shown the effectiveness of the proposed method.Finally, the results of the dissertation are summarized and further research topics are pointed out.