Robust Stability Analysis And Design Of Sampled-data Control System With Generalized Sampled-data Hold Function

With the development of the technology, modern control system becomes more and more complicated and demands for high precision. By using digital computer to control the continuous plant, sampled-data(SD) control system can be very fast and precise, thus SD control system has gained much attention.SD control systems are hybrid dynamical systems that contain both continuous and discrete signals. A hold works to transfer the discrete signal to continuous signal by a hold function. Generalized sampled-data hold function(GSHF) can be any T-periodic, absolutely integrable, and bounded function of time, and be designed according to the dynamics of a particular system. Thus it offers many advantages that usually cannot be achieved by the zero-order hold like assigning poles for several systems simultaneously, improving the gain margin and phase margin, achieving decentralized control, noise rejection and model matching. However, the robust stability analysis of SD control system with GSHF is very difficult and GSHF may lead to inter-sample ripple. This thesis is motivated by the development of GSHF. We intend to investigate the robust stability analysis and design of the uncertain sampled-data control systems with GSHF. By solving the robust stability problem, we can enrich the sampled-data control theory. By proposing new GSHF design methods, GSHF can be more applicable.In this paper, we use affine parameter-dependent model. The uncertain parameter is w(2w <g). The system is said to be robust stable if it is stable for all 2w <g.The main contents are:1) A simple linear matrix differential equation and two homogeneous equations are established and solved. The solutions of these equations turns out to have many good properties. These conclusions are the basis of the robust analysis. We will use the system matrices, uncertainty structure and GSHF to construct equations with the same structure.2) The robust stability analysis problem where the GSHF F(t) and the uncertainty radius are both known is solved. Since GSHF is a general function, the problem cannot be solved directly. So the problem with LTI hold()HA tH HF t =C e B is investigated at the beginning: First, an homogeneous equation 1 is constructed with a new parameter a >0. By solving the equation and using the related properties of the solution, an upper bound that is w free and true for all the all 2w <1 is obtained. A new robust stability theorem is achieved by using this upper bound. Then, the theorem is extended to problems with arbitrary GSHF F(t). This can be achieved with two methods: through Fourier series and through direct reconfiguration. Particularly, the results are applied to piece-wise constant(PWC) holds and a certain kind of multi-rate sampled-data control system. Finally, computation problems is solved by proving the criterion to be a unimodal function. In this thesis, the proof of the new criterion directly uses the data of the continuous-time plant and therefore it is expected to be less conservative which is verified with examples.3) The robust stability analysis problem where the GSHF F(t) is known but the uncertainty radius is unknown is solved. Robust stability radius RSR is defined to denote the robust stability quantitative of this situation. With the properties of the new criterion, RSR is proved to be the solution of a nonlinear function. A reliable numerical algorithm is also presented. Overall, this part defines a new parameter to denote the robust stability quantitatively, this is the basis of the robust stability optimization design.4) The GSHF design aimed to maximize robust stability is achieved. RSR vs. GSHF F(t) is defined as function RSR =g(F(t)) and used as the object function. The problems of signifying the design parameters by structuring F(t) and constructing constraint function are solved to make the optimization design process feasible. Overall, this part provides robust stability design method for SD control system with GSHF which hasn’t been investigated before.5) Integrated design methods that combine robust stability and system performance between the sample points are established. First, a modified performance index J that includes inter-sample ripple is formed and testified to be more effective. Then, 3 design methods are established: In design 1, RSR acts as object function and J acts as constraint function. In design 2, J acts as object function and RSR acts as constraint function. In design 3, an unified function RJ which combines RSR and J is constructed to be the object function. Overall, this part provides new design methods for uncertain SD control systems with GSHF.