TAILIEUCHUNG - Advanced Control Engineering - Chapter 9

Optimal and robust control system design Nhận xét về kiểm soát tối ưu Một hệ thống điều khiển tối ưu tìm kiếm để tối đa hóa lợi nhuận từ một hệ thống với chi phí tối thiểu. Nói chung, vấn đề kiểm soát tối ưu là tìm thấy một u kiểm soát gây ra hệ thống * x  g (x (t), u (t), t) (9:1) theo một quỹ đạo tối ưu x (t) giảm thiểu các tiêu chí hiệu suất, hoặc chi phí chức năng  t1 Ja h (x (t), u (t), t) dt (9:02). | 9 Optimal and robust control system design Review of optimal control An optimal control system seeks to maximize the return from a system for the minimum cost. In general terms the optimal control problem is to find a control u which causes the system X g x f u f t to follow an optimal trajectory xịt that minimizes the performance criterion or cost function J i h x f u r t dt to The problem is one of constrained functional minimization and has several approaches. Variational calculus Dreyfus 1962 may be employed to obtain a set of differential equations with certain boundary condition properties known as the Euler-Lagrange equations. The maximum principle of Pontryagin 1962 can also be applied to provide the same boundary conditions by using a Hamiltonian function. An alternative procedure is the dynamic programming method of Bellman 1957 which is based on the principle of optimality and the imbedding approach. The principle of optimality yields the Hamilton-Jacobi partial differential equation whose solution results in an optimal control policy. Euler-Lagrange and Pontryagin s equations are applicable to systems with non-linear time-varying state equations and non-quadratic time varying performance criteria. The Hamilton-Jacobi equation is usually solved for the important and special case of the linear timeinvariant plant with quadratic performance criterion called the performance index which takes the form of the matrix Riccati 1724 equation. This produces an optimal control law as a linear function of the state vector components which is always stable providing the system is controllable. Types of optimal control problems a The terminal control problem . This is used to bring the system as close as possible to a given terminal state within a given period of time. An example is an Optimal and robust control system design 273 automatic aircraft landing system whereby the optimum control policy will focus on minimizing errors in the state vector .

• Tự động hoá
• công nghệ diều khiển
• điều khiển tiên tiến
• điều khiển học
• hệ thống điều khiển
• kiểm soát kỹ thuật
• kỹ thuật
• công nghệ
• tự động hóa
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