Discrete-Time State Feedback Control Design for Linear Objects with Delay

The research paper is devoted to the designing discrete-time control system for linear objects with delay using a state feedback controller with observer. A lot of closed loop control systems have sensor or actuator time delays, which must be included in the mathematical model of a control object. The most important feature of such kind of control objects is the infinite dimension of their state space models. This feature makes researches use specific methods of control designing for objects with delay. Known methods of designing discrete-time control for such kind of control objects are included amongst predictive control methods or expansion of transcendental transfer functions in a Taylor or Pade series using continuous models of control objects. As a result, the obtained continuous-time control algorithms are transformed into difference equations and implemented on microcontrollers using approximate numerical methods of differentiation. Such approaches can lead to decreasing the quality of the discrete-time control system. In this paper, methods of discrete-time control design using discrete-time models of linear objects with delay are considered. The procedure of obtaining discrete-time models, for linear objects with delay, has good computational support, for example, in the MATLAB package. Discrete-time models of control objects with delay have the finite dimension of the state space. The discrete-time state feedback control for such models can be designed without any approximation or specific designing methods. In this paper, the method of designing discrete-time tracking control system for linear objects with delay using state feedback controller with observer and internal model is suggested. Results of research are illustrated with MATLAB example.