Abstract
It is well known that any controllable finite dimensional plant, whether it is stable or not, can always be stabilized. Smith's method has long been regarded as useful for the control of the plant with delay. As is known, Smith's method is valid only for the stable plant; the reason is explained in this paper from the view point of unstable pole zero cancellation. Instead, the control scheme based on the calculated value of x(t+L) using the parameter values of the plant achieves finite pole assignment regardless of the plant stability.
The frequency domain pole assignment technique for the finite dimensional plant is applied to the control of the unstable plant with delay in this paper Quite the same result as finite pole assignment could not obtained, but it is demonstrated that the unstable plant with delay cannot always be stabilized according to the relation between the magnitude of unstable poles and delay time. Stability region depicted in the gain-delay plane is presented for the case when there exists only one unstable pole. Simulation result shows that the unstable plant with delay is controlled with satisfactory stability by the proposed design method.
