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This paper discusses a design method for controlling a single-input single-output linear time-invariant sampled-data multirate control system, where the sampling interval of a plant output is longer than the holding interval of a control input. In such a sampled-data control system, the control input can be changed between the sampling instants. Hence, even if the sampled output converges to the reference input, the intersample output may oscillate. Such an intersample oscillation is eliminated when the control input is constant. In a conventional method, a control law is extended using an additional signal which is independent of the reference response in the discrete time, and the additional signal is designed so that the control input is constant in the steady state. The conventional method is designed based on the transfer function model, on the other hand, the proposed method is designed using the state-space model. Furthermore, a new design method of the additional input is proposed using the input redundancy which is defined by strongly input redundant or weakly input redundant. Finally, the effectiveness of the proposed method is demonstrated through numerical examples.

In this paper, we propose a design of the fault tolerant adaptive control system for the input redundant linear plants which has m input channels with model reference adaptive control scheme. A feature of the proposed control system is to introduce the adaptive allocator which distributes and injects external signals into the plant. We derive adaptive law which ensures stability of output of the plant which has up to (m − 1) faults, using a suitable Lyapunov function. Through a numerical simulation, we show the stability and fault-tolerance of the designed MRAC.

The present study uses linear quadratic regulator (LQR) theory to control a vibratory system modeled by a fractional-order differential equation. First, as an example of such a vibratory system, a viscoelastically damped structure is selected. Second, a fractional-order LQR is designed for a system in which fractional-order differential terms are contained in the equation of motion. An iteration-based method for solving the algebraic Riccati equation is proposed in order to obtain the feedback gains for the fractional-order LQR. Third, a fractional-order state observer is constructed in order to estimate the states originating from the fractional-order derivative term. Fourth, numerical simulations are presented using a numerical calculation method corresponding to a fractional-order state equation. Finally, the numerical simulation results demonstrate that the fractional-order LQR control can suppress vibrations occurring in the vibratory system with viscoelastic damping.

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