In order to obtain the nonlinear characteristic of an unknown control target, a method based on the steady-state oscillation control has been proposed in which the amplitude of the output signal is kept constant at a target value while frequency response measurements are performed, and this method has been used to estimate the pressure amplitude during self-oscillation of a thermoacoustic system. Stability analysis of the control system has also been reported revealing that the stability region of PI(proportional integral) compensator's gains, however, there has been insufficient comparison with conventional reference tracking control, which uses a sinusoidal reference signal for the output signal. In this paper, the two methods are quantitatively compared in the case of a second-order vibration system as the control target, and it is shown that the proposed method has the advantage of having a larger phase margin than the conventional method. Specifically, it is theoretically shown that (i) the conventional method does not allow phase inversion of the control target, but the proposed method does, and (ii) the conventional method allows only a dead time of at most half the period of the test frequency, but the proposed method allows an arbitrarily long dead time, which are further verified by numerical simulation.

In mass-produced products, each component of the control system is allowed to have a tolerance. As a result, the model parameters of the controlled object also have a certain tolerance. Therefore, the controller is designed based on the nominal characteristics while taking into account the perturbation, and the target value response characteristics also have a certain range of variation. In light of this background, a method has been proposed in which the closed-loop system is configured with a robust ILQ controller, and the controller is readjusted according to the characteristics of each controlled object using a single test data. However, this method requires that the nominal closed-loop system design is also done according to this method, and it cannot be applied to existing general ILQ servo systems. In this paper, we propose a method for updating the controller parameters to restore the response characteristics to the nominal characteristics and achieve LQ optimization for a closed-loop system designed using the conventional ILQ servo system design method for a single-input/output controlled object. We then verify its effectiveness through numerical examples.

This paper investigates the nonlinear control with integral compensation for the output voltage of boost converters through their discretized bilinear model and the Sum of Squares (SOS) method. We first obtain a discretized bilinear model of an actual boost converter through identification. Subsequently, for this discretized bilinear system, we initially design two control laws via the SOS method: one is a nonlinear state feedback stabilizing controller, and the other is a nonlinear state feedback control law maximizing the Lyapunov function decrement in each switching instant. Each of the control laws is applied together with a state observer for a bilinear system. These controllers are effective in an ideal setting without variations in the load resistance and the input voltage, but result in the steady-state errors when they vary. To circumvent the problem, we design the second type controller with integral compensation incorprated through the SOS method. Finally, we carry out control experiments to confirm the effectiveness with the proposed control law.