Reset PID Controller Design Based On Describing Function

Reset control belongs to the category of hybrid controls. Similar to the currently popular hybrid strategies, a switching surface is used to trigger sudden changes in control effort. Reset control, however, has its own uniqueness. For instance, the same control law is used to both sides of the switching surface and part of the controller states are reset whenever the triggering signal crosses the switching surface.It is well known that Bode’s gain-phase relationship imposes a hard limitation in linear feedback control design. One has to make trade-off between conflicting specifications characterized by the open-loop gain and phase properties. However, reset control can overcome this constraint to some extend and lead to more satisfying phase property without changing the gain property designed. Therefore, this thesis combines the traditional PID control and certain reset mechanism to achieve better performance. The main contributions are as follows.①In this thesis, a reset PID controller design method based on describing function is proposed which has been inspired by the nice frequency-domain feature of the Clegg integrator, and the describing function of a general reset PID controller is calculated. Then the influence of the reset law upon the frequency property is investigated, and an approximate condition under which the reset control produces phase lead is obtained.②A reset-caused gain compensation method is proposed in order to eliminate the effect of the reset law to the gain property of the system. This method allows us to increase the phase margin without changing the gain property at the same time. An illustrative example is also provided to explain the application of the proposed design procedure in loop shaping.③It is revealed that reset control is capable of compensating for the phase margin loses caused by time delay, and an approximate condition is also proposed to estimate how much delay could be compensated for by resetting.④The proposed reset PID controller design method is applied to track-following control of a kind of hard disk drive servo systems. It is shown that, cooperating with the narrowband compensator, the proposed method increases the mid-frequency disturbance attenuation level within certain frequency range without degrading stability robustness.The analysis and simulation results in this thesis show that the proposed reset PID controller design can relief the Bode’s gain-phase constraint and thus can be used to achieve better trade-off between conflicting specifications.