Research On Linear Systems Under Actuator Rate Saturation

The theory of linear system has been perfected for several decades. However, designing controller under the theory often cannot get the desired control effect, and sometimes even the stability cannot be guaranteed. One of the reason is, there is a deviation between the mathematical model and physical model, but another important reason is in the design process of the controller we didn’t fully take into account that actual physical actuator operating range is constrained by saturation nonlinearity(for example steering gear rotation rate should not be beyond certain range, etc.), so that the control signal according to the theory of computation cannot be accurately applied on the object. In view of the fact that any physical system with actuator are inevitably by the saturated nonlinear constraint, nearly 30 years of this kind of control system design problem attracted very extensive attention, many scholars proposed different methods to solve variety of control problems. However, these methods either are too difficult to calculate to achieve, or are not ideal for control effects, which largely limits the application of relevant design methods in engineering. In this paper, the linear system with actuator rate saturation is studied, and the main research content is as follow.Firstly, the theory of input saturation is introduced. The problem is analyzed from three aspects: global stabilization, semi global stabilization and local stabilization. For if the system contains saturation nonlinearity, linear feedback cannot achieve global stabilization. So, if we want to achieve the ideal goal of global stabilization, we must use nonlinear controller. The second chapter presents the form of nonlinear controller to achieve global stabilization. For linear feedback, ∞-low gain can achieve semi global stabilization, and generalized control gain can do local stabilization.Secondly, we introduce the block theory of nested saturation function. When a system is under input and actuator rate saturation simultaneously, its mathematical model can be equivalent to nested saturation function. Using LMI tool, we can handle the estimate of domain of attraction and control gain optimization. In addition, the system model can be transformed into the input satur ation when it is under actuator rate alone, and can be processed by the prior results.At last, linear systems under actuator position and rate saturation is studied. After a series of operation, we find out that the mathematical model of this kind of system belongs to summation saturation function. Further study shows that this kind of system can also be transformed into the input saturation model. For this kind of system, we chose the example of the attitude control of missile pitch plane to do the simulation. In addition, a better method treating saturation nonlinearity is introduced as the supplement of this paper.