Design And Application Of Fractional Active Disturbance Rejection Control

As an important branch of differential and integral calculation, fractional calculus expands the integer order domain's differential and integral to non-integral order domain. Non-integral differential and integral provide more precise mathematic description for actual physics objects, especially for the plants with viscoelasticity, diffusivity, memorability and so on. With the in-depth study and wide application of fractional calculus, fractional calculus has gradually penetrated into the traditional controller design, for example, proportion integral derivative control (PID), active disturbance rejection control (ADRC), internal model control (IMC), sliding mode control (SMC) and optimal control theory, etc. The combined control algorithm can not only retain the original features but also absorb the merits of fractional calculus's quick response and high freedom degree of adjustable parameters, therefore can improve the controller's whole performance.Because of the simple configuration, strong robustness, effortless tuning method and model independent, active disturbance rejection control has obtained wide practical applications in industry. The model independent characteristic makes active disturbance rejection control become a special solution for fractional order system control. Yet, some accompanying problems, such as high observer bandwidth, short sampling interval and large observation error, still need to be resolved. As a consequence, the fractional active disturbance rejection control (FADRC) algorithm is proposed by introducing the fractional calculus to the traditional active disturbance rejection control. Compared with the traditional active disturbance rejection control, three creative points are added to the improved fractional active disturbance rejection control:1. Fractional calculus is added to tracking differentiator (TD). The improved fractional tracking differentiator (FTD) takes the replace of tracking differentiator, and fractional tracking differentiator is used to get the transient process of set point and acquire process's fractional order derivative.2. The highest order of controlled object is obtained according to the model information, which is used to redesigning the extended state observer (ESO). The improved fractional extended state observer (FESO) could get precise estimations for system's states and extend state at the cost of low observer bandwidth. Besides, the improved fractional extended state observer improve robustness for the controlled object's parametric perturbations.3. Fractional calculus is added to the nonlinear state error feedback (NLSEF). The fractional order controller is used to replace integer order controller, increasing the number of controller's adjustable parameters and constructing high-efficiency control law.By the stability analyzing and robustness experiment, it can be inferred that not only the linear commensurate fractional order system but also the non-linear and incommensurate fractional order system can be well controlled by fractional active disturbance rejection control. The contrast simulation experiment for different problems shows that the fractional active disturbance rejection control owns better performance on fractional order system.