Fractional Order Two-degree-of-freedom Control Research For Cascade Time-delay Processes

The cascade control is an advanced multi-loop control structure widely used in the process control industries with flow,pressure,level and temperature control loops to attenuate the external disturbances for the rapid performance.The design of cascade control system which depends on two main purposes,setpoint tracking and disturbance rejecting,needs to be achieved.However,the traditional cascade control system is one-degree-of-freedom control structure and can serve only one purpose.If the setpoint tracking is good,its disturbance rejecting response is poor,and vice versa.The design of the primary and secondary loop controllers is a trade-off between the setpoint response and the load disturbance attenuation.Due to this,two-degree-of-freedom control structure is proposed in order to serve both two main purposes of cascade control system.When fractional-order controller is applied in the physical and engineering systems,it can not only provide more flexibility of control,but also enhance the robustness of the system.Therefore,in this work,fractional order two-degree-of-freedom control strategies-based series cascade control structure are suggested for stable,integrating and unstable processes with dead-time.Firstly,a fractional order two-degree-of-freedom PID(proportional–integral-derivative)control strategy is proposed for cascade stable time-delay process.The PID controller parameters of inner loop are obtained by equating the Maclaurin series of the expected and real closed-loop transfer functions.Based on the Bode's ideal transfer function and the internal model control(IMC)principle,the setpoint tracking controller and disturbance rejection controller of outer loop are considered in the form of PID controller cascaded with a fractional order filter.The numerical simulation results show that the suggested scheme yields noteworthy enhancement in closed-loop response.Then,a fractional two-degree-of-freedom Smith predictor control-based cascade control system is presented for two integrating processes with dead-time.The presented control structure has three controllers(named as inner loop controller,setpoint tracking controller and disturbance rejection controller of outer loop).The controller designed for the inner loop assumes the standard PID controller structure and can quickly reject disturbance.Both setpoint tracking and disturbance rejection controllers of outer loop are designed using different fractional order IMC filter,which not only decouples the setpoint tracking response from the disturbance rejection response,but also improves the flexibility of system control by introducing fractional-order control.The simulation results demonstrate the successful dynamic performance of the proposed method.Finally,a fractional order two-degree-of-freedom internal model control structure-based cascade control system is suggested for unstable time-delay processes.The proposed control structure has inner loop controller,stabilizing controller,setpoint tracking controller and disturbance rejection controller of outer loop.The inner loop controller is designed using integer order-based internal model control approach and the tuning parameters are obtained based on the prefixed robustness(maximum sensitivity,Ms).Setpoint tracking and disturbance rejection controllers of outer loop are designed using fractional order-based internal model control approach and the stabilizing PD controller is designed using Routh–Hurwitz stability criteria.The simulation results show that the proposed scheme provides enhanced setpoint tracking performance and disturbance rejection performance.