Control of delayed recycling systems with unstable first order forward loop

Abstract

Unstable time-delay systems and recycling systems are challenging problems for control analysis and design. When an unstable time-delay system has a recycle, its control problem becomes even more difficult. A control methodology for this class of systems is proposed in this paper. The considered strategy is based on the fact that if some internal system signals are available for measurement, then it will be possible to decouple the backward dynamics of the system and then a feedback controller could be designed for the forward dynamics. The key point for this strategy to be carried out is an asymptotic observer-predictor proposed to estimate these required internal signals. Necessary and sufficient conditions to assure convergence of this observer are given. After proving that the proposed control scheme tracks a step input signal and at the same time reject step disturbances, a procedure summarizing the methodology is provided. Robustness with respect to delay uncertainty and model parameters are also analyzed.

Control of delayed recycling systems with an unstable pole at forward path

“…To partially overcome this situation, in this work the problem of recycled system composed of a plant with an unstable pole and m stable poles at direct loop and a stable system of order n in the recycle loop is addressed. Note that the present work intends to deal with a more generalized recycling plant than the studied in [14] and [15], where unstable first order plant in forward loop is considered. Under these conditions, in this work it is proposed an observer-predictor based control schema in order to stabilize and control recycling systems with delay term in both paths.…”

Recycle Compensator Facilitates Rapid Parameterization of Proportional Integral/Derivative (PI/D) Controllers for Open-Loop Unstable Recycle Processes

“…Example 5: Recycle Process with an Unstable Pole in the Forward Path. Consider a recycle system with an unstable pole in the forward path, taken from the work of Marquez-Rubio et al 26 According to the block diagram given in Figure 2, the forward and recycle path transfer functions are given as The transfer function of the overall process is given as The Nyquist plot of G R (s) and the time response plot reveal that it is open-loop unstable. An attempt was made at designing PID controller for this process via optimization of time integral indices.…”

“…The simulation results obtained showed that the process could not be stabilized using the PID controller alone. The recycle compensator is specified for this system as Two-degrees-of-freedom PID controllers were parametrized for this system using the PID controller tuning rule proposed for first-order-plus delayed unstable systems by Lee et al 27 The feedback controller and the set point filter were respectively parametrized (with the IMC tuning parameter selected as τ c = 1.75) as Figure 17 shows the comparison between our compensation scheme and the observer−predictor-based control scheme proposed in the work of Marquez-Rubio et al 26 The recycle compensation scheme outperforms their scheme for both servo and regulatory control. …”

Dynamic Delayed Controllers for Unstable Recycling Systems with Time Delays

“…By another way, with an approach inspired in the Smith Predictor strategy, Márquez et. al 14 have proposed a control methodology for recycling systems but restricted to unstable first order system at the direct path. This methodology is based on an estimated feedback taken from an observer-predictor.…”

“…The dynamic delayed controllers here proposed do not only tackle a more general family of plants than the considered in Márquez et. Al [14], they are also easier to implement considering that this new proposal do not use any observer scheme to design the control law. In fact, the main idea of this work is to explore the simplest way to stabilize the recycling process with time delays and internal instability.…”