Cascade controllers design based on model matching in frequency domain for stable and integrating processes with time delay

Purpose This paper aims to present an efficient and simplified proportional-integral/proportional-integral and derivative controller design method for the higher-order stable and integrating processes with time delay in the cascade control structure (CCS). Design/methodology/approach Two approaches based on model matching in the frequency domain have been proposed for tuning the controllers of the CCS. The first approach is based on achieving the desired load disturbance rejection performance, whereas the second approach is proposed to achieve the desired setpoint performance. In both the approaches, matching between the desired model and the closed-loop system with the controller is done at a low-frequency point. Model matching at low-frequency points yields a linear algebraic equation and the solution to these equations yields the controller parameters. Findings Simulations have been conducted on several examples covering high order stable, integrating, double integrating processes with time delay and nonlinear continuous stirred tank reactor. The performance of the proposed scheme has been compared with recently reported work having modified cascade control configurations, sliding mode control, model predictive control and fractional order control. The performance of both the proposed schemes is either better or comparable with the recently reported methods. However, the proposed method based on desired load disturbance rejection performance outperforms among all these schemes. Originality/value The main advantages of the proposed approaches are that they are directly applicable to any order processes, as they are free from time delay approximation and plant order reduction. In addition to this, the proposed schemes are capable of handling a wide range of different dynamical processes in a unified way.

Stability and performance comparison analysis for linear active disturbance rejection control–based system

This paper investigates the stability and performance of the linear active disturbance rejection control (LADRC)–based system with uncertainties and external disturbance via transfer functions and a frequency-domain view. The performance of LADRC is compared with the state-observer-based state feedback control (SOSFC) and state feedback control (SFC). First, the transfer functions and the error transfer functions for LADRC, SOSFC, and SFC are studied using the state-space method. It is proven that the LADRC-, SOSFC-, and SFC-based closed-loop systems have the same transfer function from the reference input to the output and achieve the same control effects for the nominal system. Then, it is proven for the first time that the LADRC has a better anti-interference ability than the SOSFC and SFC. Besides, the asymptotic stability condition of LADRC-based closed-loop system considering large parameter perturbations is given first. Moreover, the sensitivity analysis of the closed-loop system is carried out. The results show that the LADRC has stronger robustness under parameter perturbations. According to the results, we conclude that the LADRC is of great disturbance rejection ability and strong robustness.

Continuous sliding mode control for the translational oscillator with a rotating actuator system

The stabilization and disturbance rejection of the translational oscillator with a rotating actuator (TORA) are considered in this paper. To deal with the control issues, a novel continuous sliding mode control method is designed for the TORA system. Compared with existing sliding mode control methods for the TORA system, the proposed method here is continuous. Specifically, first, a global diffeomorphism is introduced for the model of the TORA system. Then, an elaborate sliding manifold is constructed, and a continuous sliding mode control scheme is developed to ensure the convergence of the sliding manifold. Furthermore, rigorous theoretical analysis is given. Finally, simulation tests are carried out, and the obtained simulation results demonstrate that the proposed method exhibits superior stabilization control performance and strong robustness.

Boundary stabilization and disturbance rejection for an unstable time fractional diffusion-wave equation

In this paper, we study boundary stabilization and disturbance rejection problem for an unstable time fractional diffusion-wave equation with Caputo time fractional derivative. For the case of no boundary external disturbance, both state feedback control and output feedback control via Neumann boundary actuation are proposed by the classical backstepping method. It is proved that the state feedback makes the closed-loop system Mittag-Leffler stable and the output feedback makes the closed-loop system asymptotically stable. When there is boundary external disturbance, we propose a disturbance estimator constructed by two infinite dimensional auxiliary systems to recover the external disturbance. A novel control law is then designed to compensate for the external disturbance in real time, and rigorous mathematical proofs are presented to show that the resulting closed-loop system is Mittag-Leffler stable and the states of all subsystems involved are uniformly bounded. As a result, we completely resolve, from a theoretical perspective, two long-standing unsolved mathematical control problems raised in [Nonlinear Dynam., 38(2004), 339-354] where all results were verified by simulations only.

Parameter Optimization of Active Disturbance Rejection Controller Using Adaptive Differential Ant-Lion Optimizer

Parameter optimization in the field of control engineering has always been a research topic. This paper studies the parameter optimization of an active disturbance rejection controller. The parameter optimization problem in controller design can be summarized as a nonlinear optimization problem with constraints. It is often difficult and complicated to solve the problem directly, and meta-heuristic algorithms are suitable for this problem. As a relatively new method, the ant-lion optimization algorithm has attracted much attention and study. The contribution of this work is proposing an adaptive ant-lion algorithm, namely differential step-scaling ant-lion algorithm, to optimize parameters of the active disturbance rejection controller. Firstly, a differential evolution strategy is introduced to increase the diversity of the population and improve the global search ability of the algorithm. Then the step scaling method is adopted to ensure that the algorithm can obtain higher accuracy in a local search. Comparison with existing optimizers is conducted for different test functions with different qualities, the results show that the proposed algorithm has advantages in both accuracy and convergence speed. Simulations with different algorithms and different indexes are also carried out, the results show that the improved algorithm can search better parameters for the controllers.