Disturbance-rejection-based tuning of proportional–integral–derivative controllers by exploiting closed-loop plant data

A systematic data-based design method for tuning proportional–integral–derivative (PID) controllers for disturbance attenuation is proposed. In this method, a set of closed-loop plant data are directly exploited without using a process model. PID controller parameters for a control system that behaves as closely as possible to the reference model for disturbance rejection are derived. Two algorithms are developed to calculate the PID parameters. One algorithm determines the optimal time delay in the reference model by solving an optimization problem, whereas the other algorithm avoids the nonlinear optimization by using a simple approximation for the time delay term, enabling derivation of analytical PID tuning formulas. Because plant data integrals are used in the regression equations for calculating PID parameters, the two proposed algorithms are robust against measurement noises. Moreover, the controller tuning involves an adjustable design parameter that enables the user to achieve a trade-off between performance and robustness. Because of its closed-loop tuning capability, the proposed method can be applied online to improve (retune) existing underperforming controllers for stable, integrating, and unstable plants. Simulation examples covering a wide variety of process dynamics, including two examples related to reactor systems, are presented to demonstrate the effectiveness of the proposed tuning method.     

A GA-based parameters tuning method for an ADRC controller of ISP for aerial remote sensing applications

This paper presents a parameters tuning method based on the genetic algorithm (GA) for an active disturbance rejection control (ADRC) of a three-axis inertially stabilized platform (ISP) with imaging sensors. To improve the stabilization accuracy and robustness of an aerial ISP under multi-source disturbances environment, an ADRC control scheme is first proposed. Then, to accurately identify and tune the parameters in the ADRC controller, a GA-based parameters tuning method is proposed. In this way, the performance of the ADRC is superior to the empirical method. To validate the proposed method, the simulations and experiments are carried out. The results show that the proposed ADRC with GA-based parameters tuning method has significant disturbance rejection ability which can improve the stabilization accuracy obviously. Compared with the ADRC with empirically tuning method, the stabilization error (RMS) under movable base is decreased up to 50.09%.     

Two-layer observer based control for a class of uncertain systems with multi-frequency disturbances

A novel disturbance estimation approach is presented for a class of uncertain systems subject to multiple-sinusoidal disturbances with unknown frequencies. Different from existing results on disturbance observer based control (DOBC), a new methodology with a two-layer observer structure is developed to effectively estimate and reject the disturbances. In the proposed control architecture, an auxiliary observer is derived to generate a disturbance representation in a parametric uncertainty form. Furthermore, the unknown parameters can be reduced to a constant vector with the dimension of the number of harmonic components in the disturbances. Then an augmented observer is designed to estimate the corresponding unknown parameters of the disturbances. As a result, the uncertain systems with disturbances constituting of multiple unknown-frequency sinusoidal components can be controlled within the DOBC framework, where asymptotic stability can be guaranteed. The proposed approach is successfully validated on a robotic manipulating example.     

Design and implementation of continuous finite-time sliding mode control for 2-DOF inertially stabilized platform subject to multiple disturbances

Control performances of inertially stabilized platforms (ISPs) are always affected by various disturbed phenomena such as cross-couplings, mass unbalance, parameter variations, and external disturbances in real applications. To improve the dynamic response and the disturbance rejection ability of the ISP, a continuous finite-time sliding mode control (SMC) approach with cascaded control structure is proposed. By constructing a finite-time disturbance observer, the multiple disturbances are precisely estimated in real time without the complex modeling and calibration work. Under the field oriented control framework, for the stabilized loop subsystem, an improved super-twisting controller incorporating the disturbance estimates is developed whereas for the current loop subsystem, the super-twisting control method is directly employed. Finite-time convergence of the inertial angular rates is guaranteed with the continuous control action such that chattering is alleviated remarkably. Moreover, by utilizing the manner of disturbance compensation, the feedback control gains can be tuning down without sacrificing the disturbance rejection ability. Comparative experiments are performed to verify the effectiveness of the proposed control approach.     

A novel auto-tuning PID control mechanism for nonlinear systems

In this paper, a novel Runge–Kutta (RK) discretization-based model-predictive auto-tuning proportional-integral-derivative controller (RK-PID) is introduced for the control of continuous-time nonlinear systems. The parameters of the PID controller are tuned using RK model of the system through prediction error-square minimization where the predicted information of tracking error provides an enhanced tuning of the parameters. Based on the model-predictive control (MPC) approach, the proposed mechanism provides necessary PID parameter adaptations while generating additive correction terms to assist the initially inadequate PID controller. Efficiency of the proposed mechanism has been tested on two experimental real-time systems: an unstable single-input single-output (SISO) nonlinear magnetic-levitation system and a nonlinear multi-input multi-output (MIMO) liquid-level system. RK-PID has been compared to standard PID, standard nonlinear MPC (NMPC), RK-MPC and conventional sliding-mode control (SMC) methods in terms of control performance, robustness, computational complexity and design issue. The proposed mechanism exhibits acceptable tuning and control performance with very small steady-state tracking errors, and provides very short settling time for parameter convergence.     

Asymptotic stabilization of a class of nonlinear systems with long input delay in the presence of disturbance

Asymptotic stabilization of a class of nonlinear systems with known constant long input delay is addressed in the presence of external disturbance by applying sliding mode control method. Modified prediction variable scheme is employed to compensate long delays in the input, where conventional prediction variable approaches cannot be employed. This is mainly due to the fact that the external disturbance appears in the prediction variable, which renders the controller dependent on the external disturbance. In order to tackle this problem, the nonlinear disturbance observer based predictor is used. A suitable disturbance observer is designed to estimate the external disturbance that appears in the prediction variable. Respected to some existing results, the prediction-based control for more general class of the nonlinear systems in the presence of external disturbance is the main contribution of this paper. Actuator and sensor delays exist in the most common dynamic systems. So, the proposed control scheme can be employed in many conventional systems. The simulation results indicate the robustness and efficiency of the proposed controller.     

Performance-based parameter tuning method of model-driven PID control systems

In this paper, performance-based parameter tuning method of model-driven Two-Degree-of-Freedom PID (MD TDOF PID) control system has been proposed to enhance the control performances of a process. Known for its ability of stabilizing the unstable processes, fast tracking to the change of set points and rejecting disturbance, the MD TDOF PID has gained research interest recently. The tuning methods for the reported MD TDOF PID are based on internal model control (IMC) method instead of optimizing the performance indices. In this paper, an Integral of Time Absolute Error (ITAE) zero-position-error optimal tuning and noise effect minimizing method is proposed for tuning two parameters in MD TDOF PID control system to achieve the desired regulating and disturbance rejection performance. The comparison with Two-Degree-of-Freedom control scheme by modified smith predictor (TDOF CS MSP) and the designed MD TDOF PID tuned by the IMC tuning method demonstrates the effectiveness of the proposed tuning method.     

Robust friction compensation for submicrometer positioning and tracking for a ball-screw-driven slide system

Ball-screw-driven slide systems are largely used in industry for motion control applications. Their performance using standard proportional-integral-derivative (PID) control algorithm is unsatisfactory in submicrometer motion control because of nonlinear friction effects. In this article, controllers based on a bristle-type nonlinear contact model are developed and implemented for submicrometer motion. For submicrometer positioning, a proportional-derivative (PD) control scheme with a nonlinear friction estimate algorithm is developed, and its performance is compared with that of a PID controller. For tracking, a disturbance observer was added to reject external disturbances and to improve robustness. The experimental results indicate that the proposed controller has consistent performance in positioning with under 1.5% of steady-state error in the submicrometer range. For tracking performance, the proposed controller shows good and robust tracking with respect to parameter variation.     

Enhanced disturbance rejection for open-loop unstable process with time delay

The present study suggests a disturbance estimator design method for application to a recently published, two-degree-of-freedom, control scheme for open-loop, unstable processes with time delay. A simple PID controller cascaded with a lead-lag filter replaces the high-order disturbance estimator for enhanced performance. A new analytical method on the basis of the IMC design principle, featuring only one user-defined tuning parameter, is developed for the design of the disturbance estimator. Several illustrative examples taken from previous works are included to demonstrate the superiority of the proposed disturbance estimator. The results confirm the superior performance of the proposed disturbance estimator in both nominal and robust cases. The proposed method also offers several important advantages for industrial process engineers: it covers several classes of unstable process with time delay in a unified manner, and is simple and easy to design and tune.     

Precision motion control with a high gain disturbance compensator for linear motors

In this paper, we address the problem relating to the precision control of permanent magnet linear motors to track repeated motion trajectories. A high gain disturbance compensator is developed to improve the control performance degraded due to the presence of significant disturbances. An inverse gain of the overall system model is used to set up a disturbance observer. The observed disturbance is then used to generate a "knocker" signal, to be augmented to the control signal, which can provide the additional energy necessary to overcome the effects of the disturbances. A learning scheme is used to adjust the knocker signal iteratively over the repeated cycles. Simulation and experimental results are furnished to demonstrate the effectiveness of the proposed control scheme.