2-DOF Proportional–integral–derivative Controller Research Articles

DS based 2-DOF PID controller for various integrating processes with time delay

This study proposes a direct synthesis-based two-degree-of-freedom (2-DOF) controller for various types of integrating processes with time delays. This 2-DOF controller includes a proportional-integral-derivative (PID) controller to enhance load disturbance rejection performance and a set-point filter to improve servo response performance. The main PID controller parameters are expressed as process model parameters and a single adjustment variable, while the set-point filter is composed of PID controller parameters with weighted factors. The adjustment variable is tuned to achieve an optimal balance between response performance and robustness, based on the maximum magnitude of the sensitivity function (Ms). Controller parameters for various Ms values and guidelines for setting these parameters are provided in a consistent formulaic form using a curve-fitting method. These parameter-setting formulas facilitate the accurate implementation of PID controllers with specified Ms values and allow the controller design to be extended to processes with larger dimensionless time delays for a given Ms value. Although a 2-DOF controller was proposed, the adjustment variable for setting the parameters of the main PID controller and the set-point filter was solely the desired time constant. The proposed method was applied to various integrating processes with time delays, and its performance was compared with existing methods reported in the literature, based on performance indices such as settling time, overshoot, integral of absolute error, total variation in input usage, and global performance index. Simulations were conducted using six examples of various integrating processes with time delays to verify the effectiveness and applicability of the proposed controller.

LQ optimal robust multivariable PID control for dynamic positioning of ships with norm-bounded parametric uncertainties

The design of a suitable controller for dynamic positioning (DP) of ships is a challenging task keeping the hydrodynamic uncertainties in mind. The magnitude and rate constraints on the actuators make the problem more difficult. The present work employs a two-degree-of-freedom (2-DOF), multivariable, proportional–integral–derivative (PID) control for DP of a ship. To design the controller, first, the ship dynamics with hydrodynamic parameter uncertainties is represented in an uncertain state-space descriptor form. Then, the design of feedback gains of 2-DOF PID controller for the uncertain descriptor plant is converted into a state feedback design for an augmented uncertain descriptor plant. Next, a linear matrix inequality-based condition is obtained to solve this state feedback problem in order to ensure a desired linear quadratic (LQ) performance, even in presence of uncertainties. Finally, to further improve the tracking performance, the feedforward gain of the 2-DOF PID controller is designed using H∞ approach. The DP performance of the proposed controller is tested for the considered ship model along with uncertainties, actuator constraints, and environmental disturbances. A comparison with the existing PID controllers is also carried out to show superiority of the proposed controller.

Investigation of 2DOF PID Controller for Physio-Therapeutic Application for Elbow Rehabilitation

The aim of this work is to evaluate the output of a two-degree of freedom (DOF) proportional integral derivative (PID) controller for controlling elbow flexion and extension on an upper limb rehabilitation robot of an existing model. Since the usage of upper limb rehabilitation is increasing dramatically because of human impairment, 2DOF has been proposed in this work as a suitable controller. The 2DOF PID controller offers set-point-weight features and, hence, is fast in removing disturbance from the system and ensuring system stability. Importantly, as the system parameters are unknown in this work, the black-box model approach has been taken into consideration, using the MATLAB System identification toolbox to estimate a model. The best-fitted estimated model is then coupled with the proposed controller in the MATLAB/Simulink environment that, upon successful simulation works, leads, finally, to the hardware implementation. Three different amplitudes of sinusoidal current signals, such as 0.3 amps, 0.2 amps, and 0.1 amps, are applied for hardware measurements. Considering patients’ physical conditions. In this work, the 2DOF controller offers a fast transient response, settling time, negligible tracking error and 0% overshoot and undershoot.

Optimized four-parameter PID controller for AVR systems with respect to robustness

A procedure for the optimization of the proportional-integral-derivative (PID) controller under constraints to robustness of model uncertainties and sensitivity to measurement noise for a synchronous generator (SG) automatic voltage regulator (AVR) is presented in this paper. Performance indices related to the load disturbance response such as integral error (IE) and integral absolute error (IAE) are used as key criteria for the design method. They are minimized for a given maximum modulus of sensitivity function Ms. By maximizing loop gain regarding given sensitivities Ms and Mn we optimized load disturbance response. Contrary to majority AVR PID controller procedures, along with proportional, integral and derivative gain, a noise filter time constant is included in a proposed optimization algorithm to satisfy given sensitivity to the measurement noise Mn. A simple and effective solution of the optimization problem is obtained by binding a ratio between the integral and the derivative time constant Ti/Td. The optimal Ti/Td ratio is determined subsequently. Besides this, a step response to voltage reference change is modified with a reference filter to avoid large overshoots. This is achieved by limiting the maximum modulus of the resulting close-loop transfer function sensitivity Msp. The fact that zeros and poles of the second order reference filter have the same damping factor simplifies the procedure for resolving two out of six parameters. Also, two additional conditions result in the fact that three design parameters {Ms, Mn, Msp} are sufficient to determine the required six parameters of the two-degree-of-freedom (2DOF) PID controller. Such controller outperforms recently presented AVR controllers especially regarding the load disturbance rejection. Experiment tests with no-load SG and SG connected on the grid are carried out to prove the claims stated in this work concerning robustness performance and sensitivity to measurement noise. Also, we showed practical use of the proposed controller parameter tuning procedure by experimental runs performed on a lab generator.

Real-Time Implementation of a Stable 2 DOF PID Controller for Unstable Second-Order Magnetic Levitation System with Time Delay

The design of a two degree of freedom (DOF) proportional–integral–derivative (PID) controller is proposed in this paper to stabilize an unstable second-order plant having time delay. The lower and upper bounds of the controller gains for which the compensated system will exhibit a stable response, is determined using Hermite–Biehler theorem. In order to determine the bounds of the controller gains, this work proposes an extension of the Hermite–Biehler theorem, suitable for the transfer function of the maglev plant, which contains a negative dc-gain and a missing ‘s’ term in the denominator polynomial. The optimal values of the controller gains, from the range thus estimated, are found by a recent bio-inspired algorithm, namely symbiotic organisms search (SOS). The obtained results have been experimentally verified, and it has been validated that the 2-DOF PID controller exhibits better response. The robustness of the compensated system for 1-DOF and 2-DOF configurations, in the presence of external disturbance and measurement noise, has also been validated in real time, and it is observed that the 2-DOF PID controller improves the robustness of the system, as compared to its 1-DOF counterpart.

Radial position control for magnetically suspended high‐speed flywheel energy storage system with inverse system method and extended 2‐DOF PID controller

To achieve high-precision position control for the active magnetic bearing high-speed flywheel rotor system (AMB-HFRS), a novel control strategy based on inverse system method and extended two-degree-of-freedom (2-DOF) proportional–integral–derivative (PID) controller is proposed in this study. First, the inverse system method is employed to decouple the AMB flywheel rotor system with strong non-linear and coupling, into four independent subsystems. Subsequently, extended 2-DOF PID controllers are used to regulate the decoupled subsystems, to obtain good performances of disturbance rejection and tracking simultaneously. In the extended 2-DOF PID controller, a differential signal is produced by a velocity observer to improve the ability of against noise. Finally, the characteristics of stability, tracking, disturbance rejection and robustness of the control strategy proposed are analysed in theory, and its ability and effectiveness to control the radial position of the AMB-HFRS are further studied by simulations and experiments. It is shown that the control strategy proposed can keep the AMB-HFRS suspending stably from static state to the speed of 24,000 rpm, has the advantages of good tracking, high disturbance rejection, strong robustness and good ability of against noise.

Real-Time implementation and performance analysis of robust 2-DOF PID controller for Maglev system using pole search technique

In recent times, Magnetic Levitation (Maglev) technology has gained huge popularity in different fields of research. Transportation, nuclear, aerospace, biomedical, civil and electrical engineering are some of the areas where the presence of Maglev technology is prominent. But because of the inherent nonlinear and unstable behaviour, the task of designing a suitable controller becomes very challenging for the control engineers. In this paper, a simple but effective approach has been proposed for the design of 2-DOF Proportional-Integral-Derivative (PID) controller for the control of Maglev system in simulation and real-time for the very first time, to the best of author's knowledge. The controller parameter values have been analytically obtained by optimizing the location of closed loop poles in the s-plane which eventually minimizes the Integral Square Error (ISE) of the closed loop system along with the controller. As the controller parameters are found by searching the best pole location, we name it as pole search technique. The performance of the controller has been compared with those of the 1 & 2-DOF Integer Order and Fractional Order PID and I-PD controllers designed for the same Maglev plant. The result of the comparison reveals that the 2-DOF PID controller, designed in this paper, outperforms other controllers in terms of maximum overshoot, settling time, Integral Absolute Error (IAE), Integral Time Absolute Error (ITAE) and Integral Time Square Error (ITSE). Moreover, to illustrate the loop robustness property, input and output disturbances have been applied in real-time simulation environment and sensitivity and complementary sensitivity analysis have been performed. Additionally, to show the applicability of the proposed technique apart from Maglev, 2-DOF PID controller has been designed for the Ball and Beam and Coupled Tank system and their performance has been compared with the existing results.

Combined Resonant Controller and Two-Degree-of-Freedom PID Controller for PMSLM Current Harmonics Suppression

This paper presents a new control method to suppress current harmonics for permanent magnet synchronous linear motor (PMSLM) that is applied in the miniature microsecond laser cutting system. In the control method, the resonant–two-degree-of-freedom (R–2DOF) proportional–integral–derivative (PID) controller is proposed by combining a resonant controller and a two-degree-of-freedom (2DOF) PID controller. The current harmonic components are first analyzed. The resonant controller is subsequently added to the current loop in parallel to the traditional PI controller to suppress the current harmonic components. However, with the current harmonics suppression, the resonant controller can result in the overshoot in the current loop response. The 2DOF PID controller is adopted to reduce the overshoot. Thus, an R–2DOF PID controller is developed by combining the resonant controller and 2DOF PID controller. Meanwhile, the stability of the proposed controller is analyzed. Compared with the traditional PID controller and the Kalman filter, the proposed controller not only can suppress the current harmonics but can reduce the overshoot and thrust ripple as well. Finally, the simulation and experimental comparison results confirm the validity of the proposed control algorithm.

Design of Controller for Automatic Voltage Regulator Using Teaching Learning Based Optimization

Abstract In this paper, One Degree Of Freedom (1DOF) and Two Degrees Of Freedom (2DOF) Proportional + Integral + Derivative (PID) controller design is proposed and implemented on the Automatic Voltage Regulator (AVR) system using traditional Teaching Learning Based Optimization (TLBO) algorithm. Minimization of a multi-objective function guides the TLBO algorithm's exploration until the process converges with an optimal solution. A simulation study is carried to examine the performance of TLBO assisted controller design procedure for three, four and five dimensional searches. The performance of the proposed method is validated with most successful heuristic procedures, such as Particle Swarm Optimization (PSO), Bacterial Foraging Optimization (BFO) and Firefly Algorithm (FA). The result show that, 1DOF PID controller and PID controller with filter offers smooth reference tracking response and the 2DOF PID controller with the Feed Forward (FF) and Feed Back (FB) structure presents reduced time domain and error values compared to the alternatives.