Proportional Integral Derivative Feedback Control Research Articles

Pole placement tuning of proportional integral derivative feedback controller for knee extension model

Functional electrical stimulation (FES) has shown potential in rehabilitative exercises for patients recovering from spinal cord injuries. In recent developments, conventional open-loop FES control techniques have evolved into closed-loop systems that employ feedback controllers for automation. However, closed-loop FES systems often face challenges due to muscle non-linear effects, such as fatigue, time delays, stiffness, and spasticity. Therefore, an accurate non-linear knee model is required during the design stage, and precise tuning of the feedback controller parameters is vital. A proportional– integral–derivative (PID) controller is commonly used as a feedback controller due to its simplicity and ease of implementation. However, most PID tuning methods are complex and time consuming. This paper investigates the viability of employing the pole placement technique for tuning a PID controller that regulates the non-linear knee extension model. The pole placement method aims to improve the control and adaptability of the PID controller in closed-loop FES systems, specifically by facilitating knee extension exercises. MATLAB Simulink was used to assess the effectiveness of this tuning approach. Results showed that the PID controller performed satisfactorily without non-linearities, but performance varied with the inclusion of specific non-linearities. The pole placement tuning method facilitated preliminary assessments of PID controller performance, preceding highly advanced optimization.

Tension Control of Twisted String Actuators in Variation of Stiffness and Original Length of Strings

Although several studies have been conducted on the modeling and control of twisted string actuators (TSAs), most have been limited to position control; the studies on tension control are limited. This study proposes an indirect tension control method for TSAs. Through comprehensive loading/unloading experiments involving frequency richness and a wide range of tension inputs, the results showed that the conventional static model is no longer valid with a fixed stiffness and constant original length of the string. Therefore, the proposed method allows the stiffness and original length variation in the static tension model, which is then considered in the control by introducing an estimation method. Second, the proposed method indirectly controls string tension by controlling the rotation angle of the motor. The inverse calculation of the desired rotation angle of the motor to achieve the desired tension is equivalent to adaptively changing feedback gains with respect to the nonlinear varying gear ratio of the TSAs. The proposed estimation method simulated the actual string tension from the low- to high-frequency and from the low- to high-tension regions within a tolerable error range. Therefore, the proposed tension controller demonstrated superior regulating and tracking performance compared with the best-tuned direct proportional–integral–derivative feedback controller in a wide range of desired tensions and bandwidths.

Synergistic PID and Output Feedback Control on Matrix Lie Groups

In this paper, we develop multiple synergistic hybrid feedback control laws for mechanical systems on matrix Lie groups with left-invariant metrics. With the goal of globally asymptotically tracking a desired reference trajectory, we propose a hybrid proportional-derivative (PD) type control law and an output feedback version which only utilizes configuration measurements. Moreover, to ensure global asymptotic tracking in the presence of a constant and unknown disturbance in the system dynamics, we introduce two novel proportional-integral-derivative (PID) type control laws with slightly different properties in terms of gain selection and integral action. The theoretical developments are validated through numerical simulation of an underwater vehicle.

Fuzzy Feedback Control for Electro-Hydraulic Actuators

Electro-hydraulic actuators (EHA) have recently played a significant role in modern industrial applications, especially in systems requiring extremely high precision. This can be explained by EHA’s ability to precisely control the position and force through advanced sensors and innovative control algorithms. One of the promising approaches to improve control accuracy for EHA systems is applying classical to modern control algorithms, in which the proportional–integral–derivative (PID) algorithm, fuzzy logic controller, and a hybrid of these methods are popular options. In this paper, we developed a novel version of the fuzzy control algorithm and linear feedback control method, namely fuzzy linear feedback control, to improve the control performance. To achieve the highest performance, we first designed a mathematical EHA model based on the Matlab/Simulink software packages thanks to the selected parameters, which are similar to a real EHA system. Then, we respectively applied PID, fuzzy PID (FPID), and fuzzy linear feedback control (FLFC) before comparing them to have a full view of the outstanding advantages of the proposed algorithm. The simulation results showed that the proposed FLFC algorithm is approximately 99% and 77% superior in performance to the PID and feedback control algorithms, respectively.

A novel online analyzer for accurate and rapid measurement of volatile fatty acids in anaerobic wastewater treatment

Volatile fatty acids (VFAs), which are largely generated during the anaerobic acidification process, are considered to be reliable indicators of the stable process operation. However, the common methods for monitoring VFAs are offline, and they are typically manual requiring time-consuming, costly and complex instruments. This study aims to develop a novel online analyzer for automatic measuring VFAs, which was based on the 5-pH point titration, embedded with a proportional-integral-derivative (PID) feedback control system. The results show that it can achieve accurate and rapid monitoring of VFAs ranging between 0-400 mg/L (<9 min/sample) but simultaneously faces the problems of overtitration and interference of complex characteristics of wastewater. In order to improve its accuracy and stability, the effects of three general coefficients (KI,KP, and KD) of PID on the titration were investigated, and the optimal values of KI, KP, and KD were found to be 1.5, 1.0, and -1.0~0.5, respectively. Besides, the initial titration speed was set at 0.06 mL/min, equal to the minimum speed of the peristaltic pump, and the dichotomy approach was integrated into the PID feedback controller. Owing to the above improvements, the relative mean deviation and standard deviation of measuring VFAs in both synthetic and real wastewaters were mostly lower than 5.0% and 5.0 mg/L, proving the online analyzer is rapid, accurate and reliable.

Hysteresis Compensation for a Piezoelectric Actuator of Active Helicopter Rotor Using Compound Control.

Active rotor with trailing-edge flaps is a promising method to alleviate vibrations and noise level of helicopters. Hysteresis of the piezoelectric actuators used to drive the flaps can degrade the performance of an active rotor. In this study, bench-top tests are conducted to measure the nonlinear hysteresis of a double-acting piezoelectric actuator. Based on the experimental data, a rate-dependent hysteresis model is established by combining a Bouc–Wen model and a transfer function of a second order system. Good agreement is exhibited between the model outputs and the measured results for different frequencies. A compound control regime composed of a feedforward compensator and PID (Proportional–Integral–Derivative) feedback control is developed to suppress the hysteresis of this actuator. Bench-top test results demonstrate that this compound control regime is capable to suppress hysteresis at different frequencies from 10 Hz to 60 Hz, and errors between the desired actuator outputs and the measured outputs are reduced dramatically at different frequencies, revealing that this compound control regime has the potential to be implemented in an active helicopter rotor to suppress actuator hysteresis.

IMC-based diesel oxidation catalyst outlet temperature control with extended state predictor observer

It is of significant importance in the thermal regeneration process of diesel particulate filter that the diesel oxidation catalyst (DOC)-outlet gas temperature is accurately controlled to ensure efficient and safe regenerations. However, this is challenging because the DOC is a nonlinear and time-varying system which has complex oxidation reactions and large time delay, together with uncertainties and high frequency disturbances in real applications. To this end, an intuitive and effective control strategy which integrates the internal model control (IMC)-based design with the extended state predictor observer (ESPO) is proposed in this work. Firstly, a reduced first-order plus delay model, which is derived from a control-oriented one-dimensional DOC model, is deployed and experimentally validated to facilitate the model-based control design. Then, an IMC-based proportional–integral–derivative feedback control strategy, and an active disturbance rejection control (ADRC)-based ESPO are explored and designed. The IMC-based controller is designed for required set-point tracking and the ESPO is introduced for disturbance estimation and mitigation. In addition, as the regeneration is usually performed in real driving cycles, a feedforward control law based on the principle of energy balance is also well developed and integrated for compensation for the measurable transient disturbances. Simulation results show that a reduction of about 15% in recovery time can be achieved by introducing the ESPO into the IMC-based design. Performance of the proposed control strategy is finally validated on the engine bench and in on-vehicle real driving conditions under the worldwide harmonized light vehicles test cycle with new and aged DOCs. Experimental results show that, when the ESPO is introduced, it is more accurate to provide adequate set-point tracking in real applications where both the external disturbances and internal parameter uncertainties are presented.

Hybrid feedback PID-FxLMS algorithm for active vibration control of cantilever beam with piezoelectric stack actuator

FxLMS (Filtered-x Least Mean Square) algorithm and PID (Proportional Integral Derivative) controller have been widely used for AVC (Active Vibration Control). Yet, the convergence rate and vibration suppression performance are restricted by each other for both the classical FxLMS algorithm and the traditional PID controller. A hybrid PID-FxLMS algorithm which combines the feedback FxLMS algorithm and PID controller is proposed, and applied to improve the vibration control efficiency of piezoelectric cantilever beam. In order to conveniently install the piezoelectric stack on the beam structures, a new piezoelectric stack actuator is designed and installed at the root of cantilever beam. Meanwhile, a coupled finite element model of the piezoelectric stack actuator and cantilever beam is established in ABAQUS, and the state-space model of the coupled system is obtained. Subsequently, based on the obtained state-space model, an AVC simulation and experimental system is built to verify the effectiveness of the proposed algorithm. Numerical and experimental results show that convergence rate and vibration suppression performance of the hybrid PID-FxLMS algorithm are much better than that of the classical FxLMS algorithm or traditional PID controller alone, while the hybrid controller also has strong adaptability and anti-noise ability.

Feedforward Plus Feedback Control of an Electro-Hydraulic Valve System Using a Proportional Control Valve

The output feedback signal of the electro-hydraulic valve system (EHVS) affects the activation of its right or left envelope function; thus, even weak measurement noise can cause high-frequency switching between the two envelope functions, leading to chattering in the control input. Consequently, feedforward and feedback controllers in a cascaded configuration generate undesirable chattering in the output signal. We propose a practical and reliable control approach for an EHVS actuated by a proportional control valve. The proposed controller has a parallel structure comprising an inverse generalized Prandtl–Ishlinskii (P–I) model-based feedforward controller, with both hydraulic dead-zone and flow saturation limits, for compensating asymmetric hysteretic behavior. Further, the proposed controller comprises a robust proportional-integral-derivative (PID) feedback controller for achieving robustness against disturbances and noises. The proposed parallel structure is independent of the output feedback of the EHVS. Moreover, the proposed robust PID feedback controller guarantees EHVS stability by precisely selecting the cutoff frequency for the sensitivity and complementary sensitivity functions based on the amplitude spectrum of the inverse-model-based feedforward compensation error. The results verify the high reliability of the proposed EHVS control scheme for the precise control of an EHVS actuated by a proportional control valve in practice.

Deep learning controller design of embedded control system for maglev train via deep belief network algorithm

The maglev train has been successful in practice as a new type of ground transportation. Owing to the inherent nonlinearity and open-loop instability of the electromagnetic suspension (EMS) system, an analogue or a digital controller is used to control the maglev trains’ stability. With the rapid development of embedded systems and artificial intelligence, intelligent digital control has begun to replace the conventional analogue control technology creating a new approach to the EMS control system. This paper proposes a hardware module for an embedded levitation controller based on digital signal processor and field programmable gate array, hence producing an open loop mathematical model of the embedded maglev control system. The deep learning controller is then developed based on a deep belief network (DBN) algorithm and a proportional integral derivative feedback controller. The simulations are conducted in the MATLAB environment after training the DBN. Simulation results are compared with those obtained from the conventional controller. Finally, experiments are implemented to examine the feasibility in practice of the application of the DBN into a maglev embedded control system. The system, with the proposed controller, can accurately track the target airgap of 8 mm. The maximum tracking error of sinusoidal trajectory is 0.17 mm and the maximum tracking error of step trajectory is 0.98 mm. Both simulation and experimental results are included in this paper to show that the proposed deep learning controller can be more robust and less complicated to implement in maglev control applications.

Inverse Tangent Functional Nonlinear Feedback Control and Its Application to Water Tank Level Control

This paper explores the significance and feasibility of addressing a notion that the system error of a nonlinear feedback control can be decorated by an inverse tangent function in order to attain a sound energy-efficient performance. The related mathematical model and relevant evaluation of this concept are further illustrated by demonstrating a case study about the control performance of water tank level. The rationale of robust control and theoretical algorithm of Lyapunov stability theorem are outlined to evaluate the effectiveness of nonlinear feedback with inverse tangent function in terms of improving robustness of PID (Proportional–Integral–Derivative) controller and energy-saving capability. By demonstrating five simulations of different scenarios, it ultimately proves that the modified robust PID controller by inverse tangent function meets the requirement of energy-saving capacity. Comparing with the routine PID control, the mean control input of controlling water tank level can be reduced up to 39.2% by using modified nonlinear feedback controller. This nonlinear feedback PID controller is energy efficient and concise for its convenient use, which is feasible to expand its utility to other applications.

An Improved Kinematic Model Predictive Control for High-Speed Path Tracking of Autonomous Vehicles

Kinematic model predictive control (MPC) is well known for its simplicity and computational efficiency for path tracking of autonomous vehicles, however, it merely works well at low speed. In addition, earlier studies have demonstrated that tracking accuracy is improved by the feedback of yaw rate, as it improves the system transients. With this in mind, it is expected that the performance of path tracking can be improved by a cascaded controller that utilizes kinematic MPC to determine desired yaw rate rather than steering angle, and uses proportional-integral-derivative (PID) control to follow the reference yaw rate. However, directly combining MPC with PID feedback control of yaw rate results in a controller with poor tracking accuracy. The simulation results show that the cascaded MPC-PID controller has relatively stable but larger error compared to classic kinematic and dynamic MPC. Based on the analysis of vehicle sideslip angle, a novel path tracking control method is proposed, which is designed using a kinematic MPC to handle the disturbances on road curvature, a PID feedback control of yaw rate to reject uncertainties and modeling errors, and a vehicle sideslip angle compensator to correct the kinematic model prediction. The proposed controller performances involving steady-state and transient response, robustness, and computing efficiency were evaluated on Carsim/Matlab joint simulation environment. Furthermore, field experiments were conducted to validate the robustness against sensor disturbances and time lag. The results demonstrate that the developed vehicle sideslip compensator is sufficient to capture steer dynamics, and the developed controller significantly improves the performance of path tracking and follows the desired path very well, ranging from low speed to high speed even at the limits of handling.

Self-learning control for coordinated collision avoidance of automated vehicles

For the improvement of automotive active safety and the reduction of traffic collisions, significant efforts have been made on developing a vehicle coordinated collision avoidance system. However, the majority of the current solutions can only work in simple driving conditions, and cannot be dynamically optimized as the driving experience grows. In this study, a novel self-learning control framework for coordinated collision avoidance is proposed to address these gaps. First, a dynamic decision model is designed to provide initial braking and steering control inputs based on real-time traffic information. Then, a multilayer artificial neural networks controller is developed to optimize the braking and steering control inputs. Next, a proportional–integral–derivative feedback controller is used to track the optimized control inputs. The effectiveness of the proposed self-learning control method is evaluated using hardware-in-the-loop tests in different scenarios. Experimental results indicate that the proposed method can provide good collision avoidance control effect. Furthermore, vehicle stability during the coordinated collision avoidance control can be gradually improved by the self-learning method as the driving experience grows.

Model-Based Nonlinear Control of the Dielectric Elastomer Actuator With High Robustness and Precision

Abstract Dielectric elastomers (DEs) is one of the promising artificial muscle for soft robots and flexible devices. As one of the key issues for practical applications, the control of DE actuators remains challenging due to the large actuation, electromechanical coupling, and viscoelastic dissipation. Feedforward control and proportional integral derivative (PID) feedback control are recently studied for the control of DE actuators. The control performance is still limited due to the complex dynamic behavior of DE actuators with both nonlinearities and modeling uncertainties. This paper proposes a model-based feedback control for DE actuator, considering nonlinearity of large deformation, electromechanical coupling, and the modeling uncertainties. A nonlinear motion model is proposed and verified by parameter identification experiments. Based on the nonlinear model, we demonstrate a robust control strategy including nonlinear model compensation and robust feedback to decrease the tracking error. The experimental results verify that the control strategy possesses excellent validity to the DE actuator with improved performance compared to the previous strategy of feedforward and PID feedback control. The system design and control strategy of this paper may guide the future design and application of DE actuators, soft robots, and flexible devices.

Design and control of a parallel mechanism haptic master for robot surgery using magneto-rheological clutches and brakes

This article presents tracking control performances of the repulsive force and torque of a haptic master with 6 degrees of freedom, which can be applied to robot-assisted minimally invasive surgeries. The proposed haptic master is activated by two types of actuators that use magneto-rheological fluid: magneto-rheological clutch and magneto-rheological brake. The body segment (or lower part) of the haptic master generates the repulsive forces for the three translational axes using the magneto-rheological clutch, while the wrist segment (or upper part) generates the repulsive torque for the three rotational axes through the use of the magneto-rheological brake. After analyzing the kinematic and dynamic equations, an appropriately sized haptic master is designed and manufactured. The field-dependent force and torque characteristics of the magneto-rheological actuators are experimentally investigated. Then, for successful tracking control performances, a fuzzy plus proportional–integral–derivative feedback controller is used for the repulsive force while a feed-forward controller associated with a hysteretic compensator for the repulsive torque. The effectiveness of the proposed 6-degree-of-freedom haptic master is experimentally validated by demonstrating high tracking accuracy of the force and torque.

Rail pressure control strategy based on pumping characteristics for the common rail fuel system

The control of rail pressure is quite important in the common rail fuel system. Generally, the rail pressure control strategy is a combination of feedforward control and proportional–integral–derivative feedback control. A lumped parameter model of the common rail fuel system is built. Theoretically, the three main factors that affect the rail pressure are engine speed, rail pressure, and fuel injection. With these factors as the control parameters, the feedforward control logic is established. Then, with the basic fuel amount as the proportional–integral–derivative control parameter, the feedback control strategy is improved. The feedforward control is used to determine the basic fuel amount; the proportional–integral–derivative feedback control is used to fine-tune the basic fuel amount based on the deviation of target rail pressure and real rail pressure. Compared with only proportional–integral–derivative feedback control, the computation load of feedback control is reduced and the response speed is increased. In addition, experiments based on a common rail fuel system test rig are completed. The results show that the fuel efficiency of common rail fuel pump decreases with pump speed, and rail pressure increases. The steady-state rail pressure fluctuations are effectively reduced and the dynamic control precision of the common rail fuel system increases when the optimized control method is adopted.

Data-based approach for feedback–feedforward controller design using closed-loop plant data

Feedforward control of measurable disturbances is a useful complement to feedback control because feedforward control performs control actions before a disturbance response occurs in a process output. In contrast to the typical model-based design approach, a novel data-based method for designing both the feedback and feedforward controllers is presented in this paper. The controller design directly exploits closed-loop plant data and does not require an identification of process and disturbance models. A feedback proportional–integral–derivative controller and feedforward lead-lag compensator are sequentially designed on the basis of the closed-loop response data for a set-point change and for a disturbance input, respectively. Because the controller design process uses plant data integrals, the proposed method is robust against measurement noise. Moreover, the proposed design method can be applied to improve existing underperforming feedback and feedforward controllers using routine closed-loop operating data. Simulation studies demonstrated that the proposed method outperforms existing methods in designing a feedback–feedforward control system.

Removal Notice: Self-learning simulations on grouting pressure control by the artificial neural networks for a dynamic system

For the security of dam foundation, the control of grouting pressure is one of the most important issues. In order to avoid the dangerous pressure fluctuation and to improve the control precision, a feedback proportional–integral–derivative control method is proposed in this work. Because the grouting pressure is influenced by many factors such as grouting flow, grouts density and geological conditions, such a proportional–integral–derivative methodology should be tuned. To this end, back-propagation artificial neural networks were employed to model the grouting control process and sensitivity analysis algorithm. Furthermore, to obtain the optimal parameters, an iteration algorithm was adopted in each sampling interval time through the discrete Lyapunov function of the tracking error. The simulation results showed that self-learning tuning was robust and effective, which was meaningful for the realization of the automatic control device in the grouting process.

A control theoretical modelling for velocity tuning of the conveyor belt in a dynamic mixed-model assembly line

This paper proposes a control theoretical modelling to study dynamic behaviour of a mixed-model assembly line. First, an open-loop model is developed for the system, then examined via different conveyor’s velocity values. It is realised that the performance of the system is very sensitive to the velocity; therefore, a closed-loop (CL) model is developed taking feedback from the system. By the use of proportional-integral-derivative (PID) controller and SIMULINK, some interesting results are obtained applying CL model: regardless of the sequence of the products in the line, the total work-overload and idleness always equals to zero. Moreover, less working area within the workstation is required. Based on the statistical analysis, it is found that no significant increase in makespan is imposed by CL model. It is also shown that PID controller is robust not only to the disturbances of the velocity, also to the uncertainties in the assembly operation times. These results are supported by many numerical experiments dealing with different test problems, line configurations and sequences. Finally, using a discrete event simulation model, the proposed approach is applied into a seru production mode. Simulation results show that the feedback PID controller can deal with real-world assembly line problems, successfully.

Non-linear contour tracking using feedback PID and feedforward position domain cross-coupled iterative learning control

In this paper, a position domain cross-coupled iterative learning controller combining proportional–integral–derivative (PID)-type iterative learning control (ILC) and proportional–derivative (PD)-type cross-coupling control (CCC) is presented aiming at non-linear contour tracking in multi-axis motion systems. Traditional individual control methods in the time domain suffer from poor synchronization of relevant motion axes. The complicated computation of coupling gains in CCC and cross-coupled ILC (CCILC) restricts their applications for non-linear contour. The proposed position domain CCILC (PDCCILC) approach introduces a position domain design concept into CCILC to improve synchronization and performance for non-linear contour tracking and it relies less on the accuracy of coupling gains than conventional CCILC. The stability and performance analysis are conducted using a lifted system representation. The contour error vector method is applied to estimate the coupling gains in simulations and experiments. Simulation and experimental results of three typical non-linear contour tracking cases (i.e. semi-circle, parabola and spiral) based on a two-axis micro-motion stage demonstrate superiority and efficacy of the proposed feedback PID and feedforward PDCCILC compared with existing ILC and CCILC in the time domain.