Proportional-integral-derivative Sliding Mode Controller Research Articles

Robust Adaptive Super-Twisting Sliding Mode Stability Control of Underactuated Rotational Inverted Pendulum With Experimental Validation

In this study, an adaptive proportional-integral-derivative (PID) sliding mode control technique combined with the super-twisting algorithm is planned for the stabilization of rotational inverted pendulum in the appearance of exterior perturbation. The state-space model of rotational inverted pendulum in the existence of exterior disturbance is attained. Then, the super-twisting PID sliding mode controller is designed for finite time stability control of the considered underactuated control system. The upper bounds of perturbation are presumed to be unknown; consequently, the adaptive control procedure is taken into account to approximate the uncertain bounds of external disturbances. The stability control of rotational inverted pendulum system is verified by means of the Lyapunov stability theory. In order to validate the accuracy and efficiency of the recommended control technique, some simulation outcomes are prepared and compared with other existing scheme. Finally, the experimental results are implemented to show the success of the designed method.

Coordinated control of a 3DOF cartesian robot and a shape memory alloy-actuated flexible needle for surgical interventions: a non-model-based control method

SummarySuccess of any needle-based medical procedures depends on accurate placement of the needle at the target location. However, accurate targeting and control of flexible self-actuating (active) needle are challenging. We have developed a shape memory alloy-actuated flexible needle steered by a 3D Cartesian robot and performed a comparative study of four, non-model-based, coordinated control methodologies for the combined robot steering and flexible-needle insertion process for surgical interventions. Investigated four controllers are: proportional–integral–derivative (PID), PID with the cubic of positional error term (PID-P3), static PID sliding mode controller, and robust adaptive PID sliding mode controller (RAPID-SMC). Relative efficacies of these controllers are demonstrated by performing experiements using a tissue-mimicking soft material phantom. Results from experiments have reavealed that RAPID-SMC is superior to other three controllers.

Practical finite time vibration suppression of mechatronic systems using proportional–integral–derivative variable structure controls with dead-band nonlinearity

Vibration is an intrinsic phenomenon in many mechanical and mechatronic applied devices and undesirable vibration can either degrade the performance of the system or lead to unpredictable outputs. The main purpose of this article is to introduce a novel second-order proportional–integral–derivative sliding mode control methodology to suppress the undesirable vibrations of a class of applied dynamical systems with applications to mechatronic and mechanical devices. After designing a nonlinear proportional–integral–derivative terminal sliding manifold, rigorous mathematics are provided to guarantee that the origin is a practical finite time stable equilibrium point. Consequently, two efficient control laws are proposed to ensure the occurrence of the sliding motion with and/or without system unknown parameters. Motivated by situations encountered in practice, unknown lumped uncertainties are also added to the system and their impacts are tackled using adaptive control techniques. Furthermore, a hard nonlinear dead-band function is utilized in the control input and its effects such as lags and delays appeared on the control signals as well as on the system outputs are dealt with by the proposed proportional–integral–derivative variable structure controller. The proposed second-order variable structure controller not only utilizes the simple effective design approach of the proportional–integral–derivative controllers to ensure a reasonable transient performance, but also displays fast convergence properties demonstrated in non-singular terminal sliding modes. Finally, through simulation studies, it is confirmed that the proposed control strategy is effective in vibration attenuation of microelectromechanical resonators.

Performance investigation and control parameters choice for sliding mode control of coupled tanks system

In several food processing and chemical industries, liquid is pumped and kept in interrelating coupled tanks. However, automatic regulation of the liquid level and flow control between these tanks is a challenging problem because of the complexity and high non linearity of such system. This paper deals with the liquid level control of two horizontal coupled tanks system. A comprehensive comparative study is made for most popular sliding mode control (SMC) algorithms found in literature, namely Proportional-Derivative Sliding Mode Control (PD-SMC), Proportional-Integral-Derivative SMC (PID-SMC), Fractional Order SMC and finally dynamic SMC. Special emphasis is put on the effect of the sensor noise on the controller performance. Simulated experiments including robustness to variation in plant parameters and step input disturbances are made. Control algorithms parameters are selected to optimize designed performance indices by using MATLAB optimization toolbox. Simulation results reveal that dynamic SMC is superior to other control algorithms in the presence of sensor noise and has a significant reduction in the actuator chattering phenomenon.

Adaptive RBF-PIDSMC control method with estimated model parameters for a piezo-actuated stage

The aim of this work is to find an adaptive control scheme to realize precise position tracking for a piezo-actuated stage, which is usually very difficult to control due to the essential nonlinearity and unknown uncertainty. Firstly, a proportional-integral-derivative (PID) sliding mode controller is designed based on the established model and the estimated parameters. Then, in order to reduce the influence of model error, a radial basis function (RBF) neural network is integrated to the controller to improve the control performance. Eventually, an adaptive RBF based PID-type sliding mode controller (RBF-PIDSMC) is proposed and its stability is derived mathematically based on Lyapunov theory. Simulation results of the proposed controller are compared with the PID sliding mode controller to verify its tracking performance. Positioning tracking experiments with two different trajectories are also conducted to verify the correctness and effectiveness of the proposed controller. We can conclude that the proposed controller can be used to track commanded position trajectory for the piezoelectric stage.

A new robust closed-loop control system for electrosurgical generators

Commercially available electrosurgical generator (ESG) depends on circuit topologies that are responsive to changes in resistance of the tissue. This change in resistance varies the amount of power delivered, especially amid arcing. Changes in resistance along the body make it even harder to keep the power delivery and voltage in limits. An important property of ESG is to be able to keep the output power constant in the constant power region. In this work, a closed-loop control system is designed and tested for ESG to improve its performance in the nonlinear constant power region. A quantitative study of a buck converter and boost inverter is presented along with the closed-loop response for the ESG unit. A comparative analysis of two control methods, i.e., proportional integral derivative (PID) and proportional integral derivative sliding mode control (PIDSMC), is presented for the ESG unit. Results confirm that the presented closed-loop system can highly improve the performance of the ESG system and PIDSMC is found to be a more suitable choice.

Control of SMES systems in distribution networks with renewable energy integration: A perturbation estimation approach

Electrical energy storage system (EESS) plays a crucial role to handle the intermittency and randomness of renewable energy, such that the power reliability can be significantly enhanced. This paper attempts to design an adaptive fractional-order sliding-mode control (AFOSMC) approach for a typical EESS technology, e.g., superconducting magnetic energy storage (SMES) systems, to improve its dynamical responses against varirous operation conditions. At first, a sliding-mode state and perturbation observer (SMSPO) is applied to estimate the combined effect of unmodelled dynamics, parameter uncertainties, and external disturbances of SMES systems. Then, a fractional-order sliding-mode control (FOSMC) is utilized to completely compensate the perturbation estimat, such that a noticeable robustness can be achieved. Moreover, only the dq-axis currents need to be measured while the perturbation estimate replaces its upper bound, thus AFOSMC be easily achieved with appropriate control costs. For the purpose of validating its control performance, a distribution network involving SMES system with renewable energy penetration is studied. The control performance of conventional proportional-integral-derivative (PID) control, interconnection and damping assignment passivity-based control (IDA-PBC), sliding-mode control (SMC), and fractional-order sliding-mode control (FOSMC) is compared to that of AFOSMC under three scenarios. Simulation results show that AFOSMC can greatly outperform other approaches in both tracking speed and overall costs, e.g., its active power error is only 63.55%, 83.44%, 69.60%, and 76.67% of that of PID control, IDA-PBC, SMC, and FOSMC under reactive and active power supply, while the required control costs is only 76.69%, 91.28%, 83.50, and 86.76% to the above three controllers. Finally, a hardware-in-the-loop (HIL) test based on dSpace is implemented to verify its practicability under various scenarios.

Comparison of Fractional Order PID Controller and Sliding Mode Controller with Computational Tuning Algorithm

The industry processes involving punching, lifting, and digging usually require high precision, high force and long operating hours that increase the prestige in the usage of the electrohydraulic actuator (EHA) system. These processes with the companion of the EHA system usually possess high dynamic complexities that are hard to be controlled and require well-designed and powerful control system. Therefore, this paper will involve the examination of the designed controllers which is applied to the EHA system. Firstly, the conventional proportional-integral-derivative (PID) controller which is the famous controller in the industry is designed. Then, the improved PID controller, which is known as the fractional order PID (FO-PID) controller is designed. After that, the design of the gradually famous robust controller in the education field, which is the sliding mode controller (SMC) is performed. Since the controller's parameters are essentially influencing the performance of the controller, the meta-heuristic optimization method, which is the particle swarm optimization (PSO) tuning method is applied. The variation in the system's parameter is applied to evaluate the performance of the designed controllers. Referring to the outcome analysis, the increment of 59.3% is obtained in the comparison between PID and FOPID, while the increment of 67.13% is obtained in the comparison of the PID with the SMC controller. As a conclusion, all of the controllers perform differently associated with their own advantages and disadvantages.

Globally finite-time stable three-dimensional trajectory-tracking control of underactuated UUVs

In this paper, the subject of the spatial trajectory-tracking control for underactuated unmanned underwater vehicles (UUVs) is addressed in the presence of model parameter perturbation and unknown ocean currents. The spatial trajectory-tracking guidance is established based on the dynamic virtual vehicle method, which continuously computes the desired motion states of an UUV to be used by the motion control system. The globally finite-time control strategy is proposed based on the proportional-integral-derivative sliding mode control (PID-SMC), which globally stabilizes all trajectory-tracking errors in the finite time. By all simulation results showing, this trajectory-tracking control strategy can drive the underactuated UUV with ±20% model parameter perturbation to track the predefined desired trajectory accurately in the three-dimensional space. All simulation results fully indicate that the tracking controller offer highly flexibility and strongly robustness in connection with the model parameters uncertainties.

Design of Smoothing FOPID Sliding Mode Controlled Robotic Manipulator for Robotic-Assisted Surgery

Robotic-assisted surgery (RAS) is a mode of technical advancement in the medical field that utilizes robotic articulation to aid surgeries. The fine-motion and precise control of robotic manipulator is prerequisite in surgical applications. In this paper, the improved control methodology for controlling the 3DOF (degree of freedom) robotic manipulator’s motion named as smoothing fractional order proportional integral derivative-sliding mode control (FOPID-SMC) for the attainment of finest results by eliminating the perturbations has been showcased. The performance of smoothing FOPID-SMC controller in robotic manipulator is compared with the conventional SMC controllers. The simulation results prominently illustrate the efficacy of the proposed methodology, and superior tracking and robust performance with alleviated chattering compared to the classical methodologies.

Real-time implementation of SMC–PID for Magnetic Levitation System

Magnetic levitation is significant in almost all arenas of engineering. This principle is used to levitate objects such as a bullet train, flywheel, etc. This paper presents an experimental set-up of Magnetic Levitation System (MLS) in which a ball is levitated to a desired position and is sustained at a desired level for a stipulated time. The ball position is measured using an optoelectronic sensor and a controller is used to determine the time span of the ball at desired heights. To achieve this, a Sliding Mode Controller (SMC) is designed in such a way so as to regulate the current, which in turn controls the position through an electromagnet. Real-time observations of such ball positions have been recorded and compared to those of conventional PID (Proportional Integral Derivative) and robust SMC. Disturbance rejection, servo operation and set point tracking have also been tested and verified for the same. The outcome of such results processed through MATLAB proves that SMC’s performance is predominant over other controllers.

Dynamic global proportional integral derivative sliding mode control using radial basis function neural compensator for three-phase active power filter

An adaptive dynamic special global sliding mode controller that is based on proportional integral derivative (PID) sliding surface using radial basis function (RBF) neural network (NN) for a three- phase active power filter (APF) was presented in this paper. To overcome the problems associated with the schemes of the conventional sliding mode control, a global PID sliding manifold is introduced to realize the whole process of robustness and inhibition of the steady state error, accelerating the system response meanwhile. In addition, the nested dynamic sliding mode controller can reduce the influence of chattering that may lead to malfunction of the insulated gate bipolar transistor (IGBT) caused by sign function in the control law, achieving a better property. Moreover, owing to the parameter uncertainties and the external disturbances, a RBF neural estimator is added to eliminate the chattering phenomenon that further optimizes the performance of the system. Eventually, simulation studies in the MATLAB/SimPower Systems Toolbox verify the outstanding performance of the designed RBFNN dynamic global PID sliding mode controller in three different conditions, and some comparisons are made at the same time to demonstrate the excellent properties of the raised control method.

SU‐F‐J‐10: Sliding Mode Control of a SMA Actuated Active Flexible Needle for Medical Procedures

Purpose:In medical interventional procedures such as brachytherapy, ablative therapies and biopsy precise steering and accurate placement of needles are very important for anatomical obstacle avoidance and accurate targeting. This study presents the efficacy of a sliding mode controller for Shape Memory Alloy (SMA) actuated flexible needle for medical procedures.Methods:Second order system dynamics of the SMA actuated active flexible needle was used for deriving the sliding mode control equations. Both proportional‐integral‐derivative (PID) and adaptive PID sliding mode control (APIDSMC) algorithms were developed and implemented. The flexible needle was attached at the end of a 6 DOF robotic system. Through LabView programming environment, the control commands were generated using the PID and APIDSMC algorithms. Experiments with artificial tissue mimicking phantom were performed to evaluate the performance of the controller. The actual needle tip position was obtained using an electromagnetic (EM) tracking sensor (Aurora, NDI, waterloo, Canada) at a sampling period of 1ms. During experiment, external disturbances were created applying force and thermal shock to investigate the robustness of the controllers.Results:The root mean square error (RMSE) values for APIDSMC and PID controllers were 0.75 mm and 0.92 mm, respectively, for sinusoidal reference input. In the presence of external disturbances, the APIDSMC controller showed much smoother and less overshooting response compared to that of the PID controller.Conclusion:Performance of the APIDSMC was superior to the PID controller. The APIDSMC was proved to be more effective controller in compensating the SMA uncertainties and external disturbances with clinically acceptable thresholds.

Adaptive neural dynamic global PID sliding mode control for MEMS gyroscope

In this paper, a dynamic global proportional integral derivative (PID) sliding mode controller based on an adaptive radial basis function (RBF) neural estimator is developed to guarantee the stability and robustness in the presence of a lumped uncertainty for a micro electromechanical systems (MEMS) gyroscope. This approach gives a new dynamic global PID sliding mode manifold, which not only enables system trajectory to run on the global sliding mode surface at the start point more quickly and eliminates the reaching phase of the conventional sliding mode control, but also restrains the steady-state error and reduces the chattering via a dynamic PID sliding surface. A RBF neural network (NN) system is employed to estimate the lumped uncertainty and eliminate the chattering phenomenon at the same time. Additionally, adaptive laws and dynamic global PID sliding control gains that ensure the asymptotic stability of the close-loop system are proposed, together with the techniques for deciding which kind of basis function should be selected. Finally, simulation results demonstrate the effectiveness of RBFNN dynamic global PID sliding mode control method, meanwhile some comparisons are made to verify the good properties of the suggested control approach.

Globally finite-time stable tracking control of underactuated UUVs

This paper addresses the problem of trajectory tracking control for underactuated unmanned underwater vehicles (UUVs) with model parameter perturbation and constant unknown current in the horizontal plane. The globally finite-time tracking control strategy is adopted driving an UUV to track a predefined trajectory. Firstly, the horizontal trajectory tracking guidance laws are established by the virtual vehicle method, where the tracking error equations are derived. Secondly, the kinematic controllers are designed with equivalent control of the proportional-integral-derivative sliding mode control (PID-SMC). Thirdly, two dynamic controllers, including a speed controller and a steering controller, are designed by resorting to a first-order sliding mode surface and a second-order one, respectively. It is well proved that the proposed strategy can guarantee global convergence of all tracking errors within finite time. Simulations show that the control laws can achieve strongly robust and preferably control performance for the horizontal trajectory tracking control in the presence of the mode parameter perturbation and constant unknown current.

An Output-Tracking-Based Discrete PID-Sliding Mode Control for MIMO Systems

Due to its ability to reject disturbance, sliding mode control (SMC) has been widely employed in various control applications with the presence of uncertainty and/or disturbance. However, chattering, caused by the switching function used in SMC, can greatly deteriorate its performance, and thus, limit its applications. In addition to chattering, the application of SMC to a multi-input–multi-output (MIMO) system becomes more challenging due to the coupling effects between the control variables. This paper presents the development of an output-tracking-based discrete proportional-integral-derivative SMC (PID-SMC) for MIMO systems, in which the problem of output tracking is defined to the one of state tracking by using the model reference approach. The developed control scheme allows for both achieving the zero steady-state error and eliminating the chattering problem. For validation, experiments were performed on a commercially available three degrees-of-freedom nanopositioning stage with the developed control scheme, as compared to a traditional PID controller. Experimental results illustrate that with the developed control scheme, the positioning performance of the stage can be significantly improved, including the zero steady-state error and eliminated chattering.

A new variable structure PID-controller design for robot manipulators

In this brief, a new variable structure proportional-integral-derivative (PID) controller design approach is considered for the tracking stabilization of robot motion. The work corroborates the utility of a certain PID sliding mode controller with PID sliding surface for tracking control of a robotic manipulator. Different from the general approach, the conventional equivalent control term is not used in this controller because that needs to use the matching conditions and exact full robot dynamics knowledge, which involves unavailable parameter uncertainties. Though the sliding surface includes also the integral error term, which makes the robot tracking control problem complicated, the existence of a sliding mode and gain selection guideline are clearly investigated. Moreover, different from uniformly ultimately boundedness, the global asymptotic stability of the robot system with proposed controller is analyzed. The sliding and global stability conditions are formulated in terms of Lyapunov full quadratic form and upper and lower matrix norm inequalities. Reduced design is also discussed. The proposed control algorithm is applied to a two-link direct drive robot arm through simulations. The simulation results indicate that the control performance of the robot system is satisfactory. The chattering phenomenon is handled by the use of a saturation function replaced with a pure signum function in the control law. The saturation function results in a smooth transient performance. The proposed approach is compared with the existing alternative sliding mode controllers for robot manipulators in terms of advantages and control performances. A comparative analysis with a plenty of simulation results soundly confirmed that the performance of developed variable structure PID controller is better under than those of both classical PID controller and an existing variable structure controller with PID-sliding surface.