Nonlinear Proportional Derivative Controller Research Articles

Non Linear Control System for Humanoid Robot to Perform Body Language Movements

In social robotics, especially with regard to direct interactions between robots and humans, the robotic movements of the body, arms and head must make an adequate displacement to guarantee an adequate interaction, both from a functional and social point of view. To achieve this, the use of closed-loop control techniques that consider the complex nonlinear dynamics and disturbances inherent in these systems is required. In this paper, an implementation of a nonlinear controller for the tracking of trajectories and a profile of speeds that execute the movements of the arms and head of a humanoid robot based on the mathematical model is proposed. First, the design and implementation of the arms and head are initially presented, then the mathematical model via kinematic and dynamic analysis was performed. With the above, the design of nonlinear controllers such as nonlinear proportional derivative control with gravity compensation, Backstepping control, Sliding Mode control and the application of each of them to the robotic system are presented. A comparative analysis based on a frequency analysis, the efficiency in polynomial trajectories and the implementation requirements allowed selecting the non-linear Backstepping control technique to be implemented. Then, for the implementation, a centralized control architecture is considered, which uses a central microcontroller in the external loop and an internal microcontroller (as internal loop) for each of the actuators. With the above, the selected controller was validated through experiments performed in real time on the implemented humanoid robot, demonstrating proper path tracking of established trajectories for performing body language movements.

Research on parallel control of CMAC and PD based on U model

In this paper, the nonlinear U model with time-varying coefficients is investigated and the transformation of the nonlinear model is accomplished by the Newton iterative algorithm. Based on the nonlinear U model, a control algorithm with cerebellar model articulation controller and proportional derivative (PD) in parallel is proposed. The algorithm learns online through a neural network while optimizing the output of the PD, which ultimately enables the actual output of the system to track up to the desired output. Considering that the nonlinear object has the characteristic of rapid change with time, the article improves the PD algorithm to nonlinear PD control algorithm to complete the design of the system. The algorithm automatically adjusts the weights according to the error magnitude to complete the controller parameter adjustment, thus reducing the error of the system. The simulation results show that the nonlinear PD algorithm is better than the PD algorithm, meanwhile, the tracking speed and control precision of the system are improved.

Robust Output Feedback Sliding Mode State and Disturbance Observer-based Controller Design for Nonlinear Systems

This study uses an output feedback disturbance observer-based proportional derivative (PD) controller with variable damping ratios for a class of single-input, single-output nonlinear systems in the presence of unknown disturbances. The proposed sliding mode state and disturbance observer, in which the switching term of the output estimation error is employed to counteract the effect of external disturbance, ensures that the estimation error is finally bounded in a neighborhood and reconstructs simultaneously the system state and unknown disturbance. Herein, the characteristics of the proposed observer are presented in the frequency domain, followed by the corresponding analysis in the time domain. A nonlinear PD controller with a variable damping ratio designed using the estimation state and disturbances should achieve low overshoot and short settling time. Finally, the simulation results demonstrate the validity of the proposed method.

Robust nonlinear PD controller for ship steering autopilot system based on particle swarm optimization technique

This paper proposes a new approach for robust nonlinear proportional derivative (PD) controller. In this approach a nonlinear function (sigmoid) is added to the conventional proportional integral derivative (PID) controller with filtering for the derivative, in order to improve system response and to reduce the effects of the nonlinearity and uncertainty due to variations of hydrodynamic coefficients of ship with the speed. The gains of nonlinear PD controller are tuned by applying particle swarm optimization (PSO) technique. The simulated results by MATLAB program give satisfactory performance with regard to maximum overshoot, settling time and zero steady state error for step, ramp and proposed trajectory as input to the system. The robustness of the autopilot was checked by changing the plant parameters and adding disturbance to the plant input. The used autopilot is nonlinear PD controller because the gain of integral term by PSO is approximately zero which simplifies the controller construction. The results show that the proposed controller has superior transient response and robustness on the conventional PID designed by using symmetrical optimum criterion with pole assignment technique.

Sensitivity analysis and vibration control of asymmetric nonlinear rotating shaft system utilizing 4-pole AMBs as an actuator

This article aimed to control the lateral vibrations of an asymmetric vertically supported nonlinear rotating shaft system. The system is molded as a two-degree-of-freedom nonlinear system having external and multi-parametric excitations. A combination of both the linear and nonlinear proportional-derivative controller is proposed to control the system dynamics. Four poles active magnetic bearing system is utilized as an active actuator through which controllable magnetic forces are applied to stabilize the considered system. The mathematical model that governing the whole system dynamics is derived. Applying the asymptotic analysis, the slow flow equations of motions are obtained. The system oscillatory behaviors before and after control are explored. The main acquired results showed that the asymmetric rotating shaft system without control could exhibit large vibration amplitudes even for very small eccentricity because asymmetry induced parametric excitations. Moreover, the system may have a single-stable solution, bi-stable solutions, tri-stable solution, or quadri-stable solutions at the same spinning-speed depend on the shaft angular velocity ( Ω ). Besides, the system asymmetry is resulting in the appearance of backward whirling motion besides the forward whirling one. However, the proposed nonlinear controller showed its capability of eliminating the all mentioned undesired phenomena, where the controlled system responded as a linear one with very small forward whirling motion only. Finally, the conditions to prevent the occurrence of rub/impact force between the rotating shaft and the electromagnetic pole legs are discussed.

Act of nonlinear proportional derivative controller for MFC laminated shell

This manuscript presents connect a Proportional-Derivative (PD) controller with a macro-fiber composite (MFC) laminated shell system. Nonlinear equations of the MFC laminated shell have been established. The simultaneous resonance case considered as worst resonance. The main motivation of this research is applying a suitable vibration control to reduce or diminish the high vibration caused by the model. So, we used here PD controller in controlling the behavior MFC laminated shell structure. The goal of using the PD controller is to increase the system stability by improving control since it has an ability to predict the future error of the framework response. This control method makes stability increased, maximum peak overshoot decreased, settling time decreases. This controller is applied to recover the framework transient response. A second-order approximate solution has gained via applying multiple time scale perturbation (MTSP) technique. Every expected resonance case at this approximation order is extracted. After adding the PD-controller of the current framework, it eliminates the vibration amplitudes of the considered structure. Frequency (angular speed) response curves examined at special uncontrolled and controlled coefficients of the system. Finally, the conclusion shows a high efficiency of the measured control algorithm for eliminating vibrations of the modified system. A comparison between other approaches control algorithms had been prepared. The results are compared with the numerical simulations, and this shows a good verification for the approximate solution and for the control algorithm used in this manuscript. A comparison with earlier available papers is involved at the end.

Nonlinear Vibrations Analysis and Dynamic Responses of a Vertical Conveyor System Controlled by a Proportional Derivative Controller

In this paper, we introduce a nonlinear vibrations analysis and dynamic responses of a vertical conveyor system under multi excitation forces. By adding the nonlinear proportional derivative controller (NPD) to the vibrating motion of the vertical vibration conveyor, the energy was transferred between uncontrolled and controlled system. We calculate the approximate solutions of the vibrating system utilizing the method of multiple scales. In addition, we investigate the stability at worst resonance cases using phase plane technique, equations of frequency response, and averaging method. The vertical vibration conveyor behavior was studied numerically at the values of its different parameters. The results exhibit the efficiency of NPD control unit to avoid the oscillations of the vertical conveyor system. Numerical simulations have been carried out using MAPLE and MATLAB software’s to ensure the fidelity of our results. Comparisons are made between analytical and numerical results. Also, findings of the present work are discussed in details and compared with published works.

Nonlinear Structural Control Analysis of an Offshore Wind Turbine Tower System

This paper investigates the vibration control, stability, and energy transfer of the offshore wind turbine tower system with control force and nonlinearity terms. A nonlinear proportional derivative (NPD) controller was connected to the system to reduce a high oscillation amplitude and to transfer the energy in the wind turbine system. Furthermore, the averaging method and Poincaré maps were used with respect to the controlled system to study the stability and bifurcation analysis in the worst resonance cases. The curves of force response and frequency response were plotted before and after the control unit was added to the wind turbine system. In addition, we discuss the performances of the control parameters on the vibration magnitudes. Numerical simulations were carried out with Maple and Matlab algorithms to confirm the analytical results. The results show the effectiveness of the NPD controller in suppressing the nonlinear oscillations of the wind turbine system.

Observation-Based Nonlinear Proportional–Derivative Control for Robust Trajectory Tracking for Autonomous Underwater Vehicles

This paper deals with the design, improvement, and implementation of a nonlinear control strategy to solve the trajectory tracking problem for an autonomous underwater vehicle under model uncertainties and external disturbances. First, a disturbance observer based on high-order sliding mode control is designed to counteract the negative impact of both parametric uncertainties and bounded external disturbances. Then, the nonlinear control is enhanced through injecting the disturbance estimation into the designed controller. The stability of the closed-loop system with the enhanced proposed nonlinear controller is proven by Lyapunov arguments. Finally, real-time experimental results are also provided to demonstrate the effectiveness of the proposed controller.

Experimental Evaluation of a Sectorial Fuzzy Controller Plus Adaptive Neural Network Compensation Applied to a 2-DOF Robot Manipulator

In this paper we propose a novel control architecture that employs an adaptive neural network (NN) for feedforward compensation and a sectorial fuzzy controller in the feedback loop applied to the trajectory tracking control of robot manipulators. Both simulation and experimental results are presented in comparison with the original classic Proportional-Derivative (PD) plus feedforward controller, from which this new proposal is based, and two preliminary versions of the application of feedforward sectorial fuzzy control and feedforward adaptive neural nonlinear PD control to the trajectory tracking control of a two-degree of freedom (2-DOF) robot manipulator. The proposed controller has, in general, better performance than its counterparts in terms of transient response and steady-state error while it maintains one of the main characteristics of fuzzy controllers: Its tolerance to parameter deviation.

A simple nonlinear PD control for faster and high-precision positioning of servomechanisms with actuator saturation

Abstract This paper investigates the problem of high performance motion control for servomechanisms subject to actuator saturation. A very simple but quite effective nonlinear proportional-derivative (PD) control is proposed for faster and high-precision positioning of such systems. The particular reasoning behind our concern on nonlinear PD (NPD) control is that most of practical servomechanisms so far are still controlled by classic proportional-integral-derivative (PID)/PD or nonlinear PID (NPID)/NPD algorithms and these controls do not explicitly take into account actuator constraint. Lyapunov’s direct method is employed to prove global asymptotic positioning stability. The appealing advantages of the proposed control are that it has simple intuitive structure with high computational efficiency and does not involve modelling parameter. An additive feature is that the proposed control has the ability to ensure that actuator constraint is not breached, and thus it completely avoids the instability and degraded or unpredictable motion and thermal or mechanical failure from excessive torque. Simulations and experimental results demonstrate that the proposed approach offers a comparable result over the existing model-dependent nonlinear controls and a much improved performance over the commonly-used model-independent linear PD control for servomechanisms with actuator constraint.

Modeling and Control of a Micro AUV: Objects Follower Approach.

This work describes the modeling, control and development of a low cost Micro Autonomous Underwater Vehicle (-AUV), named AR2D2. The main objective of this work is to make the vehicle to detect and follow an object with defined color by means of the readings of a depth sensor and the information provided by an artificial vision system. A nonlinear PD (Proportional-Derivative) controller is implemented on the vehicle in order to stabilize the heave and surge movements. A formal stability proof of the closed-loop system using Lyapunov’s theory is given. Furthermore, the performance of the -AUV is validated through numerical simulations in MatLab and real-time experiments.

Design and control of a prosthetic leg for above-knee amputees operated in semi-active and active modes

This paper proposes a new prosthesis operated in two different modes; the semi-active and active modes. The semi-active mode is achieved from a flow mode magneto-rheological (MR) damper, while the active mode is obtained from an electronically commutated (EC) motor. The knee joint part of the above knee prosthesis is equipped with the MR damper and EC motor. The MR damper generates reaction force by controlling the field-dependent yield stress of the MR fluid, while the EC motor actively controls the knee joint angle during gait cycle. In this work, the MR damper is designed as a two-end type flow mode mechanism without air chamber for compact size. On other hand, in order to predict desired knee joint angle to be controlled by EC motor, a polynomial prediction function using a statistical method is used. A nonlinear proportional-derivative controller integrated with the computed torque method is then designed and applied to both MR damper and EC motor to control the knee joint angle. It is demonstrated that the desired knee joint angle is well achieved in different walking velocities on the ground ground.

A high-performance flight control approach for quadrotors using a modified active disturbance rejection technique

In practice, the parameters of the flight controller of the quadrotors are commonly tuned experimentally with respect to a certain type of reference, such as the step reference and the unit-ramp reference. In this way, the performance of the flight controller might be affected by the variations of the references in real-time flights. Besides, real-time dynamic effects such as measure noises, external disturbances and input delays, which are usually neglected in the reported works, could easily deteriorate the performances of the flight controllers. This work is thereby motivated to develop a high-performance flight control approach utilizing a modified disturbance rejection technique for the quadrotors suffering from input delays and external disturbances. This control approach is developed in a cascaded structure and the attitude angles are chosen as the pseudo control inputs of the translational flight of the quadrotors. To facilitate the development, the dynamic model of the quadrotors is firstly formulated by including the effects of input delays, and the dynamics of the pseudo control variables are identified through real-time experiments. Based on the identified model, the flight control approach is proposed with a modified active disturbance rejection technique, which consists of a time optimal tracking differentiator, an extended state observer/predictor, and a nonlinear proportional–derivative controller. The tracking differentiator is designed to generate smooth transient profiles for the references, and the extended state observer/predictor is implemented for lumped disturbance estimation and state estimation considering the input delays. With the aid of the tracking differentiator and the extended state observer/predictor, the nonlinear proportional–derivative controller can thereby establish a fast tracking control and effectively reject the estimated disturbances. To verify the feasibilities of this development, comparative tests are carried out in both simulations and experiments. The results show that in the presence of small lumped disturbances, such as the measurement zero-drift, the steady-state errors of the proposed control approach for the ramp responses are less than 2 cm, and in the tests of sinusoidal trajectory tracking, the cross-tracking errors are less than 0.04 m. When with large disturbance airflow that is equivalent to strong breeze, the steady-state error achieved by the proposed flight controller is also less than 10 cm. All of these facts demonstrate the effectiveness of this development.

Finite-time angular velocity observers for rigid-body attitude tracking with bounded inputs

Summary The attitude tracking of a rigid body without angular velocity measurements is addressed. A continuous angular velocity observer with fractional power functions is proposed to estimate the angular velocity via quaternion attitude information. The fractional power gains can be properly tuned according to a homogeneous method such that the estimation error system is uniformly almost globally finite-time stable, irrespective of control inputs. To achieve output feedback attitude tracking control, a quaternion-based nonlinear proportional-derivative controller using full-state feedback is designed first, yielding uniformly almost globally finite-time stable of the attitude tracking system as well as bounded control torques a priori. It is then shown that the certainty equivalent combination of the observer and nonlinear proportional-derivative controller ensures finite-time convergence of the attitude tracking error for almost all initial conditions. The proposed methods not only avoid high-gain injection, as opposed to the semi-global results, but also overcome the unwinding problem associated with some quaternion-based observers and/or controllers. Numerical simulations are presented to verify the effectiveness of the proposed methods.

Improving the nonlinear proportional-derivative control for an MEMS torsional mirror with parametric uncertainties

Fast settling, accurate positioning, and a large tilt angle range are important for MEMS mirrors. Here, residual vibration and the pull-in phenomenon—both major problems affecting the performance of an electrostatically actuated mirror—are investigated. Based on the analysis of a nonlinear proportional-derivative (PD) control with parametric uncertainties, a closed-loop feedback control strategy with a combined control scheme is proposed. This method, combining nonlinear PD control and sliding mode control (SMC), not only inherits the virtue of a good dynamic performance from the nonlinear PD control, but also further improves the robustness with SMC for such MEMS mirrors. Furthermore, this method can be convenient when tuning design gains of the controller to obtain a faster error convergence rate. Numerical simulation results show that with this combined control scheme not only the transient response of the MEMS mirror is improved but the influence of parametric uncertainties and external disturbance is also reduced.

Nonlinear Proportional-Derivative Control Incorporating Closed-Loop Control Allocation for Spacecraft

A novel saturated proportional-derivative control law incorporated with closed-loop control allocation is proposed for spacecraft attitude stabilization in this paper. More specifically, a saturated proportional-derivative-based baseline nonlinear controller is designed to guarantee the globally asymptotic stability under control input/signal constraints. Then, a closed-loop constrained optimal control allocation scheme is employed to distribute the moments synthesized by the baseline controller over the redundant actuators in the presence of constraints due to actuator amplitude and rate constraints. The optimal control solution is to be found by penalizing the control allocation errors and rates using optimal quadratic programming algorithms. A significant feature of this work is that the asymptotic stability with the closed-loop control allocation is guaranteed theoretically. Simulation results are presented to illustrate the performance of the proposed scheme.

Nonlinear pd controllers with gravity compensation for robot manipulators

Abstract A Nonlinear Proportional-Derivative (NPD) controller with gravity compensation is proposed and applied to robot manipulators in this paper. The proportional and derivative gains are changed by the nonlinear function of errors in the NPD controller. The closed-loop system, composed of nonlinear robot dynamics and NPD controllers, is globally asymptotically stable in position control of robot manipulators. The comparison of the simulation experiments in the position control (the step response) of a robot manipulator with two degrees of freedom is also presented to illustrate that the NPD controller is superior to the conventional PD controller in a position control system. The experimental results show that the NPD controller can obtain a faster response velocity and higher position accuracy than the conventional PD controller in the position control of robot manipulators because the proportional and derivative gains of the NPD controller can be changed by the nonlinear function of errors. The NPD controller provides a novel approach for robot control systems.

Adaptive Neural Network Motion Control of Manipulators with Experimental Evaluations

A nonlinear proportional-derivative controller plus adaptive neuronal network compensation is proposed. With the aim of estimating the desired torque, a two-layer neural network is used. Then, adaptation laws for the neural network weights are derived. Asymptotic convergence of the position and velocity tracking errors is proven, while the neural network weights are shown to be uniformly bounded. The proposed scheme has been experimentally validated in real time. These experimental evaluations were carried in two different mechanical systems: a horizontal two degrees-of-freedom robot and a vertical one degree-of-freedom arm which is affected by the gravitational force. In each one of the two experimental set-ups, the proposed scheme was implemented without and with adaptive neural network compensation. Experimental results confirmed the tracking accuracy of the proposed adaptive neural network-based controller.

Active Suspension System Based on Linear Switched Reluctance Actuator and Control Schemes

In this paper, an active suspension system utilizing a low-cost high-performance linear switched reluctance actuator with proportional-derivative (PD) control is presented. With the tracking differentiator (TD) calculating the displacement and its derivatives directly under the presence of noise, velocity and acceleration can be evaluated, and accurate position control can be achieved. Comparison is made between linear and nonlinear PD control methods in terms of various system parameters and road profiles. A nonlinear PD controller with better dynamic responses is evaluated and developed for real-time suspension application. The proposed PD control schemes are simulated, tested, and analyzed to prove its robustness and reliability. Finally, a quarter-car active suspension system prototype is built to demonstrate the effectiveness of the proposed control schemes with experiment results.