Nonlinear PD Research Articles

Dual objective nonlinear PD sliding mode control based on a reference model for an active suspension system

Dual objective nonlinear PD sliding mode control based on a reference model for an active suspension system

On designing a configurable UAV autopilot for unmanned quadrotors.

Unmanned Aerial Vehicles (UAVs) and quadrotors are being used in an increasing number of applications. The detection and management of forest fires is continually improved by the incorporation of new economical technologies in order to prevent ecological degradation and disasters. Using an inner-outer loop design, this paper discusses an attitude and altitude controller for a quadrotor. As a highly nonlinear system, quadrotor dynamics can be simplified by assuming several assumptions. Quadrotor autopilot is developed using nonlinear feedback linearization technique, LQR, SMC, PD, and PID controllers. Often, these approaches are used to improve control and to reject disturbances. PD-PID controllers are also deployed in the tracking and surveillance of smoke or fire by intelligent algorithms. In this paper, the efficiency using a combined PD-PID controllers with adjustable parameters have been studied. The performance was assessed by simulation using matlab Simulink. The computational study conducted to assess the proposed approach showed that the PD-PID combination presented in this paper yields promising outcomes.

Adaptive Nonlinear PD Controller of Two-Wheeled Self-Balancing Robot with External Force

Adaptive Nonlinear PD Controller of Two-Wheeled Self-Balancing Robot with External Force

DESIGN OF A VARIABLE GAIN NONLINEAR FUZZY CONTROLLER AND PERFORMANCE ENHANCEMENT DUE TO GAIN VARIATION

In this paper, variable gain nonlinear PD and PI fuzzy logic controllers are designed and the effect of the variable gain characteristic of these controllers is analyzed to show its contribution in enhancing the performance of the closed loop system over a conventional linear PID controller. Simulation results and time domain performance characteristics show how these fuzzy controllers outperform the conventional PID controller when used to control a nonlinear plant and a plant that has time delay.

Mathematical Modelling and Analysis of the Simplest Fuzzy Two-Input Two-Output Two-Term Controller of Takagi−Sugeno Type

Mathematical modelling of the simplest Takagi−Sugeno fuzzy Two-Input Two-Output (TITO) Proportional-Integral/Proportional-Derivative (PI/PD) controller is presented in this paper. Mathematical model of fuzzy PI/PD controller is proposed using Algebraic Product (AP) t-norm, Bounded Sum (BS) t-co-norm and Center of Gravity (CoG) defuzzifier. The inputs are fuzzified by fuzzy sets having <i>L</i> and <inline-formula id="M2"> <math id="mathml_M2" display="inline" overflow="scroll"><mi>Γ</mi></math></inline-formula> type membership functions. The rule base consists of five rules with different linear models in the consequent parts. Both static and dynamic coupling is taken into account while deriving the models. The model of the fuzzy PI/PD controller reveals that it is a variable gain/structure controller. Also, each output of the TITO fuzzy controller is the sum of two nonlinear PI or PD controllers with variable gains. The properties and the gain variations of the controllers are investigated.

Nonlinear tracking differentiator and PD controller for piezoelectric actuators in a robotic hand

This article deals with the modeling and control design for piezoelectric actuators of a micro-robotic system. Piezoelectric actuators generally exhibit complex and nonlinear behavior due to their inherent asymmetric hysteresis phenomenon, creep nonlinearity, and oscillatory characteristics. Moreover, these actuators are subject to an external disturbance force caused by the interaction with the manipulated objects. It has been shown in practice that these characteristics have a negative and significant impact on the performance of piezoelectric actuators, which increases the difficulty of their control. The main objective of this paper is to account simultaneously for all undesired and complex characteristics outlined above. To this end, our main idea is to lump the hysteresis and creep phenomena, as well as the disturbing manipulation force together as one total disturbance term. The total disturbance is first estimated in real-time via a nonlinear tracking differentiator, then feedback control law is designed to compensate for the disturbance and achieve a good transient profile. To validate and demonstrate the efficacy of the proposed approach, experiments are conducted, and results obtained are discussed.

Safety action over oscillations of a beam excited by moving load via a new active vibration controller.

This paper presents a mixed active controller (NNPDCVF) that combines cubic velocity feedback with a negative nonlinear proportional derivative to reduce the nonlinear vibrating behavior of a nonlinear dynamic beam system. Multiple time-scales method treatment is produced to get the mathematical solution of the equations for the dynamical modeling with NNPDCVF controller. This research focuses on two resonance cases which are the primary and 1/2 subharmonic resonances. Time histories of the primary system and the controller are shown to demonstrate the reaction with and without control. The time-history response, as well as the impacts of the parameters on the system and controller, are simulated numerically using the MATLAB program. Routh-Hurwitz criterion is used to examine the stability of the system under primary resonance. A numerical simulation, using the MATLAB program software, is obtained to show the time-history response, the effect of the parameters on the system and the controller. An investigation is done into how different significant effective coefficients affect the resonance's steady-state response. The results demonstrate that the main resonance response is occasionally impacted by the new active feedback control's ability to effectively attenuate amplitude. Choosing an appropriate control Gaining quantity can enhance the effectiveness of vibration control by avoiding the primary resonance zone and unstable multi-solutions. Optimum control parameter values are calculated. Validation curves are provided to show how closely the perturbation and numerical solutions are related.

Clinical Trajectory control for lower Knee rehabilitation using ADRC method

The design and study of the Active Disturbance Rejection Control (ADRC) approach for control and disturbance rejection for lower knee rehabilitation utilizing a residential exoskeleton system are provided in this paper. Linear ADRC (LADRC) and Nonlinear ADRC (NADRC) are two controllers that are considered for control purposes based on the structure of ADRC. The contrasts between them are thoroughly discussed in this work. The LADRC is made up of a tracking differential (TD), a linear proportional derivative (LPD) controller, and a linear extended state observer (LESO), whereas the NADRC is made up of the same LESO but with a nonlinear PD (NPD) and a modified optimized TD (MTD). In terms of robustness against the ability to reject applied disturbances, a comparison of LADRC and NADRC has been done. The fundamental challenge with ADRC is that its constituent parameters must be fine-tuned. Grey Wolf Optimizer (GWO) has been proposed for tuning the parameters of ADRC to have the least amount of error variation in order to improve the controlled system's dynamic performance. When a prescribed disturbing torque is applied, the results of a MATLAB simulation show that the LADRC has greater disturbance rejection capabilities than the NADRC.

On global trajectory tracking control of robot manipulators with a delayed feedback

In this paper, the trajectory tracking control problem of a robot manipulator with cylindrical joints is considered by means of a nonlinear PD controller taking into account the delayed feedback structure. The conclusion about stability of a closed-loop system is obtained on the basis of the development of the direct Lyapunov method in the study of the stability property for a non-autonomous functional differential equation by constructing a Lyapunov functional with a semi-definite time derivative.

Practical robust nonlinear PD controller for cable-driven parallel manipulators

Practical robust nonlinear PD controller for cable-driven parallel manipulators

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.

New controller (NPDCVF) outcome of FG cylindrical shell structure

This paper presents a new active controller technique effect of functionally graded (FG) cylindrical shell structure model within joint harmonic and parametric excitations. The new active controller involves Nonlinear Proportional-Derivative (NPD) plus Negative Cubic Velocity Feedback (NCVF) as a new nonlinear control method (NPDCVF). The motivation of this study is the well-known observation that NPDCVF control method can offer a means to improve the performance of plant systems. The coupled nonlinear differential equations with two modes have been derived applying the von Kármán nonlinear theory, Galerkin’s process, and the static condensation technique. Static condensation is the process of decreasing the number of free displacements or degrees of freedom. We have added other three different controller methods over the structure to select the best controller. The three applied controller methods to the considered structure are: Integral Resonant Control (IRC), Positive Position Feedback (PPF), and Nonlinear Integral Positive Position Feedback (NIPPF) which are applied to the considered structure. We establish that the best one for dipping the high vibration amplitudes is the NPDCVF as a new controller. The perturbation technique is useful to solve the present model including quadratic and cubic nonlinearities subjected to mixed harmonic and parametric forces within the simultaneous primary resonance case (Ω=ω1,Ω=ω2) as the worst resonance case of the system. All numerical outcomes have been completed with the help of MATLAB Ra 18.0 program software over the investigated model. The obtained results have proved that this new controller is excellent for improving the structure by reducing the risky vibrations caused during primary resonances. Frequency response equations have helped in observing the stability examination of the obtained numerical solutions. The actions of several factors performed on the controlled model have been examined and described. Some comparisons have also been prepared with the available recent published papers of a similar model.

Self-Adjusting Fuzzy Logic Based Control of Robot Manipulators in Task Space

End effector tracking control of robot manipulators subject to dynamical uncertainties is the main objective of this article. Direct task space control that aims minimizing the end effector tracking error directly is preferred. In the open loop error system, the vector that depends on uncertain dynamical terms is modeled via a fuzzy logic network and a self-adjusting adaptive fuzzy logic component is designed as part of the nonlinear proportional derivative based control input torque. The stability of the closed-loop system is investigated via Lyapunov based arguments and practical tracking is proven. The viability of the proposed control strategy is shown with experimental results. Extensions to uncertain Jacobian case and kinematically redundant robots are also presented.

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.

Differential Correspondences and Control Theory

When a differential field K having n commuting derivations is given together with two finitely generated differential extensions L and M of K, an important problem in differential algebra is to exhibit a common differential extension N in order to define the new differential extensions L∩M and the smallest differential field (L,M ) ⊂ N containing both L and M. Such a result allows to generalize the use of complex numbers in classical algebra. Having now two finitely generated differential modules L and M over the non-commutative ring D = K [d1,...,dn] = K [d] of differential operators with coefficients in K, we may similarly look for a differential module N containing both L and M in order to define L∩M and L+M. This is exactly the situation met in linear or non-linear OD or PD control theory by selecting the inputs and the outputs among the control variables. However, in many recent books and papers, we have shown that controllability was a built-in property of a control system, not depending on the choice of inputs and outputs. The purpose of this paper is thus to revisit control theory by showing the specific importance of the two previous problems and the part plaid by N in both cases for the parametrization of the control system. An important tool will be the study of differential correspondences, a modern name for what was called Bäcklund problem during the last century, namely the elimination theory for groups of variables among systems of linear or nonlinear OD or PD equations. The main difficulty is to revisit differential homological algebra by using noncommutative localization as a way to generalize the symbolic calculus in the style of Heaviside and Mikusinski. Finally, when M is a D-module, this paper is using for the first time the fact that the system R = homK (M,K) is a D-module for the Spencer operator acting on sections, avoiding thus behaviours, trajectories and signal spaces in a purely formal way, contrary to a few recent works on this difficult subject.

Trajectory tracking control of delta parallel robot based on disturbance observer

Delta parallel robot is widely used in the manufacturing process of food, medicine, electronics and military industries, which is a highly nonlinear system with strongly uncertain dynamics. Therefore, there are many difficulties in the controller design of delta robot. Based on the simplified dynamic model, a nonlinear PD+ controller with nonlinear disturbance observer is proposed for Delta parallel robot in this article, which can realize high-precision trajectory tracking in high-speed and high-acceleration motion. Then, the asymptotic stability of the closed-loop system’s equilibrium point is proven by utilizing Lyapunov techniques and LaSalle’s invariance theorem. It is obvious that the proposed controller is significantly less dependent on the accuracy of the dynamic model. Besides, a disturbance observer based on the generalized momentum is constructed, which can effectively observe and compensate the disturbances. What’s more, the constructed disturbance observer avoids the calculation of the inverse of inertia matrix, which will greatly improve the response speed of the controller. The simulation results show that the proposed controller can assure better trajectory tracking accuracy in high-speed and high-acceleration motion. And the disturbance observer can effectively estimate the disturbance. The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article:This work was supported by the National Natural Science Foundation of China (grant number51474320).

Robust trajectory‐tracking in finite‐time for robot manipulators using nonlinear proportional‐derivative control plus feed‐forward compensation

AbstractIn this article, we propose a novel nonlinear control scheme for the trajectory tracking in finite‐time of robot manipulators. Our control proposal is composed of two parts: a proportional‐derivative (PD) nonlinear feedback and a feed‐forward compensation term. The (discontinuous) nonlinear PD term is designed like a twisting sliding mode controller that ensures robust global uniform finite‐time stabilization of the tracking error, in spite of model uncertainties and nonvanishing perturbations. Moreover, in order to decrease the (possible) chattering phenomena, we also propose two alternatives: a variable‐gain version and a continuous version of the PD term. The feed‐forward term allows us to deal intelligently with Coriolis and gravity effects because the compensation for these terms is generated off‐line. In the continuous case, practical stability is guaranteed in the presence of model uncertainties and nonvanishing perturbations. The stability conclusions are established, in both cases, designing novel strict Lyapunov functions.

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.

Single saturated PD control for asymptotic attitude stabilisation of spacecraft

This study revisits the problem of attitude stabilisation for rigid spacecraft with actuator constraints in the framework of non-linear proportional–derivative (PD) control methodology. A simple single saturated PD (SSPD) control is proposed. The most appealing features of the proposed SSPD control are that it completely embeds the control action within only a single saturation function for every actuator and omits the elaborate discrimination of the terms that shall be bounded for the commonly-used saturated control and hence it is easy for practical implementation with an improved performance. Lyapunov's direct method is employed to show asymptotic attitude stabilisation. Two illustrative examples are presented to demonstrate the improved performance of the proposed approach.

Population pharmacokinetics and pharmacodynamics of a novel vascular adhesion protein-1 inhibitor using a multiple-target mediated drug disposition model

ASP8232 is a novel inhibitor of vascular adhesion protein-1 that was under evaluation for reducing residual albuminuria in patients with diabetic kidney disease. To characterize the pharmacokinetics (PK) of ASP8232 and its effect on vascular adhesion protein 1 (VAP-1) plasma activity and VAP-1 concentrations (pharmacodynamics, PD) in an integrated and quantitative manner, a target mediated drug disposition model was developed based on pooled data from four completed clinical trials with ASP8232 in healthy volunteers, and in patients with diabetic kidney disease and diabetic macular edema, respectively. In this model, the binding of ASP8232 to its soluble and membrane-bound target in the central and peripheral compartments were included. The model was able to adequately describe the non-linear PK and PD of ASP8232. The observed difference in PK between healthy volunteers and renally impaired patients could be explained by an effect of baseline estimated glomerular filtration rate on ASP8232 clearance and relative bioavailability. The relationship between ASP8232 concentration and VAP-1 inhibition was successfully established and can be applied to simulate drug exposure and degree of VAP-1 inhibition for any given dose of ASP8232 across the spectrum of renal function.