Optimal PD/PID control of smart base isolated buildings equipped with piezoelectric friction dampers

Long-period pulses in near-field earthquakes lead to large displacements in the base of isolated structures.To dissipate energy in isolated structures using semi-active control,piezoelectric friction dampers（PFD） can be employed.The performance of a PFD is highly dependent on the strategy applied to adjust its contact force.In this paper,the seismic control of a benchmark isolated building equipped with PFD using PD/PID controllers is developed.Using genetic algorithms,these controllers are optimized to create a balance between the performance and robustness of the closed-loop structural system.One advantage of this technique is that the controller forces can easily be estimated.In addition,the structure is equipped with only a single sensor at the base floor to measure the base displacement.Considering seven pairs of earthquakes and nine performance indices,the performance of the closed-loop system is evaluated.Then,the results are compared with those given by two well-known methods：the maximum possive operation of piezoelectric friction dampers and LQG controllers.The simulation results show that the proposed controllers perform better than the others in terms of simultaneous reduction of floor acceleration and maximum displacement of the isolator.Moreover,they are able to reduce the displacement of the isolator systems for different earthquakes without losing the advantages of isolation.

N-PD cross-coupling synchronization control based on adjacent coupling error analysis

In order to improve the trajectory tracking precision and reduce the synchronization error of a 6-DOF lightweight robot, nonlinear proportion-deviation （N-PD） cross-coupling synchronization control strategy based on adjacent coupling error analysis is presented. The mathematical models of the robot, including kinematic model, dynamic model and spline trajectory planing, are established and verified. Since it is difficult to describe the real-time contour error of the robot for complex trajectory, the adjacent coupling error is analyzed to solve the problem. Combined with nonlinear control and coupling performance of the robot, N-PD cross-coupling synchronization controller is designed and validated by simulation analysis. A servo control experimental system which mainly consists of laser tracking system, the robot mechanical system and EtherCAT based servo control system is constructed. The synchronization error is significantly decreased and the maximum trajectory error is reduced from 0.33 mm to 0.1 mm. The effectiveness of the control algorithm is validated by the experimental results, thus the control strategy can improve the robot＇s trajectory tracking precision significantly.

Repetitive PD control strategy with inverse transfer function compensation for CVCF inverter

A novel repetitive control strategy for the output waveform of single-phase CVCF inverters is presented. In this scheme, the inverse transfer function of inverter is used as a compensator to obtain stable and satisfy harmonic rejection. Besides, PD controller is adopted to improve transient performance. Simulation and experimental results, which are gotten from a DSP-based 400Hz, 5.5KW inverter, indicate that the proposed control scheme can achieve not only low THD during steady-state operation but also fast transient response during load step change.

Decentralized PD Control for Non-uniform Motion of a Hamiltonian Hybrid System

In this paper, a decentralized proportional-derivative （PD） controller design for non-uniform motion of a Hamiltonian hybrid system is considered. A Hamiltonian hybrid system with the capability of producing a non-uniform motion is developed. The structural properties of the system are investigated by means of the theory of Hamiltonian systems. A relationship between the parameters of the system and the parameters of the proposed decentralized PD controller is shown to ensure local stability and tracking performance. Simulation results are included to show the obtained non-uniform motion.

Stability Improvement of Power System by Using PI ＆ PD Controller

This paper presents the model of a SVC （Static VAR Compensator） which is controlled externally by a PI （Proportional Integral） ＆ PD （Proportional Differential） controllers for the improvements of voltage stability and damping effect of an on line power system. Both controller parameters has been optimized by using Ziegler-Nichols close loop tuning method. Both single phase and three phase （L-L） faults have been considered in the research. In this paper, a power system network is considered which is simulated in the phasor simulation method ＆ the network is simulated in four steps; without SVC, With SVC but no externally controlled, SVC with PI controller ＆ SVC with PD controller. Simulation result shows that without SVC, the system parameters become unstable during faults. When SVC is imposed in the network, then system parameters become stable. Again, when SVC is controlled externally by PI ＆ PD controllers, then system parameters becomes stable in faster way then without controller. It has been observed that the SVC ratings are only 50 MVA with controllers and 200 MVA without controllers. So, SVC with PI ＆ PD controllers are more effective to enhance the voltage stability and increases power transmission capacity of a power system. The power system oscillations are also reduced with controllers in compared to that of without controllers. So with both controllers the system performance is greatly enhanced.

Intelligent Dynamic Inversion Controller Design for Ball and Beam System

The Ball and beam system(BBS)is an attractive laboratory experimental tool because of its inherent nonlinear and open-loop unstable properties.Designing an effective ball and beam system controller is a real challenge for researchers and engineers.In this paper,the control design technique is investigated by using Intelligent Dynamic Inversion(IDI)method for this nonlinear and unstable system.The proposed control law is an enhanced version of conventional Dynamic Inversion control incorporating an intelligent control element in it.The Moore-PenroseGeneralized Inverse(MPGI)is used to invert the prescribed constraint dynamics to realize the baseline control law.A sliding mode-based intelligent control element is further augmented with the baseline control to enhance the robustness against uncertainties,nonlinearities,and external disturbances.The semi-global asymptotic stability of IDI control is guaranteed in the sense of Lyapunov.Numerical simulations and laboratory experiments are carried out on this ball and beam physical system to analyze the effectiveness of the controller.In addition to that,comparative analysis of RGDI control with classical Linear Quadratic Regulator and Fractional Order Controller are also presented on the experimental test bench.

Quadcopter UAV Modeling and Automatic Flight Control Design

The mathematical model of quadcopter-unmanned aerial vehicle （UAV） is derived by using two approaches： One is the Newton-Euler approach which is formulated using classical meehanics; and other is the Euler-Lagrange approach which describes the model in terms of kinetic （translational and rotational） and potential energy. The proposed quadcopter＇s non-linear model is incorporated with aero-dynamical forces generated by air resistance, which helps aircraft to exhibits more realistic behavior while hovering. Based on the obtained model, the suitable control strategy is developed, under which two effective flight control systems are developed. Each control system is created by cascading the proportional-derivative （PD） and T-S fuzzy controllers that are equipped with six and twelve feedback signals individually respectively to ensure better tracking, stabilization, and response. Both pro- posed flight control designs are then implemented with the quadcopter model respectively and multitudinous simulations are conducted using MATLAB/Simulink to analyze the tracking performance of the quadcopter model at various reference inputs and trajectories.

Portable Dynamic Positioning Control System on A Barge in Short-Crested Waves Using the Neural Network Algorithm

This paper develops a nonlinear mathematical model to simulate the dynamic motion behavior of the barge equipped with the portable outboard Dynamic Positioning （DP） system in short-crested waves. The self-tuning Proportional- Derivative （PD） controller based on the neural network algorithm is applied to control the thrusters for optimal adjustment of the barge position in waves. In addition to the wave, the current, the wind and the nonlinear drift force are also considered in the calculations. The time domain simulations for the six-degree-of-freedom motions of the barge with the DP system are solved by the 4th order Runge-Kutta method which can compromise the efficiency and the accuracy of the simulations. The technique of the portable alternative DP system developed here can serve as a practical tool to assist those ships without being equipped with the DP facility while the dynamic positioning missions are needed.

Nonlinear observer-controller design for dynamic positioning of ships

The main focus is nonlinear model-based dynamic positioning (DP) control system design. A nonlinear uniform global exponential stability (UGES) observer produces noise-free estimates of the position, the slowly varying environmental disturbances and the velocity, which are used in a proportional-derivative (PD) + feedforward control law. The stability of this observer-controller system is proved by introducing a specific nonlinear cascaded system. The simulation results have successfully demonstrated the performance of designed DP control system.

Proportional integral derivative controller design using Legendre orthogonal functions

The Legendre orthogonal functions are employed to design the family of PID controllers for a variety of plants. In the proposed method, the PID controller and the plant model are represented with their corresponding Legendre series. Matching the first three terms of the Legendre series of the loop gain with the desired one gives the PID controller parameters. The closed loop system stability conditions in terms of the Legendre basis function pole(λ) for a wide range of systems including the first order, second order, double integrator, first order plus dead time, and first order unstable plants are obtained. For first order and double integrator plants, the closed loop system stability is preserved for all values of λ and for the other plants, an appropriate range in terms of λ is obtained. The optimum value of λ to attain a minimum integral square error performance index in the presence of the control signal constraints is achieved. The numerical simulations demonstrate the benefits of the Legendre based PID controller.

Design and control of multiple spacecraft formation flying in elliptical orbits

Spacecraft formation flying is an attractive new concept in international aeronautic fields because of its powerful functions and low cost. In this paper, the formation design and PD closed-loop control of spacecraft formation flying in elliptical orbits are discussed. Based on two-body relative dynamics, the true anomaly is applied as independent variable instead of the variable of time. Since the apogee is considered as the starting point, the six integrating constants are calculated. Therefore, the algebraic solution is obtained for the relative motion in elliptical orbits. Moreover, the formation design is presented and both circular formation and line formation are provided in terms of an algebraic solution. This paper also discusses the PD-closed loop control for precise formation control in elliptical orbits. In this part, the error-type state equation is put forward and the linear quadratic regulator （LQR） method is used to calculate PD parameters. Though the gain matrix calculated from LQR is time-variable because the error-type state equation is time variable, the PD parameters are also considered as constants because of their small changes in simulation. Finally, taking circular formation as an example, the initial orbital elements are achieved for three secondary spacecraft. And the numerical simulation is analyzed under PD formation control with initial errors and J2 perturbation. The simulation results demonstrate the validity of PD closed-loop control scheme.

Stability and bifurcation control of a neuron system under a novel fractional-order PD controller

In this paper, we address the problem of bifurcation control for a delayed neuron system. By introducing a new fractional-order Proportional-Derivative(PD) feedback controller, this paper aims to control the stability and Hopf bifurcation through adjusting the control gain parameters. The order chosen in PD controller is different with that of the integer-order neuron system. Sufficient conditions for guaranteeing the stability and generating Hopf bifurcation are constructed for the controlled neuron system. Finally,numerical simulation results are illustrated to verify our theoretical derivations and the relationships between the onset of the Hopf bifurcation and the gain parameters are obtained.

A Three-axis PD Control Model for Bumblebee Hovering Stabilization

Flight stabilization in insects is normally achieved through a closed-loop system integrating the intemal dynamics and feedback control. Recent studies have reported that flight instability may exist in most flying insects but how insects achieve the flight stabilization still remains poorly understood. Here we propose a control model specified for bumblebee hovering stabilization by applying a three-axis PD （proportional-derivative）-controller to a free-flying bumblebee computational model with six Degrees of Freedom （DoFs）. Morphological and kinematic models of a realistic bumblebee in hovering are built up based on measurements whereas a versatile bio-inspired dynamic flight simulator is employed in simulations. A simplified flight dynamic model is further developed as a fast model for control parameter tuning. Our results demonstrate that the stabilizing control model is capable of achieving the hovering stabilization with small perturbations in terms of 6-DoF, implying that the simplified linear algorithms can still work reasonably for bumblebee hovering. A further sensitivity analysis of the control parameters reveals that yaw control via manipulating pitch angle of the wing is mostly sensitive, implicating that bumblebee may utilize alternative yaw control strategies.

Stability and bifurcation analysis of a fractional-order single-gene regulatory model with delays under a novel PD^α control law

In this paper,we propose a novel fractional-order proportional-derivative(PD)strategy to achieve the control of bifurcation of a fractional-order gene regulatory model with delays.The stability theory of fractional differential equations proved that with delays,some explicit conditions for the local asymptotical stability and Hopf bifurcation are given for the controlled fractional-order genetic model.It is demonstrated that the fractional-order gene regulatory model becomes controllable by adjusting the control gain parameters.In addition,the effect of fractional-order parameter on the dynamical behaviors is shown.Finally,numerical simulations are carried out to testify the validity of the main results and the availability of the fractional-order PD controller.

Proportional-derivative Control of Second-order Tethered Satellites System Based on Extended State Observer and Feed-forward Compensation

This paper researches the proportional-derivative(PD)feedback control with feed-forward compensations from input for a triangular tethered satellite system(TTSS),and the extended state observer(ESO)design which is further incorporated in control to estimate the structural uncertainties in system.By expanding Lagrangian equations under chosen variables,the dynamic equations of TTSS are derived which is the second-order nonlinear equation.Then the feedback control under typical feed-forward compensations is discussed as the nonlinear functions in system are counteracted,and the controlled outputs are computed by deriving the transfer functions of the transformed structures.Moreover,in case of the uncertain structures in system which may constrain the control e®ect,ESO-based PD control is further proposed,and the observed error and controlled accuracy are analyzed by Lyapunov functions.Simulation results on the designed controls are presented to validate the theoretic analyses.

Cascaded navigation control for agricultural vehicles tracking straight paths

In precision agriculture(PA),an agricultural vehicle navigation system is essential and the navigation control accuracy is important in this system.As straight path tracking is the major operating mode of agricultural vehicles on large fields,a cascaded navigation control method for straight path tracking is proposed in this study.Firstly,a cascaded navigation control structure for the agricultural vehicle was discussed.Based on this structure,the navigation control task was decomposed into two cascaded control tasks,namely,the path tracking control task and the steering control task.Secondly,a relative kinematics model of agricultural vehicles was deduced,and an optimal Proportional-Derivative(PD)method based on the deduced model was developed in the path tracking control task.Then,an improved PD method based on a transition process was proposed in the steering control task to enhance the performance of the steering control subsystem.Finally,the effectiveness and the superiority of the proposed method were verified by a series of experiments.Results of the experimental data analysis show that mean value of the lateral position deviation is 0.02 m and standard deviation of the lateral position deviation is 0.04 m,which proves that the proposed method has achieved satisfactory effects on the straight path tracking of agricultural vehicles.

An active vibration control method based on energy-fuzzy for cantilever structures excited by aerodynamic loads

In wind tunnel tests for the full-model fixed with sting,the low structural damping of the long cantilever sting results in destructive low-frequency and large-amplitude vibration.In order to obtain high-quality wind tunnel test data and ensure the safety of wind tunnel tests,an energy-fuzzy adaptive PD(Proportion Differentiation)control method is proposed.This method is used for active vibration control of a cantilever structure under variable aerodynamic load excitation,and real-time adjustment of parameters is achieved according to the system characteristics of vibration energy.Meanwhile,a real-time method is proposed to estimate the real-time vibration energy through the vibration acceleration signal,and the average exciting power of aerodynamic load is obtained by deducting the part of the power contributed by the vibration suppressor from the total power.Furthermore,an energy-fuzzy adaptive PD controller is proposed to achieve adaptive control to the changes of the aerodynamic load.Besides,the subsonic and transonic experiments were carried out in wind tunnel,the results revealed that comparing to fixed gain PD controllers,the energy-fuzzy adaptive PD controller maintains higher performance.

Shape control of spacecraft formation using a virtual spring-damper mesh

This paper derives a distance-based formation control method to maintain the desired formation shape for spacecraft in a gravitational potential field. The method is an analogy of a virtual spring-damper mesh. Spacecraft are connected virtually by spring-damper pairs. Convergence analysis is performed using the energy method. Approximate expressions for the distance errors and control accelerations at steady state are derived by using algebraic graph representations and results of graph rigidity. Analytical results indicate that if the underlying graph of the mesh is rigid, the convergence to a static shape is assured, and higher formation control precision can be achieved by increasing the elastic coefficient without increasing the control accelerations. A numerical example of spacecraft formation in low Earth orbit confirms the theoretical analysis and shows that the desired formation shape can be well achieved using the presented method, whereas the orientation of the formation can be kept pointing to the center of the Earth by the gravity gradient. The method is decentralized, and uses only relative measurement information. Constructing a distributed virtual structure in space can be the general application area. The proposed method can serve as an active shape control law for the spacecraft formations using propellantless internal forces.