On the stability of two-step predictive controller based on state observer

For input saturated Hammerstein systems, the two-step predictive control strategy is adopted. The first step calculates the desired intermediate variable applying unconstrained linear modal and predictive control. The second step obtains the real-time control action by solving algebraic equation and desaturation. The case of immeasurable state is considered where the observer gain matrix is solved by Sylvester equation. The sufficient closed-loop stability condition is given and the designing and tuning algorithm for the domain of attraction is proposed. The theoretical results are validated by an example.

ROBUST ADAPTIVE CONTROL SCHEME FOR IMPROVING LOW-SPEED PROFILE TRACKING PERFORMANCE OF HYBRID STEPPING MOTOR SERVO DRIVE

A robust adaptive control approach is presented to improve the performance of the control scheme proposed in the authors＇ previous work, aiming at producing a low ripple hybrid stepping motor servo drive for precision profile tracking at a low speed. In order to construct a completely integrated control design philosophy to reduce torque ripple and at the same time to enhance tracking performance, the properties of nonlinear uncertainties in the system dynamics are uncovered, and then incorporated into the design of the controller. The system uncertainties concerned with ripple dynamics and other external disturbances are composed of two categories. The first category of uncertainties with linear parameterization arising from the detention effect is dealt with by the wellknown adaptive control method. A robust adaptive method is used to deal with the second category of uncertainties resulting from the non-sinusoidal flux distribution. The μ-modification scheme is used to cease parameter adaptation by the robust adaptive control law, thus ensuring that the trajectory tracking error asymptotically converges to a pre-specified boundary. Experiments are performed with a typical hybrid stepping motor to test its profile tracking accuracy. Results confirm the proposed control scheme.

A Back-stepping Based Trajectory Tracking Controller for a Non-chained Nonholonomic Spherical Robot

Spherical robot has good static and dynamic stability, which provides it with strong viability in hostile environment, but the lack of effective control methods has hindered its application and development. This article deals with the dynamic trajectory tracking problem of the spherical robot BHQ-2 designed for unmanned environment exploration. The dynamic model of the spherical robot is established with a simplified Boltzmann-Hamel equation, based on which a trajectory tracking controller is designed by using the back-stepping method. The convergence of the controller is proved with the Lyapunov stability theory. Numerical simulations show that with the controller the robot can globally and asymptotically track desired trajectories, both linear and circular.

Real-time multi-step prediction control for BP network with delay

Real time multi step prediction of BP network based on dynamical compensation of system characteristics is suggested by introducing the first and second derivatives of the system and network outputs into the network input layer, and real time multi step prediction control is proposed for the BP network with delay on the basis of the results of real time multi step prediction, to achieve the simulation of real time fuzzy control of the delayed time system.

Iterative Learning Control Algorithm with a Fixed Step

Iterative Learning Control （ILC） captures interests of many scholars because of its capability of high precision control implement without identifying plant mathematical models, and it is widely applied in control engineering. Presently, most ILC algorithms still follow the original ideas of ARIMOTO, in which the iterative-learning-rate is composed by the control error with its derivative and integral values. This kind of algorithms will result in inevitable problems such as huge computation, big storage capacity for algorithm data, and also weak robust. In order to resolve these problems, an improved iterative learning control algorithm with fixed step is proposed here which breaks the primary thought of ARIMOTO. In this algorithm, the control step is set only according to the value of the control error, which could enormously reduce the computation and storage size demanded, also improve the robust of the algorithm by not using the differential coefficient of the iterative learning error. In this paper, the convergence conditions of this proposed fixed step iterative learning algorithm is theoretically analyzed and testified. Then the algorithm is tested through simulation researches on a time-variant object with randomly set disturbance through calculation of step threshold value, algorithm robustness testing,and evaluation of the relation between convergence speed and step size. Finally the algorithm is validated on a valve-serving-cylinder system of a joint robot with time-variant parameters. Experiment results demonstrate the stability of the algorithm and also the relationship between step value and convergence rate. Both simulation and experiment testify the feasibility and validity of the new algorithm proposed here. And it is worth to noticing that this algorithm is simple but with strong robust after improvements, which provides new ideas to the research of iterative learning control algorithms.

High order single step time delay compensation algorithm for structural active control

The optimal instantaneous high order single step algorithm for active control is first discussed and then, the n+1 time step controlling force vector of the instantaneous optimal algorithm is derived from way of n time state vector. An estimating algorithm, is developed from this to solve the problem of active control with time delay compensation. The estimating algorithm based on this high order single step β method (HSM) foundation, is proven by simulation and experiment analysis, to be a valid solution to problem of active control with time delay compensation.

A novel methodology for constructing a multi-wing chaotic and hyperchaotic system with a unified step function switching control

This paper aims at developing a novel method of constructing a class of multi-wing chaotic and hyperchaotic system by introducing a unified step function. In order to overcome the essential difficulties in iteratively adjusting multiple parameters of conventional multi-parameter control, this paper introduces a unified step function controlled by a single parameter for constructing various multi-wing chaotic and hyperchaotic systems. In particular, to the best of the authors＇ knowledge, this is also the first time to find a non-equilibrium multi-wing hyperchaotic system by means of the unified step function control. According to the heteroclinic loop Shilnikov theorem, some properties for multi-wing attractors and its chaos mechanism are further discussed and analyzed. A circuit for multi-wing systems is designed and implemented for demonstration, which verifies the effectiveness of the proposed approach.

Nonlinear system PID-type multi-step predictive control

A compound neural network was constructed during the process of identification and multi-step prediction. Under the PID-type long-range predictive cost function, the control signal was calculated based on gradient algorithm. The nonlinear controller’s structure was similar to the conventional PID controller. The parameters of this controller were tuned by using a local recurrent neural network on-line. The controller has a better effect than the conventional PID controller. Simulation study shows the effectiveness and good performance.

Adaptive backstepping finite-time sliding mode control of spacecraft attitude tracking

This paper investigates the finite-time attitude tracking problem for rigid spacecraft. Two backstepping finite-time slid- ing mode control laws are proposed to solve this problem in the presence of inertia uncertainties and external disturbances. The first control scheme is developed by combining sliding mode con- trol with a backstepping technique to achieve fast and accurate tracking responses. To obtain higher tracking precision and relax the requirement of the upper bounds on the uncertainties, a se- cond control law is also designed by combining the second or- der sliding mode control and an adaptive backstepping technique. This control law provides complete compensation of uncertainty and disturbances. Although it assumes that the uncertainty and disturbances are bounded, the proposed control law does not require information about the bounds on the uncertainties and disturbances. Finite-time convergence of attitude tracking errors and the stability of the closed-loop system are ensured by the Lya- punov approach. Numerical simulations on attitude tracking control of spacecraft are provided to demonstrate the performance of the proposed controllers.

Active micro-vibration control based on improved variable step size LMS algorithm

The contradiction of variable step size least mean square(LMS)algorithm between fast convergence speed and small steady-state error has always existed.So,a new algorithm based on the combination of logarithmic and symbolic function and step size factor is proposed.It establishes a new updating method of step factor that is related to step factor and error signal.This work makes an analysis from 3 aspects:theoretical analysis,theoretical verification and specific experiments.The experimental results show that the proposed algorithm is superior to other variable step size algorithms in convergence speed and steady-state error.

Automatic control strategy for step feed anoxic/aerobic biological nitrogen removal process

Control of sludge age and mixed liquid suspended solids concentration in the activated sludge process is critical for ensuring effective wastewater treatment. A nonlinear dynamic model for a step-feed activated sludge process was developed in this study. The system is based on the control of the sludge age and mixed liquor suspended solids in the aerator of last stage by adjusting the sludge recycle and wastage flow rates respectively. The simulation results showed that the sludge age remained nearly constant at a value of 16 d in the variation of the influent characteristics. The mixed liquor suspended solids in the aerator of last stage were also maintained to a desired value of 2500 g/m3 by adjusting wastage flow rates.

MINIMUN TIME OPTIMAL CONTROL OF STEPPING MOTOR

The paper describes a new method of the stepping motor moimun time optimal control with closed-loop control. A mathematical model and optimal control strategy for the optimal control of stepping motor are proposed. Realizing technology for accelerating

One step to generate quantum controlled phase-shift gate using a trapped ion

This paper presents a very simple scheme for generating quantum controlled phase-shift gate with only one step by using the two vibrational modes of a trapped ion as the two qubits. The scheme couples two vibration degrees of freedom coupled with a suitable chosen laser excitation via the ionic states.

Electromagnetic control of the instability in the liquid metal flow over a backward-facing step

The tile-type electromagnetic actuator(TEA)and stripe-type electromagnetic actuator(SEA)are applied to the active control of the perturbation energy in the liquid metal flow over a backward-facing step(BFS).Three control strategies consisting of base flow control(BFC),linear model control(LMC)and combined model control(CMC)are considered to change the amplification rate of the perturbation energy.CMC is the combination of BFC and LMC.SEA is utilized in BFC to produce the streamwise Lorentz force thus adjusting the amplification rate via modifying the flow structures,and the magnitude of the maximum amplification rate could reach to 6 orders.TEA is used in LMC to reduce the magnitude of the amplification rate via the wall-normalwise Lorentz force,and the magnitude could be decreased by 2 orders.Both TEA and SEA are employed in CMC where the magnitude of the amplification rate could be diminished by 3 orders.In other words,the control strategy of CMC could capably alter the flow instability of the liquid metal flow.

Amplification mechanism of perturbation energy in controlled backward-facing step flow

A body force resembling the streamwise Lorentz force which decays exponentially in the wall-normalwise direction is applied in the primary and secondary separation bubbles to modify the base flow and thereby adjust the amplification rate of the perturbation energy.The amplification mechanisms are investigated numerically via analyzing the characteristics of the terms in the Reynolds-Orr equation which describes the growth rate of the perturbation energy.The results demonstrate that the main convective term always promotes the increase in the growth rate while the viscous terms usually play the reverse role.The contours of the product of the wall-normalwise and streamwise perturbation velocities distribute on both sides of the isoline,which represents the zero wall-normalwise gradient of the streamwise velocity in the base flow,due to the Kelvin-Helmholtz(KH)instability.For the case without control,the isoline downstream the reattachment point of the primary separation bubble is closer to the lower wall,and thus the viscous term near the lower wall might suppress the amplification rate.For the case in which the body force only acts on the secondary separation bubble,the secondary separation bubble is removed,and the magnitude of the negative wall-normalwise gradient of the base flow streamwise velocity decreases along the streamwise direction,and thus the growth rate of the perturbation energy is smaller than that for the case without control.For the case where the body force acts on both the separation bubbles,the secondary separation bubble is removed,the isoline stays in the central part of the channel,and thereby the viscous term has less effects on the amplification rate of which the peak value could be the maximum one for some control number.

Optimized Runge-Kutta Methods with Automatic Step Size Control for Compressible Computational Fluid Dynamics

We develop error-control based time integration algorithms for compressible fluid dynam-ics(CFD)applications and show that they are efficient and robust in both the accuracy-limited and stability-limited regime.Focusing on discontinuous spectral element semidis-cretizations,we design new controllers for existing methods and for some new embedded Runge-Kutta pairs.We demonstrate the importance of choosing adequate controller parameters and provide a means to obtain these in practice.We compare a wide range of error-control-based methods,along with the common approach in which step size con-trol is based on the Courant-Friedrichs-Lewy(CFL)number.The optimized methods give improved performance and naturally adopt a step size close to the maximum stable CFL number at loose tolerances,while additionally providing control of the temporal error at tighter tolerances.The numerical examples include challenging industrial CFD applications.

A force control high-order single-step-β method (HSM) for substructure pseudo-dynamic testing

This paper proposes a new technique which introduces the high-order single-step-β method(HSM)into the experimental study on the substructure pseudo-dynamic testing(SPDT).The technique is based on the proposed concept of equivalent shear stiffness which can meet the requirement of the HSM algorithm.A study is done to theoretically validate the technique by the numerical analysis of two-storey shear building structure,in comparison of the proposed substructure pseudo-dynamic testing algorithm with the central difference method(CDM).Then,a full-scale SPDT model,the three-storey frame-supported reinforced concrete short-limb masonry shear wall structure,is designed and tested to simulate the seismic response of the corresponding six-storey structure and verify the proposed force control HSM technique.Meanwhile,the techniques of both stiffness correction and force control are suggested to control algorithmic error,control error and measurement error.The results indicate that the force control HSM can be used in the full-scale multi-degree-of-freedom(MDOF)substructure pseudo-dynamic testing before descent segment of structure restoring force properties.

Direct Digital Frequency Control Based on the Phase Step Change Characteristic between Signals

We present a new digital phase lock technology to achieve the frequency control and transformation through high precision multi-cycle group synchronization between signals without the frequency transformation circuit. In the case of digital sampling, the passing zero point of the phase of the controlled signal has the phase step characteristic, the phase step of the passing zero point is monotonic continuous with high resolution in the phase lock process, and using the border effect of digital fuzzy area, the gate can synchronize with the two signals, the quantization error is reduced. This technique is quite different from the existing methods of frequency transformation and frequency synthesis, the phase change characteristic between the periodic signals with different nominal is used. The phase change has the periodic phenomenon, and it has the high resolution step value. With the application of the physical law, the noise is reduced because of simplifying frequency transformation circuits, and the phase is locked with high precision. The regular phase change between frequency signals is only used for frequency measurement, and the change has evident randomness, but this randomness is greatly reduced in frequency control, and the certainty of the process result is clear. The experiment shows that the short term frequency stability can reach 10-12/s orders of magnitude.

A STEP-BY-STEP INTEGRAL METHOD FOR ACTIVELY CONTROLLED STRUCTURES

A new active control method was proposed, in which the analytical control law was deduced by using a step by step integral method to differential equation of motion under the condition of static error being zero. This control law is terse in mathematical expression and convenient for practical use. The simulation results demonstrate that the proposed method can provide much more remarkable peak response reduction of seismically excited structures than the classical LQR method.