Optimal feedback gains of a delayed proportional-derivative(PD) control for balancing an inverted pendulum

In the dynamics analysis and synthesis of a controlled system, it is important to know for what feedback gains can the controlled system decay to the demanded steady state as fast as possible. This article presents a systematic method for finding the optimal feedback gains by taking the stability of an inverted pendulum system with a delayed proportional-derivative controller as an example. First, the condition for the existence and uniqueness of the stable region in the gain plane is obtained by using the D-subdivision method and the method of stability switch. Then the same procedure is used repeatedly to shrink the stable region by decreasing the real part of the rightmost characteristic root. Finally, the optimal feedback gains within the stable region that minimizes the real part of the rightmost root are expressed by an explicit formula. With the optimal feedback gains, the controlled inverted pendulum decays to its trivial equilibrium at the fastest speed when the initial values around the origin are fixed. The main results are checked by numerical simulation.

Fractionally Delayed Kalman Filter

The conventional Kalman filter is based on the assumption of non-delayed measurements. Several modifications appear to address this problem, but they are constrained by two crucial assumptions: 1) the delay is an integer multiple of the sampling interval, and 2) a stochastic model representing the relationship between delayed measurements and a sequence of possible non-delayed measurements is known. Practical problems often fail to satisfy these assumptions, leading to poor estimation accuracy and frequent track-failure. This paper introduces a new variant of the Kalman filter, which is free from the stochastic model requirement and addresses the problem of fractional delay.The proposed algorithm fixes the maximum delay(problem specific), which can be tuned by the practitioners for varying delay possibilities. A sequence of hypothetically defined intermediate instants characterizes fractional delays while maximum likelihood based delay identification could preclude the stochastic model requirement. Fractional delay realization could help in improving estimation accuracy. Moreover, precluding the need of a stochastic model could enhance the practical applicability. A comparative analysis with ordinary Kalman filter shows the high estimation accuracy of the proposed method in the presence of delay.

Deep Learning Based Signal Detector for OFDM Systems

In this paper,we propose a novel deep learning(DL)-based receiver design for orthogonal frequency division multiplexing(OFDM)systems.The entire process of channel estimation,equalization,and signal detection is replaced by a neural network(NN),and hence,the detector is called a NN detector(N^(2)D).First,an OFDM signal model is established.We analyze both temporal and spectral characteristics of OFDM signals,which are the motivation for DL.Then,the generated data based on the simulation of channel statistics is used for offline training of bi-directional long short-term memory(Bi-LSTM)NN.Especially,a discriminator(F)is added to the input of Bi-LSTM NN to look for subcarrier transmission data with optimal channel gain(OCG),which can greatly improve the performance of the detector.Finally,the trained N^(2)D is used for online recovery of OFDM symbols.The performance of the proposed N^(2)D is analyzed theoretically in terms of bit error rate(BER)by Monte Carlo simulation under different parameter scenarios.The simulation results demonstrate that the BER of N^(2)D is obviously lower than other algorithms,especially at high signal-to-noise ratios(SNRs).Meanwhile,the proposed N^(2)D is robust to the fluctuation of parameter values.

TSKARNA-norm Adaption Based NLMS with Optimized Fractional Order PID Controller Gains for Voltage Power Quality

The operation of a dynamic voltage restorer(DVR)is studied using a three-phase voltage source converter(VSC)-based topology to alleviate voltage anomalies from a polluted supply voltage.The control algorithm used included two components.The first is an adaptive Takagi-Sugeno-Kang(TSK)-based adaptive reweighted L1 norm adaption-based normalized least mean square(TSK-ARNA-NLMS)unit,which is proposed for the extraction of fundamental active and reactive components from the non-ideal supply and is further employed to generate the load reference voltage and switching pulse for the VSC.The step size was evaluated using the proposed TSK-ARNA-NLMS controller,and the TSK unit was optimized by integration with the marine predator algorithm(MPA)for a faster convergence rate.The second,a fractional-order PID controller(FOPID),was employed for AC-and DC-link voltage regulation and was approximated using the Oustaloup technique.The FOPID()PI Dγμprovides more freedom for tuning the settling time,rise time,and overshoot.The FOPID coefficients(Ki,Kd,Kp,γ,andμ)were optimized by employing an advanced ant lion optimization(ALO)meta-heuristics technique to minimize the performance index,namely,the integral time absolute error(ITAE)and assess the accuracy of controllers.The DVR performance was validated under dynamic-and steady-state conditions.

Gain Flattened Raman Fiber Amplifier Using Parameter Optimization and DCF Fiber

We investigate two configurations of Raman fiber amplifier in the 1530-1570 nm region. The gain spectrum variation is decreased from 8.31 dB to 2.48 dB when appropriately adjust the individual two pumps and optical fiber.

Designing broadband fiber optic parametric amplifier based on near-zero single ZDW PCF with ultra-flat nature

We propose a broadband fiber optic parametric amplifier（FOPA） based on a near-zero ultra-flat dispersion profile with a single zero-dispersion wavelength（ZDW） by using a selective liquid infiltration technique.The amplifier gain and bandwidth is investigated for a variety of fiber lengths, pump power, and operating wavelengths. It is observed that sufficient peak gains and broader bandwidths can be achieved with a small negative anomalous dispersion（β2≤ 0） and a positive value of the 4th-order dispersion parameter（t β4）around the pump. We can optimize an FOPA with a bandwidth of more than 220 nm around the communications wavelength.

On-line Ladle Lining Temperature Estimation by Using Bounded Jacobian Nonlinear Observer

The knowledge of transient temperature of the ladle wall is a key factor in optimizing energy consumption in steelmaking process.The transient temperature needs to be estimated.A nonlinear lumped parameter model was used to model the thermal dynamics of the ladle.Then,the bounded Jacobian nonlinear observer was utilized to estimate the temperature.With this method,the estimation model became a closed-loop model and the observer gains were obtained by solving linear matrix inequalities and simply implemented to the system.Comparison between the simulation and recorded data at a participating steel plant in Thailand showed that the nonlinear observer accurately estimated the temperature of the ladle lining.This estimated temperature was very useful in determining suitable tapping temperature for energy conservation and steel quality.