Unit Step Response Research Articles

Small Signal Analysis of Energy Factor and Mathematical Modeling for Power DC–DC Converters

Mathematical modeling for power dc-dc converters is a historical problem accompanying dc-dc conversion technology since the 1940s. The traditional mathematical modeling is not available for complex structure converters since the differential equation order increases very high. We have to search for other ways to establish mathematical modeling for power dc-dc converters. We have defined energy factor (EF) and new mathematical modeling for power dc-dc converters that have attracted much attention in recent years. This paper describes the small signal analysis of EF and mathematical modeling for power dc-dc converters in continuous conduction mode and discontinuous conduction mode. EF and the subsequential parameters can illustrate the unit-step response and interference recovery. This investigation may be helpful for system design and dc-dc converters characteristics. Two dc-dc converters: Buck converter and super-lift Luo-converter as the samples, are analyzed in this paper to demonstrate the applications of EF, pumping energy, stored energy (SE), capacitor/inductor SE ratio, energy losses, time constant tau, and damping time constant taud

Asymmetric PI Controller for Mechatronic Systems

An asymmetric PI (aPI) controller based on a control algorithm, which is the modification of the PI control method, has been suggested. The principal characteristic feature of the aPI controller is that different values of proportional and integral constants are used at positive and at negative errors. Contrary to the classical PI controller, the proposed controller allows us to improve the positive disturbance rejection of control systems without sacrificing the unit step response dynamics. Results of the investigation of the concrete control systems based on the aPI controller are also presented. Using the dynamic system simulation program Simulink performed the investigation.

Data-dependent jitter in serial communications

We present a method for predicting data-dependent jitter (DDJ) introduced by a general linear time-invariant LTI system based on the system's unit step response. We express the exact DDJ of a first-order system and verify the validity of the solution experimentally. We then propose a perturbation technique to generalize the analytical expression for DDJ. We highlight the significance of the unit step response in characterizing DDJ and emphasize that bandwidth is not a complete measure for predicting DDJ. We separate the individual jitter contributions of prior bits and use the result to predict the DDJ of a general LTI system. In particular, we identify a dominant prior bit that signifies the well-known distribution of deterministic jitter, the two impulse functions. We also show a jitter minimization property of high-order LTI systems. We verify our generalized analytical expression of DDJ for several real systems including an integrated CMOS 10-Gb/s trans-impedance amplifier by comparing the theory and measurement results. The theory predicts the jitter with as low as only 7.5% error.

Modeling stream–aquifer interactions with linear response functions

The problem of stream–aquifer interactions is pertinent to conjunctive—use management of water resources and riparian zone hydrology. Closed form solutions expressed as convolution integrals of impulse response and unit step response functions are derived for channel flow and stream–aquifer interactions. The solutions, obtained using Laplace transforms, relate channel reach discharge, stream–aquifer exchange rates, and associated flow volumes to hydrologic processes and regulatory and management control measures. Channel flow is modeled using a simple mass balance equation and the Muskingum linear storage relationship, and groundwater flow is approximated by a linearized representation of the one-dimensional Boussinesq equation. Within a given channel reach, the aquifer is assumed to be homogeneous, separated from the channel by a semipervious layer, and with a time-variable prescribed head or no-flow boundary condition at a finite distance normal to the channel flow direction. Discrete-time unit response functions are derived for arbitrary channel inflow hydrographs and other system's excitations, which extend the utility of the model to a wider spectrum of water management problems. Although the closed-form solutions are based on simplifying assumptions which may limit the utility of the solutions, applications to example flow scenarios nonetheless illustrate the robustness of the solutions to a variety of applications such as the bank storage problem, effect of drought periods, and groundwater–surface water interactions in the presence of water management controls.

Energy factor and mathematical modelling for power DC∕DC converters

The mathematical modelling of power DC/DC converters is a historical problem that has accompanied DC/DC conversion technology since the 1940's. Traditional mathematical modelling is not available for complex structure converters because of the very high-order differential equations involved. The authors propose a new model to cover all power DC/DC converters. The energy stored in power DC/DC converters has been much considered in the past. A DC/DC converter behaves in this way because it has some energy storing components. When the converter changes from one steady state to another, the corresponding stored energy changes. Therefore, there must be a transient process from one steady state to the new steady state. The authors have theoretically defined a new concept, namely energy factor (EF), and researched the relationship between it and mathematical modelling for power DC/DC converters. The EF and its associated parameters illustrate the unit-step response and interference recovery which may be helpful for system design and in anticipating DC/DC converter characteristics. Two DC/DC converters are analysed, the Buck converter and the super-lift Luo converter, to demonstrate the application of EF, pumping energy (PE), stored energy (SE), capacitor/inductor stored energy ratio (CIR), energy losses (EL), time constant τ and damping time constant τd.

Model Classification Applied to the Autotuning of Industrial Proportional−Integral−Derivative Regulators

This paper presents a technique for the automatic tuning of industrial proportional-integral-derivative (PID) regulators, based on a classifier that selects an appropriate model structure for the system to be controlled starting from a simplified and normalized representation of its unit step response. The PID tuning is then performed within the well-established framework of the internal model control approach, showing that structural information is particularly beneficial for model-based synthesis. Both simulations and a physical application, based on a laboratory thermal process, are reported.

Intelligent PID controller based on ant system algorithm and fuzzy inference and its application to bionic artificial leg

A designing method of intelligent proportional-integral-derivative(PID) controllers was proposed based on the ant system algorithm and fuzzy inference. This kind of controller is called Fuzzy-ant system PID controller. It consists of an off-line part and an on-line part. In the off-line part, for a given control system with a PID controller, by taking the overshoot, setting time and steady-state error of the system unit step response as the performance indexes and by using the ant system algorithm, a group of optimal PID parameters K*p, T/*i and T*d can be obtained, which are used as the initial values for the on-line tuning of PID parameters. In the on-line part, based on K*p, T*i and T*d and according to the current system error e and its time derivative, a specific program is written, which is used to optimize and adjust the PID parameters on-line through a fuzzy inference mechanism to ensure that the system response has optimal transient and steady-state performance. This kind of intelligent PID controller can be used to control the motor of the intelligent bionic artificial leg designed by the authors. The result of computer simulation experiment shows that the controller has less overshoot and shorter setting time.

Design of PID controller with incomplete derivation based on ant system algorithm

A new and intelligent design method for PID controller with incomplete derivation is proposed based on the ant system algorithm ( ASA) . For a given control system with this kind of PID controller, a group of optimal PID controller parameters Kp* , Ti*, and Td* can be obtained by taking the overshoot, settling time, and steady-state error of the system's unit step response as the performance indexes and by use of our improved ant system algorithm. Kp* , Ti*, and Td* can be used in real-time control. This kind of controller is called the ASA-PID controller with incomplete derivation. To verify the performance of the ASA-PID controller, three different typical transfer functions were tested, and three existing typical tuning methods of PID controller parameters, including the Ziegler-Nichols method (ZN),the genetic algorithm (GA),and the simulated annealing (SA), were adopted for comparison. The simulation results showed that the ASA-PID controller can be used to control different objects and has better performance compared with the ZN-PID and GA-PID controllers, and comparable performance compared with the SA-PID controller.

Discrete system order reduction using multipoint step response matching

The proposed method of linear time invariant discrete system order reduction is based on multipoint step response matching for both pole and zero evaluation of the low order model. Depending on the number of zeros and poles of the low order model, the number of points are selected on the time axis of the unit step response such that the unknown poles and zeros can be determined by solving a set of nonlinear equations using Newton's method.

Numerical Electromagnetic Field Analysis of Unit Step Response Characteristics of Impulse Voltage Measuring Systems

Unit step response characteristics of impulse voltage measuring systems are studied with the help of numerical electromagnetics code (NEC-2). Prior to this analysis, the accuracy of a transient analysis by this method is investigated for a simple structure. An impulse voltage measuring system, under application of step voltage, behaves like an antenna until a traveling wave makes several roundtrips in its lead wire. NEC-2 code can analyze such dynamic electromagnetic field around a three-dimensional (3-D) conductor system. In the present paper, the role of a shield ring of a divider for lightning impulse voltage is intensively investigated and discussed.

PID Based Low Frequency Sampling GPC Algorithm

Model predictive control(MPC) is widely used in the metallurgical industry in recent years. Based on PID control, a low frequency response sequence is obtained by time-domain extraction of an unit step response sequence from "a generalized controlled process"(a real process plus a PID feedback loop). The parameters of this generalized controlled process can be estimated by approaching the low frequency response sequence. The high frequency property of a process is dealt with by a PID algorithm based on the past output errors, whereas the low frequency property is controlled by a predictive control algorithm. Consequently the computational burden of predictive control is greatly lightened, and sufficient time is available for online identification of model parameters due to the low frequency sampling of MPC algorithm. The effectiveness of this method is confirmed by a simulation example for a process with a nonlinear term.

Fuzzy-GA PID controller with incomplete derivation and its application to intelligent bionic artificial leg

An optimal PID controller with incomplete derivation is proposed based on fuzzy inference and the genetic algorithm, which is called the fuzzy-GA PID controller with incomplete derivation. It consists of the off-line part and the on-line part. In the off-line part, by taking the overshoot, rise time, and settling time of system unit step response as the performance indexes and by using the genetic algorithm, a group of optimal PID parameters K*p, T*i, and T*i are obtained, which are used as the inital values for the on-line tuning of PID parameters. In a on-line part, based on K*p, T*i, and T*d and according to the current system error e and its time derivative, a dedicated program is written, which is used to optimize and adjust the PID parameters on line through a fuzzy inference mechanism to ensure that the system response has optimal dynamic and steady-state performance. The controller has been used to control the D. C. motor of the intelligent bionic artificial leg designed by the authors. The result of computer simulation shows that this kind of optimal PID controller has excellent control performance and robust performance.

Unified initial condition response analysis of Lur'e systems and linear time-invariant systems

A unified framework to the initial condition response (ICR) analysis of non-linear time-varying systems of the Lur'e type and linear time-invariant (LTI) systems is considered. To quantify the transient behaviour resulting from initial conditions, an ICR measure is defined. An appropriate upper bound for the ICR measure can be calculated based upon the condition number of a positive definite matrix, associated with a quadratic Lyapunov function. Owing to the particular structure of the Lur'e systems, bounding the ICR measure is transformed into a minimization problem, constrained by either two simultaneous Lyapunov matrix inequalities or a single algebraic Riccati inequality. In the LTI case, the ICR measure is merely the supremum of the induced norm of the state transition matrix and its calculation involves solving a Lyapunov matrix equation. The ICR measure bound is significant from the engineering standpoint since it enables the calculation of the non-saturating domain of the state variables. In the LTI case, this bound also provides a quantification of impulse and unit step responses. The results are illustrated by several examples.

An LMI-based approach to critical control system design for rate-limited exogenous inputs

This paper considers a linear matrix inequality approach to the design of critical control systems for rate-limited exogenous inputs. The sufficient condition for ensuring the critical requirement is derived from the exponential convergence condition of the unit step response. By changing the variables, it is transformed into the set of BMI and LMI conditions. The problem amounts to a convex feasibility problem with a line search. The obtained controller has the same order as a plant. To show the validity of the proposed method, a numerical example of multi-conditioned critical control system design is presented.

Optimization of the PD coefficient in a flight simulator control via genetic algorithms

In this study the design of motion‐based flight simulators is carried out by specifying the performance required of the motion cueing mechanism, to generate translational and angular motions as a 6–3 Stewart Platform Mechanism (SPM). These motions are intended to approximate the specific forces and angular accelerations encountered by the pilot in the simulated aircraft. Firstly, the dynamics of this 6–3 SPM is given in closed form as in our earlier study. Then, for the control of obtained dynamic model, a leg‐length based PD algorithm is applied. In the optimization of the applied PD algorithm's coefficients, Real Coded Genetic Algorithms are used. So as to have faster and effective system's performance, the fitness function chosen, in Genetic Algorithms, having maximum overshoot value, settling time and steady state error which are obtained from the unit step response. The performance of the system studied is compared to the similar studies in the literature exist.

Design of sampled-data critical control systems based on the fast-discretization technique

The fast-discretization is known as an approximate but efficient technique for design and analysis of sampled-data systems. In this paper, we propose a fast-discretization-based design for sampled-data critical control systems. Supposing a tracking problem or a slow-changing disturbance rejection problem, we assume that an exogenous input is a persistent and/or transient input with bound on the rate of change. It is shown that the critical constraint for such exogenous inputs can be given in the form of the inequality constraint on the unit step response. The design parameters are determined by a numerical search method subject to this constraint. However, instead of evaluating it strictly, we check the corresponding constraint which is obtained from the fast-discretized system. Although this approach is approximate, it provides an efficient numerical procedure for a computer-aided design. To show the validity of the proposed method, an example of a multi-objective critical control system design is presented.

単位ステップ応答波形記録の雷インパルス電圧応答パラメータへの影響

単位ステップ応答波形記録の雷インパルス電圧応答パラメータへの影響

雷インパルス測定システム解析のための逆コンボルーション

This paper proposes a new numerical deconvolution algorithm, which has advantage in speed over other two techniques. In the paper, three basic algorithms have been examined to analyse standard lightning impulse voltage from the given output response and unit step response of a measuring system. Full and front-chopped impulses are assumed as an input voltage. The numerically reconstructed inputs are compared with the analytical impulses. The proposed fast method, not precise enough under certain circumstances, is studied a cause of its error and its algorithm is modified to avoid cancellation error. The modified deconvolution method has been tested in possible circumstances and proven most accurate amongst three.

Hydraulics of Stream Flow Routing with Bank Storage

Bank storage is a process in which volumes of water are temporarily retained by alluvial stream banks during storm events and gradually released to partially sustain baseflow. This process has important hydrologic and ecological implications. In this paper, analytical solutions are developed for routing stream flow, lateral stream-aquifer interactions, and aquifer storage. In effect, the streamflow routing Muskingum method is modified for bank storage. The analysis is based on one-dimensional lateral groundwater flow in semiinfinite homogeneous unconfined aquifers, which are in contact with streams through semipervious bed sediments. Impulse response and unit step response functions are derived for the stream-aquifer system, using Laplace transformations. These response functions relate stream outflow, stream-aquifer flow, bank storage, and cumulative reach discharge volume to discrete-time inflow hydrographs through convolution integrals. The impulse response function decreases with increasing aquifer hydraulic conductivity at earlier times, but increases with the conductivity and persists at later times. The unit step response function decreases with aquifer conductivity uniformly in time. The dependence of stream flow and bank storage on aquifer hydraulic conductivity, streambed leakance, stream width, and aquifer diffusivity is investigated. The analysis is extended to discrete input data, and modification of the methodology to route discrete-time inflow hydrographs of general form is achieved, using discrete-time kernels. The presented analysis establishes the time domain for validity of the analytical solutions in terms of the Muskingum parameters and an aquifer-related parameter.

A technique for the evaluation of lightning-induced voltages in complex low-voltage power-installation networks

In order to gain knowledge of the effects of lightning-electromagnetic field pulses (LEMP) in low-voltage power installations (LVPIs), the transient response of two electrical networks was measured when they were exposed to lightning electromagnetic fields in the summer of 1998. Both networks were isolated from the energy supply. One network was a simple circuit installed in a room of a single storey wooden residential house and the other consisted of the house's whole electrical wiring circuit. The main goal of this paper is to develop a practical method with which to estimate the transient response of LVPIs to LEMP. The method uses the information contained in a small portion of the time domain waveform of the electric field, which can be approximated as a unit step function and the corresponding induced voltage, which, in turn can be approximated as the unit step response. It is shown how this unit step response can be used in determining the induced overvoltage in the network due to any complex electric-field waveform. Advantages, limitations and considerations associated with the application of this method are also discussed.