China
Africa
Explore chapters and articles related to this topic
Filter Fundamentals
Published in T. Deliyannis, Yichuang Sun, J.K. Fidler, Continuous-Time Active Filter Design, 2019
T. Deliyannis, Yichuang Sun, J.K. Fidler
In Fig. 1.22, a typical step response of a lowpass filter is shown. Characteristic quantities associated with this response are values of the rise time tp the delay time τo, the settling time ts, and the overshoot. These quantities are defined as follows: The rise time tr is defined as the time it takes the step response to rise from 10 percent to 90 percent of its final value.The delay time τo is the time it takes for the step response to rise to 50 percent of its final value.The settling time ts is the time that elapses between the moment of appearance of the first peak and the moment beyond which the step response does not differ by more that 2 percent from its final value.The overshoot is the percent of the final value difference between the maximum and the final value of the step response.
Dynamic Systems and Control Theory
Published in Mohammad Monir Uddin, Computational Methods for Approximation of Large-Scale Dynamical Systems, 2019
Another common and frequently used tool to analyze the system is the step response. Typically, this is the first characteristic step response to be analyzed for a newly designed system. Similar to the impulse response, the step response of a system is the output of the system when a unit step function is used as the input.step function(Unit step function)The unit step function is defined asunit step functionustep(t)={0,ift<01,ift≥0
Transverse Vibration of Rotor Systems Integrated with Active Magnetic Bearings
Published in Rajiv Tiwari, Rotor Systems: Analysis and Identification, 2017
For linear control systems, the characterization of the transient response is often done by the use of the step function as an input. The response of a control system when the input is a step function is called the step response. The commonly used definitions in the step response are the settling time and the rise time. The settling time is the time needed for the system output to reach and stay within the steady-state value (which is ideally equal to the reference input). The steady-state value for a step input is shown in Figure 18.15. The absolute allowable difference between y(t) and ysteady state is used to find the settling time, and usually this difference is specified to be 5%. That is, the settling time is the minimum time after which the system response remains within ±5% of the steady-state value ysteady state due to a step input. The rise time is the time needed for the system output y(t) to increase from 10% to 90% of the steady-state value ysteady state.
Order reduction of linear time-invariant systems using Eigen permutation and Jaya algorithm
Published in Engineering Optimization, 2019
Akhilesh K. Gupta, Deepak Kumar, Paulson Samuel
In this article, ISE is considered as a fitness function which is defined as the integral of the squared error between the step responses of the original and reduced models over the interval [0, ∞], which is represented as However, the proposed approach selects [0, ] as an interval for the reduction problem to minimize the approximation error, where is the settling time. The computational resources used for implementation of the proposed approach are MATLAB® version 8.1.0.604 (R2013a) on the operating system Microsoft Windows 7 version 6.1 (Build 7601: Service Pack 1). The primary objective of the proposed work is to obtain an ROM with a close approximation to that of the original system, which is performed by minimization of the fitness function. The unit step response provides information about the stability as well as the dynamic behaviour of the system. Therefore, the minimization of the ISE between the step responses preserves the dynamic behaviour of the original system into the ROM. The other error indices, integral time square error (ITSE), IAE and integral time absolute error (ITAE), are defined as
Robust Design of Tilted Integral Derivative Controller for Non-integer Order Processes with Time Delay
Published in IETE Journal of Research, 2021
Kurnam Gnaneshwar, P. K. Padhy
Controller design can generally be categorized as a response, optimization, and model-based [14–16]. In the case of response base techniques, the step response of the process is mainly used to design the controller. In optimization techniques, performance indice play a vital role in order to get optimal controller parameters. As a result, optimal performance can be obtained. This indice is mainly designed using the time and frequency domain parameters. Guha et al. [11] are presented a novel approach for cascaded TID controller design for control of tie-line power and frequency of interconnected non-linear power system. The proposed controller performance is compared with different variations of TID controllers and literature-based techniques under both sensitivity and robust analysis. It is evidenced that the proposed controller includes both advantages of FO calculus and cascade control algorithm. Therefore, its performance is better than the existing techniques. Ahmed et al. [12] are developed a modified TID controller structure for LFC of a two-area interconnected power system, ID-T controller. The optimal parameters of the controller are estimated using the optimization technique. A comparative analysis of different methods verifies the proposed controller performance. It is concluded that the proposed ID-T controller is efficient over the FOPID controller under other operating conditions. Saheb and Ahmed [17] have presented a review of numerous performance indices designed based on time and frequency domain specifications with pros and cons. A new performance indice is proposed to overcome the limitations of the existing indices. It is designed using time-domain parameters and includes some additional weights to obtain the desired response. An analytical approach is provided to select the weights. Comparative analysis of numerous indices evidence that the proposed one provides an optimal response than that existing indices. Sahu et al. [18] addressed a novel approach for regulating the LFC using a TIDF controller. The controller parameters are estimated using the Differential Evaluation optimization method using ITAE indice. The effectiveness of the proposed method is verified through sensitivity, robustness analysis by load disturbance, uncertainty in the system parameters. Simulation results reveal that the proposed TID controller performance is better than the PID controller in terms of transient response, different operating conditions.