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Dynamic Systems and Control Theory
Published in Mohammad Monir Uddin, Computational Methods for Approximation of Large-Scale Dynamical Systems, 2019
When subjected to the step input, the system will initially have an undesirable output. This is called the transient response. transient response The transient response occurs because a system is approaching its final output value. If the time goes to infinity, system response is called steady-state response. steady-state response The steady-state response of the system occurs when the transient response has ended. The amount of time to take place the transient response is known as the rise time. The amount of time it takes for the transient response to end and the steady-state response to begin is known as the settling time. It is common practice for systems engineers to try and improve the step response of a system. In general, it is desirable to have the transient response reduced, the rise and settling times be shorter, and the steady-state to approach a desired “reference” output. Using the MATLAB command step, we can compute the step response of the step response system (2.4). However, for a large-scale system, we can apply the implicit Euler method that is implicit Euler method summarized in Algorithm 6 for computing the step response of the system (2.4).
Electrohydraulic Systems Control
Published in Qin Zhang, Basics of Hydraulic Systems, 2019
The purpose of control is to obtain a desired response from a certain command input. The transient response of a control system is therefore one of the most important characteristics, and often requires adjustment until the system provides a satisfactory response. The standard performance measure of the transient response is often defined in terms of the step response of a system. A valve-controlled hydraulic system is a speed control system by nature, and we can use a second-order Laplace transfer function to express the dynamic behaviors of a typical valve-controlled hydraulic cylinder system, as described in Section 8.2. Figure 9.3 shows a typical transient response of a second-order control system to a step input. The speed of response is measured by the rise time (Tr), peak time (Tp), overshoot (Po), settling time (Ts), and steady-state error (Es), and indicates how fast a control system reacts to the step input.
Basic Feedback Concept
Published in Bogdan M. Wilamowski, J. David Irwin, Control and Mechatronics, 2018
Tong Heng Lee, Kok Zuea Tang, Kok Kiong Tan
One of the most important characteristics of control systems is their transient response. Since the purpose of control systems is to provide a desired response, the transient response of control systems often must be adjusted until it is satisfactory. Feedback provides such a means to adjust the transient response of a control system and thus a flexibility to improve on the system performance. Consider the open-loop control system shown in Figure 2.1 with G(s) = K/(Ts + 1) and C(s) = a. Clearly, the time constant of the system is T. Now consider the closed-loop control system shown in Figure 2.3 with the same feedforward transfer function as that for Figure 2.1. It is straightforward to show that the time constant of this system has been reduced to T/(1 + Ka). The reduction in the time constant implies a gain in the system bandwidth and a corresponding increase in the system response speed. Using the speed control problem of a dc motor as an example (i.e., K = 1, T = 10, a = 10), the time constant of the closed-loop system is computed as Tc = (1/11)T = 10/11, i.e., the closed-loop system is about 10 times faster compared to the open-loop system.
Critical damping design method of vibration isolation system with both fractional-order inerter and damper
Published in Mechanics of Advanced Materials and Structures, 2022
Yandong Chen, Jun Xu, Yongpeng Tai, Xiaomei Xu, Ning Chen
The main aim of including an inerter in a VIS is to utilize its inertia effect, i.e. to increase the mass effect. Therefore, in general, the isolation system is equipped with independent dampers [12–16]. In textbooks of classical vibration theory, the concept of critical damping in Refs. [41, 42] is analyzed in detail in the study of single-degree-of-freedom damped vibration systems, and its value can be analytically solved using a characteristic equation (CE). Similarly, the calculation of the critical damping of a second-order system in control system engineering [43, 44] has a similar introduction. Åström [43] indicated that in industrial control applications, the overshoot is frequently 8–10%. Ogata [44] mentioned that, in practice, if the resonant peak is between 1.1 and 1.5, the system is considered to have a good performance, and the corresponding damping ratio is approximately 0.3–0.8, and the overshoot is approximately 5–40%. One of the basic characteristics of the transient response of a second-order system is overshoot, which primarily depends on the damping [43, 44]. In other words, by selecting the desired overshoot, the damping ratio can be obtained, and vice versa. The calculation of critical damping is key to the design of damper parameters.
Design of suboptimal model-matching controllers using squared magnitude function for MIMO linear systems
Published in Automatika, 2021
Suraj Damodaran, T. K. Sunil Kumar, A. P. Sudheer
The desired transient response specifications include natural frequency, settling time, damping factor, etc. The initial model dynamics can be expressed in the form of TFM as where . Here, each , represents an element of the initial model TFM relating the ith output to the kth input. The Laplace transform of the desired responses is denoted by , with steady-state values denoted by Si. The desired profiles of can be taken in the form of the response of a standard second-order low-pass filter for Ri(s), taken as a step signal of amplitude Si, i.e., where ωn is the natural frequency and ζ is the damping ratio, both of which can be determined from the desired time-domain specifications such as settling time, overshoot, rise time, etc. The (i,k)th off-diagonal elements of the initial model TFM are designed to have a pole at s = −λ(i,k) and zero at s = ∞, which is utilized along with Equation (3) in Equation (2) to yield the expressions for diagonal elements of the initial model: where u = 1, 2, … , min(p,q); k = 1, 2, … , q.
A novel hybrid many optimizing liaisons gravitational search algorithm approach for AGC of power systems
Published in Automatika, 2020
Prangya Mohanty, Rabindra Kumar Sahu, Sidhartha Panda
The PID controller is well known and most accepted feedback controllers in industrial applications because of its usefulness, simple design, cost-effective and effectiveness for linear plants. The controller with only proportional action has the ability to reduce rise time, but steady-state error cannot be removed. By using integral action this steady-state error can be eradicated but the transient response of the system becomes poorer. This transient response can be improved by using derivative action and it also reduces overshoot and stability of the system. But, the conventional PID controllers may be ineffectual because of its linear structure, particularly, for complex systems associated with delay time and uncertainties. Alternatively, the fuzzy logic controller (FLC) can handle nonlinearity and uncertainties and can be designed to get the desired system performance. Fuzzy PID structure has been proposed in literature to get overall improved performance [22,23]. Therefore, fuzzy PID are chosen in this study for AGC. The configuration of fuzzy PID structure is displayed in Figure 2 which is a mixture of fuzzy PD and PID structures from [24], with input scaling parameters (K1 and K2) of FLC and gains of PID (KP, KI, KD). The controllers take individual ACEs (e1 (t) and e2 (t)) as inputs as expressed by: