K10620 digvijay
- 1. TOPIC Design and analysis of percentage overshoot of unit step response Submitted to: MR. SOMESH CHATURVEDI Asst. Prof. Department of electrical engineering Career Point University Kota Submitted by: Digvijay UID-K10620 VIth sem/IIIrd year Dept. Of mechanical engineering CAREER POINT UNIVERSITYCAREER POINT UNIVERSITY
- 2. CONTENT • Introduction • Definition • Circuit Diagram • Procedure / working • Principle • Industrial application • Advantage • Recent treads / future scope • Reference
- 3. Introduction • In control theory, overshoot refers to an output exceeding its final, steady-state value. For a step input, the percentage overshoot (PO) is the maximum value minus the step value divided by the step value. In the case of the unit step, the overshoot is just the maximum value of the step response minus one. Also see the definition of overshoot in an electronics context. • The percentage overshoot is a function of the Damping ratio ζ and is given by
- 4. Definition • The step response of a system in a given initial state consists of the time evolution of its outputs when its control inputs are Heaviside step functions. In electronic engineering and control theory, step response is the time behavior of the outputs of a general system when its inputs change from zero to one in a very short time. The concept can be extended to the abstract mathematical notion of a dynamical system using an evolution parameter. From a practical standpoint, knowing how the system responds to a sudden input is important because large and possibly fast deviations from the long term steady state may have extreme effects on the component itself and on other portions of the overall system dependent on this component.
- 5. Circuit Diagram Ideal negative feedback model; open loop gain is AOL and feedback factor is β.
- 6. Procedure / working • The unit step function is just a piecewise function with a jump discontinuity at t = a. Recall from calculus that a jump discontinue its is an x-value for which the limit doesn’t axis. • Step response of feedback amplifiers • This section describes the step response of a simple negative feedback amplifier shown in Figure 1. The feedback amplifier consists of a main open-loop amplifier of gain AOL and a feedback loop governed by a feedback factor β. This feedback amplifier is analyzed to determine how its step response depends upon the time constants governing the response of the main amplifier, and upon the amount of feedback used. • A negative-feedback amplifier has gain given by (see negative feedback amplifier): • With one dominant pole In many cases, the forward amplifier can be sufficiently well modeled in terms of a single dominant pole of time constant τ
- 7. :- • Two-pole amplifiers In the case that the open-loop gain has two poles (two time constants, τ1, τ2), the step response is a bit more complicated. • Analysis The two-pole amplifier's transfer function leads to the closed-loop gain. • Nonlinear dynamical system For a general dynamical system, the step response is defined as follows: It is the evolution function when the control inputs (or source term, or forcing inputs) are Heaviside functions: the notation emphasizes this concept showing H(t) as a subscript.
- 8. Principle • Second-Order System RespOnse Characteristics(contd.) Percent overshoot Settling time • Higher order system • Some fundamental properties of linear system The principle of superposition The Derivative Property The integral property The Effect Of Zeros On the System Response
- 9. Industrial application • MATLAB is used in order to study different parameters and to plot different response curves
- 10. Advantage • In order to obtain the desired performance of the system, we use compensating networks. Compensating networks are applied to the system in the form of feed forward path gain adjustment. • Compensate a unstable system to make it stable. • A compensating network is used to minimize overshoot. • These compensating networks increase the steady state accuracy of the system. An important point to be noted here is that the increase in the steady state accuracy brings instability to the system.
- 11. Reference • www.google.com • www.wikipedia.com • Control theory book.