![Coding
step(sys)
step(sys,Tfinal)
step(sys,t)
step(sys1,sys2,...,sysN)
step(sys1,sys2,...,sysN,Tfinal)
step(sys1,sys2,...,sysN,t)
y = step(sys,t)
[y,t] = step(sys)
[y,t] = step(sys,Tfinal)
[y,t,x] = step(sys)
[y,t,x,ysd] = step(sys)
[y,...] = step(sys,...,options)](https://image.slidesharecdn.com/matlab-160513013936/85/Matlab-7-320.jpg)
Matlab
- 1. Design and Analysis of Damping Ratio of Unit Step Response Submitted by: Akshat Jain
- 2. Table Of Contents • Introduction • Definition • Damping ratio • Oscillating Cases • Step response • Principle • Working Procedure • Damping type • First Order System • Second Order System • MATLAB coding • Application • Advantages and Limitations • Recent trend And Future Scope • Conclusion • Reference
- 3. Introduction • Assuming that the system is asymptotically stable, and then the system response in the long run is determined by its steady state component only. For control systems it is important that steady state response values are as close as possible to desired ones (specified ones) so that we have to study the corresponding errors, which represent the difference between the actual and desired system outputs at steady state, and examine conditions under which these errors can be reduced or even eliminated. • Modern day control engineering is a relatively new field of study that gained significant attention during the 20th century with the advancement of technology. It can be broadly defined or classified as practical application of control theory. Control engineering has an essential role in a wide range of control systems, from simple household washing machines to high-performance F-16 fighter aircraft. It seeks to understand physical systems, using mathematical modeling, in terms of inputs, outputs and various components with different behaviors, use control systems design tools to develop controllers for those systems and implement controllers in physical systems employing available technology
- 4. Definition Damping Ratio: • The damping ratio is a parameter, usually denoted by ζ (zeta) that characterizes the frequency response of a second order ordinary differential equation. It is particularly important in the study of control theory. It is also important in the harmonic oscillator. • The damping ratio provides a mathematical means of expressing the level of damping in a system relative to critical damping. For a damped harmonic oscillator with mass m, damping coefficient c, and spring constant k, it can be defined as the ratio of the damping coefficient in the system's differential equation to the critical damping coefficient:
- 5. Step response • 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.
- 6. Working Procedure• Working Procedure • Using the natural frequency of a harmonic oscillator • • and the definition of the damping ratio above, we can rewrite this as: • This equation can be solved with the approach. • where C and s are both complex constants. That approach assumes a solution that is oscillatory and/or decaying exponentially. Using it in the ODE gives a condition on the frequency of the damped oscillations, • Undamped: Is the case where corresponds to the undamped simple harmonic oscillator, and in that case the solution looks like • , as expected. • Underdamped: If s is a complex number, then the solution is a decaying exponential combined with an oscillatory portion that looks like • . This case occurs for , and is referred to as underdamped. • Overdamped: If s is a real number, then the solution is simply a decaying exponential with no oscillation. This case occurs for , and is referred to as overdamped. • Critically damped: The case where is the border between the overdamped and underdamped cases, and is referred to as critically damped. This turns out to be a desirable outcome in many cases where engineering design of a damped oscillator is required (e.g., a door closing mechanism). • One of the most common test inputs used is the unit step function,
- 7. Coding step(sys) step(sys,Tfinal) step(sys,t) step(sys1,sys2,...,sysN) step(sys1,sys2,...,sysN,Tfinal) step(sys1,sys2,...,sysN,t) y = step(sys,t) [y,t] = step(sys) [y,t] = step(sys,Tfinal) [y,t,x] = step(sys) [y,t,x,ysd] = step(sys) [y,...] = step(sys,...,options)
- 8. Application • Identification from step response is one of the most significant topics in process control. Although there is a concern about its persistency of excitation, the step input might be the most commonly used excitation signal for identification in process industries. These methods are commonly used in industrial applications because they involve minimal computation. Due to the limitations of the graphical techniques in terms of their applicability and accuracy, more computationally involved methods have been developed subsequently. An important development in identification from step response is the introduction of the integral equation approach for simultaneous estimation of the delay proposed by Wang and Zhang. Based on this procedure, over the last few years a number of new methods have been proposed to deal with the different practical issues in step response based identification • In evaluating the uncertainty of the standard measuring system for lightning-impulse high voltage, which is composed of the standard voltage divider, the digital recorder and the calibrators, step-response tests of the standard voltage divider may be useful. In this paper, convolution algorithm is employed to calculate output impulse-voltage waveforms from measured step-response waveforms.. Therefore, for the standard voltage divider, step- response parameters, i.e. experimental response time, partial response time, settling time, and overshoot have almost nothing to do with the error of the virtual front time.
- 9. Advantages • Using a computer to control a process has a number of important advantages over controlling the same process manually. • Computer systems respond more quickly than humans. A computer system can take readings from sensors and turn devices on and off many thousands of times a second. • Once the initial purchase cost has been paid, control systems are usually reasonably cheap to run. Most computer control systems have lower operating costs than similar systems which are manned by humans. • Computer control systems are very reliable. Unlike a human a control system will not lose concentration. Computer systems can continue to operate reliably twenty four hours a day.
- 10. Recent Trend & Future Scope • Originally, control engineering was all about continuous systems. Development of computer control tools posed a requirement of discrete control system engineering because the communications between the computer-based digital controller and the physical system are governed by a computer clock. The equivalent to Laplace transform in the discrete domain is the Z-transform. Today, many of the control systems are computer controlled and they consist of both digital and analog components. • Therefore, at the design stage either digital components are mapped into the continuous domain and the design is carried out in the continuous domain, or analog components are mapped into discrete domain and design is carried out there. The first of these two methods is more commonly encountered in practice because many industrial systems have many continuous systems components, including mechanical, fluid, biological and analog electrical components, with a few digital controllers.
- 11. Conclusion • Since modern small microprocessors are so cheap (often less than $1 US), it's very common to implement control systems, including feedback loops, with computers, often in an embedded system. The feedback controls are simulated by having the computer make periodic measurements and then calculate from this stream of measurements (see digital signal processing, sampled data systems). • Computers emulate logic devices by making measurements of switch inputs, calculating a logic function from these measurements and then sending the results out to electronically controlled switches. • Logic systems and feedback controllers are usually implemented with programmable logic controllers which are devices available from electrical supply houses. They include a little computer and a simplified system for programming. Most often they are programmed with personal computers. • Logic controllers have also been constructed from relays, hydraulic and pneumatic devices as well as electronics using both transistors and vacuum tubes (feedback controllers can also be constructed in this manner).
- 12. Reference • https://en.wikipedia.org/wiki/Step_response • http://lpsa.swarthmore.edu/Transient/TransInputs/TransStep.html • http://in.mathworks.com/help/control/ref/step.html?requestedDomain=in.mat hworks.com • http://ocw.mit.edu/courses/mathematics/18-03sc-differential-equations-fall- 2011/unit-iii-fourier-series-and-laplace-transform/unit-step-and-unit-impulse- response/MIT18_03SCF11_s25_2text.pdf • https://www.youtube.com/watch?v=_g-lzZ5e0h0 • http://in.mathworks.com/help/control/ref/damp.html • http://www.electrical4u.com/transient-state-and-steady-state-response-of- control-system/ • https://www.maplesoft.com/content/EngineeringFundamentals/11/MapleDocu ment_11/Block%20Diagrams,%20Feedback%20and%20Transient%20Response%2 0Specifications.pdf • https://en.wikipedia.org/wiki/Control_engineering • http://adsabs.harvard.edu/abs/2011IJTPE.131..455M