Absolutely stable system: An absolutely stable system is the one that provides bounded output even for the variation in the parameters of the system.Thus we can say that the position of the poles in the s-plane corresponds to the stability of the system. A system is specifically considered to be an unstable system, if its output does not approach 0, thereby representing some value even in the absence of input.Thus if a stable system is having poles -a 1 and -a 2 then, then -a 1 is considered to the dominant pole of that particular system. The poles that are present close to the origin are said to be dominant poles.The presence of even a single pole in the right half makes the system unstable. If a system having poles in the right domain of the s-plane, then such a system is called an unstable system.Then it is called to be an unstable system. However, if there exist repetitive poles in the imaginary axis of the s-plane.If for a system, the poles are present in the imaginary axis and are non-repetitive in nature, then it is said to be a marginally stable system.Now there exist two conditions for the poles that are present in the imaginary axis:.However, as the poles progress towards 0 or origin, then, in this case, the stability of the system decreases. When the poles of the transfer function of the system are located on the left side of the s-plane then it is said to be a stable system.Now the question arises, how poles can give information regarding the stability of the system? It is to be noted here that poles of the transfer function, is a factor defining the stability of the control system. Sometimes we come across asymptotically stable systems which are defined as the systems whose output progresses 0, when the input is not present, even when the parameters of the system show variation. The figure shown below represents the unbounded signal: So, generally, the signals whose graph shows continuous rise thereby showing infinite value such as ramp signal are known as unbounded signals. Therefore, conversely, we can say that an unstable system provides an unbounded output when the applied input is bounded in nature. Thus such a signal is said to be bounded and if such an output is provided by a system then it is said to be a stable system. Thus, if maxima and minima of any signal are finite then this means all the other values between maxima and minima will also be finite.Īs we can see that here the maxima and minima of the signal represented above is having finite values. More specifically, we can say, the bounded signal holds a finite value of maxima and minima. Now the question arises what is bounded signal?īounded value of a signal represents a finite value. We have already discussed that a stable system generates bounded output for bounded input ( BIBO). However, the steady-state output of the system is dependent on the poles of the applied input. Therefore, we can say that stability is a factor of the system which is independent of the input of the system. It is to be noted here that stability or instability is the characteristic property of the control system and thus depends on the closed-loop poles of the system. Thus we can say that a stable system is designed so as to get the desired response of the system without any intolerable variation with the changes in the system parameters. Along with this, the system must be stable enough so that the output must not get affected by the undesirable variations in the parameter of the system or disturbances. In order to get the specified output, the various parameters of the system must be controlled. We have already studied about the control system, that the various units of the control system combinedly operate so as to provide a specific output of the system. As it is an important characteristic thus the performance of the control system shows a high dependency on stability.
0 kommentar(er)
