How to stabilize the system response with feedback

How can stabilize the simple system?

How to stabilize the system response with feedback

In the previous discussion has been discussed about how to simplify the system response using a simple manner, namely by eliminating the roots of the characteristic equation value that causes instability, now we discussing“how to stabilize the response system using feedback”. The system that will be discussed is the same as the existing system on the previous discussion:

if given feedback will be obtained as follows:

From the results above, the value of C(s) are:

From the equation above, the value of H(s) can be searched by outlining the value (s + 1) (s-2) in advance which becomes s2-s-2. To get the value that caused the system will be stable, then the value of H(s) must be filled with a value that can change the value equation has roots that cause the system is stable, for example, to replace s2-s-2 with s2 + 3s + 2 then the value of H(s) must be filled with a value 4s + 3. The value of H (s) can be changed according to taste.

So the result is as follows:

The roots of the characteristic equation is -2 and -1. By looking at the roots of the characteristic equation are all negative, it can be concluded that the system is stable.

To prove necessary inverse of the equation, namely:

In accordance with the Laplace transform table above equation if given the inverse would be

The graph of the equation is:

From the graph above getting the response time goes nearly zero and it is proving that the system is stable. At the beginning of system response slightly upward, to fix it can replace the value of H(s) so as to have a better response.

DEFFINING INTELLIGENT CONTROL

Intelligent control is a class of control techniques that use various artificial intelligence computing approaches like neural networks, fuzzy logic, and genetic algorithms. Intelligent controllers are envisioned emulating human mental faculties such as adaptation and learning, planning under large uncertainty , coping with large amounts of data etc in order to effectively control complex processes.”Intelligent control”is only a name that appears to be useful today. In the same way the “modern control” of the 60’s has now become “conventional control”. What is called ”Intelligent control” today maybe called just ”control” in the not so distant future.

In the following, several alternative definitions and certain essential characteristic of intelligent system.

INTELLIGENT SYSTEM

An intelligent system has the abiliity to act appropriately in an unertain environment, where an appropriate action is that which increase the probability of succes, and succes is the achievment of behavioral subgoals that support the system’s ultimate goal.

CONTROL AND INTELLIGENT SYSTEM

Control system consists of data structures or objects (the plant models and the control goals) and processing unit or methods (the conrol laws):

An intellegent control system is designed so that it can autonomously achive a high level goal, while its components,control goals,plan model,and control laws are not completely defined, either because they were not known at the designed time or because they changed unexpectedly

The concepts intelligent and control are closely related and the term “intelligent control” has a unique and distinguishable meaning. An intelligent system must define and use goals. Control is then required to move the system to these goals and to define such goals.

POINTS OF VIEW OF INTELLIGENT CONTROL (On Autonomy and Intelligence in Control by P.J. Antsaklis)

In the design of controllers for complex dynamical systems there are needs today that cannot be succesfully addresed by the existing cocnventional control Theory. They mainly pertain to the areal of uncertanty. Heuristic methods may be needed to tune the parameters of an adaptive control law. New control laws to perfform novel control functions to meet new objective should be designed while the system is in operation.  Learning from past experience and planning control actions may be necessary. Failure detection and identification is needed.

How to Stabilize Simple System

How to stabilize the system response

In the previous discussion has been discussed about how to determine whether a system is stable or not? And we give a simple example of the system of order-2. This time we will discuss simple ways to stabilize an unstable system. Plan to be used equally in the foregoing discussion are:

On the system that led to unstable, which were the roots of the 
characteristic equation is positive, therefore the root cause of the instability must be eliminated. Thus becomes:

the inverse of the equation above, it will be :

the graph is:

From the above chart shows that the response of stable close to the value 0. To get the value of (s-2)  in a system is not easy but way above is the simplest way than the other way is the addition of feedback. As for using the feedback means, God willing, will be discussed in further discussion. 

Thank you