Simulation and modeling - Old Questions

a. Markov Chain

If the future states of a process are independent of the past and depend only on the present , the process is called a Markov process. A discrete state Markov process is called a Markov chain. A Markov Chain is a random process with the property that the next state depends only on the current state.

Markov chains are used to analyze trends and predict the future. (Weather, stock market, genetics, product success, etc.

b. Feedback system

The system takes feedback from the output i.e. input is coupled with output. A significant factor in the performance of many systems is that coupling occurs between the input and output of the system. The term feedback is used to describe the phenomenon.

One example of feedback system in which there is continuous control is the aircraft system. Here the input is a desired aircraft heading and the output is the actual heading. The gyroscope of the autopilot is able to detect the difference between the two headings. A feedback is established by using the difference to operate the control surface. Since change of heading will then affect the signal being used to control the heading.

The difference between the desired signal θ_t and actual heading θ₀ is called the error signal, since it is a measure of the extent to which the system from the desired condition. It is denoted by є.

We also know that, in terms of angular acceleration

From equation (1), (2) & (3)

Dividing both sides by I, and making the following substitutions in equation (4)

 (where  is damping factor)

    This is a second order differential equation.