## Friday, December 23, 2011

### Why Modeling is Important?

By K.H. Ng

First of all, the open problem is what is a model? Specifically, what is a model in control system sense? The word model is generally quite wide and has many uses. A fashion model is for displaying certain cloths design, a market model is used to predict the profit and deficit, while a business model is the strategic planning in an organization.

Model in control system sense is more to a mathematical model. An extremely simple model is y = 2 * x. Give x to a function and it will return the double of the original value. A more complicated model is the Fourier series, where given a variable in function of time, it will return the amplitudes of the DC gain, sine harmonics and cosine harmonics.

While in control system, dynamic systems are more of interest where the ordinary differential equation comes in the game. This is when the variables and the derivatives comes to form a balanced equation for example the Newton's Second Law of Motion or the Kirchoff Voltage Law.

A dynamic model gives the output when excited with certain inputs. In other words, a model gives the output description in function of time when given a certain inputs, also in function of time. For example, when a motor is given an voltage for one second, what is the expected angle it will turn?

There are various method to analyze a model. Or put differently, there are many methods to work on a certain model. One might go for the most basic time domain method, which is the convolution of linear time invariant system. Another simpler method is to apply La Place transform to a signal and work from there. The most recent and popular approach is the state space approach.

Now comes to the main part of the article, why it is important? Although one might not use a model in controlling certain plant, it is important in the controller design process. For example, when someone wants to control a motor, they do not just buy a motor and test it. They start off with the model. And also, plants might not be cheap to start with.

Another example is water level control in a tank. One do not buy a tank and experiment on it. They would have to come up with a model of the tank, the pumps, the pipes, etc. After deriving the model, one can obtain the water level in function of time given the opening of a water flow valve in function of time.

To have a model is important to validate a controller design. Let's give an example of PID controller. To determine the effectiveness of the controller in controlling water level, it is important to have the model at hand for simulation purposes.

A model can be linear or non linear. But most plants in the real world is a non linear one. Even Ohm's Law is not linear if the voltage variation is too large. Also given an example in a motor. Motors have a certain dead zone where small voltage will not move the motor. The usual cause is friction. Motors also have saturation where the current cannot gets too high or it will burn out the motor.

Therefore, it is a challenge to come up with the nonlinear model. Modeling a non linear plant is never an easy task. It takes experience and a lot of computation to come up with the perfect model. There are also many method emerging in modeling. Some are fuzzy modeling, neural nets modeling, statistical modeling, etc.

In the end of the day, model is just a part of control system design and analysis. But understanding the plant to control is very important for understanding of the whole control system.