## Thursday, May 3, 2012

### Why go for closed loop when open loop is suffice?

Control system can be divided into two types: closed loop and open loop. Generally speaking, closed loop system is more complicated to implement compared to open loop system. But why go for close loop when open loop is suffice? Let's see.

Review
Before going into control system, let's review some of basic terminology in block diagram. There are three basic elements in a block diagram: summing junction, pick up point, and multiplication block.

 Figure 1: Summing junction

Figure 1 shows a summing junction where C is addition of A and B. A simple example of this block is addition of two encoder signal values.

 Figure 2: Pick up point

Figure 2 shows a pick up point, where the A signal is duplicated into two places. An example of this diagram is the duplication of encoder reading to be used in two different place.

 Figure 3: Multiplication block

Figure 3 shows a multiplication block, where C is multiplication of A and B. An example of this is; A is applied voltage, B is motor, and C is the motor speed. In other word, if voltage is applied at a motor, the motor will turn with a specific speed.

Open Loop versus Closed Loop System
The main function of control system is to bring actual output to desired output. In other word, we would like to have the output, Y to be exactly same with the reference, R. In short, Y = R.

 Figure 4: Open loop system

Consider the block equation of the open loop system. Y will be equal to R if product of C and P is equal one and we have zero disturbance, D. However, the plant parameter value, P, is usually hard to obtain, so it is quite hard to obtain a suitable controller value, C.

Let's put that the controller value was obtained to produce C.P = 1. But somehow, the plant parameter changed (because of robot weight change, low battery, etc), a new C has to be obtained, which is tedious and hard. In addition, it is quite impossible to ignore disturbance, D (because of gravity, friction, and other non-linearity).

 Figure 5: Closed loop system
On the other hand, consider a closed loop system with unity feedback, H = 1. If a high C value was selected, the first fraction term will be almost equal to one and the second fraction term will be zero. As result, output, Y, will be almost equal to the reference, R, and the disturbance, D, has been rejected.

Conclusion
It would be more advantageous to use a closed loop system rather than an open loop system although the implementation of closed system is more complicated. However, it is not as simple as "closing the loop". Consideration has to be put in: a) System transient response, b) System stability, and c) Steady state error.