Open Loop and Closed Loop Control

Welcome to the first lesson of control system lectures for beginners course. This lecture is on open-loop control system versus closed-loop control systems. This will improve your understanding about control system and the two types of control systems.

A control system is a mechanism that alters the future behavior or state of a system. Now in order to be considered as a control system and not simply a changed state system, the behavior or the outcome must tend towards a state that is desired.

Control theory is a branch of mathematics that is concerned with the strategy to select the appropriate input. It deals with how to go about generating that outcome. Without Control Theory the designer is relegated to selecting appropriate actions through trial and error.

All control systems have two basic parts the system to be controlled usually called the plant and an input into the plant.

The input acts on the plant which responds over time to produce a system output. This type of control system is called an open-loop system because the input does not depend on the system output.

Open Loop Control System

The control system in which the output quantity has no effect upon the input quantity is called the open-loop control system.

Open-loop control systems are typically reserved for simple processes that have well-defined input output behaviors. Now look at some examples of open loop control system.

Example 1 

An example of an open-loop control system a dishwasher. The goal of a dishwasher which is the plant is clean dishes which is the output. Once the user sets the wash time which controls the time to clean the dishes, the dishwasher will run for that set time.

Now this is true regardless of the cleanliness of the dishes. If the dish is loaded were clean to begin with, the dishwasher would still run for the prescribed time. Further if you loaded the dishwasher with ten plates full of cake the set time might not be enough to clean them.

Example 2

Another common example of open-loop control is a sprinkler system for your lawn. In this control system, input is set time and the system output is the moisture content of the soil.

Again the user sets the timer which controls the amount of time to run the sprinklers. While the sprinklers are running the plant (grass in this case) is being watered. Again an open-loop sprinkler system would still run even if it was raining outside.

Example 3

For a more complicated example, imagine trying to obtain a constant speed in your car without the benefit of the built-in automatic cruise control. To do this you went to road between the front of your seat and the gas pedal to depress it halfway down.

The output of the control system is the speed of the car and the input is the position of the gas pedal. Again the car itself is the plant. The car begins to accelerate down a flat road until the force applied to the system is balanced by the force of friction. At this point the car stops accelerating and maintains a constant speed.

But what happens when the car encounters a hill or a Valley. Without varying the input that is adjusting the gas pedal the car will slow down or speed up and the desired constant speed will not be maintained.

This is the primary drawback to open-loop control. The input to the system has no way to compensate for variations in the system. To account for these changes you must vary the input to your system with respect to the output and this type of control system is called a closed loop control system.

Closed Loop Control System

Control systems in which the output has an effect upon the input quantity in order to maintain the desired output value are called closed-loop control systems.

In addition to calling a closed loop control, this can also be referred to as feedback control, negative feedback control or automatic control. For the time being we’ll use these terms interchangeably although there are slight variations between some of them that we won’t address in this lecture.

In closed loop control you measure the output of the system with a sensor and compare the result against a reference signal. Often this reference signal is referred to as the desired state or the commanded state. An error term is generated and then fed through a controller where the error is converted into a system input value.

When drawn in block diagram form it’s easy to see why this is referred to as a control loop. The negative part of the negative feedback control term is based on the comparator juncture where the feedback is subtracted.

How Closed Loop Control System Works?

So how does closed loop control work in practice. Let’s take the case of the dishwasher.

Example-1

There could be a sensor in the dishwasher that measures the cleanliness of the plates. The reference signal would be some sort of desired cleanliness level that would be set either by the manufacturer or by the user.

This desired cleanliness level would be compared to the measured level. An error term would be generated which would be fed through a controller which would monitor when to shut off the dishwasher.

Example-2

A sprinkler system could also benefit from closed-loop control. The sensor could be a device planted in the soil that measures the moisture content of the plant.

Remember that in this case the plant is both the grass and the soil, the reference signal would be a desired soil moisture content. The error signal would be generated which would then be fed through a controller and the controller would adjust the amount of time that the sprinklers ran. The sprinklers would then run until the moisture level reached a specified value and then they would be shut off.

Example 3

Now lets look closed loop control for the car with cruise control. Closed-loop control would work something like this
the sensor is a speedometer which measures the speed of the car. The reference speed would be the speed that the car was going when the cruise control was set.

Now assume that the car starts in a steady-state position on flat road and what I mean by that is that the speed is constant at your desired speed and also that the gas pedal is depressed the amount needed to generate that speed.

For this example let’s say the desired speed is a hundred miles per hour. Therefore the speedometer would also read a hundred miles per hour and since the measured speed exactly matches the reference be the error term is zero. The gas pedal would stay exactly where it is.

Once the car encounters the hill the speed starts to slow. Now the reference speed is greater than the measured speed and the error term becomes positive which signals the controller to speed up. If the car encounters are downhill the speed will increase now the reference speed is less than the measured speed and the error term will be negative. The beauty of the feedback control system is that it is capable of reacting to changes to the plant automatically by constantly driving the error term to zero.

Transfer Function

I want to leave you with one more thought regarding closed-loop control. If we take a block diagram and assign letters that abstractly represent the various parts of a control system we can gain new insight into how feedback control is manipulating a system.

For example if we label the reference signal V and we call the controller some abstract process D through the plant G which produces an output we’ll call Y which can be fed back through the sensor H to generate an error term E.

We can then reduce this block diagram even further. For example we can multiply D and G to combine into a single block. To reduce further however takes a small amount of algebra. The error signal is the reference signal V minus the output Y times the sensor process H. The output Y is the error term times D times G.

E = V-yH
y = E.D.G
E = y/DG

Now solve this equation for e which will give you Y over DG.  Now you can set both equations equal to each other and through a few more algebraic steps you can solve for the variable Y with respect to V.

DG (V-yH) = y
DGV = y(1+DGH)

y = DG/(1+DGH)

We can now rewrite this back in block diagram form these two block diagram representations are equivalent of each other.

Now doesn’t this new process look a lot like an open-loop control system only with a modified plant the feedback path has altered the original plant to be something new.

Furthermore the open-loop behavior of this new plant has the exact characteristics we wanted from the original plant namely that it follows our input.