Everything You Need To Know About Control Systems

Control systems can help you automate simple to complex operations.

Control systems engineering is a specialized field of electronics and communication, which is extensively focused on building systems that control their environment in a certain way.

In a way, you could say control systems function more mechanically than through symbolic digital contraptions, which makes them simpler in design and gives them a unique architecture. In fact, if you could zoom in and see all the mechanical activity happening inside it, you’d see vast combinations of filters and sensors working in unison — Much like how humans take buses, move through different places, and get to work without bumping into each other.

Do you know the most complex control system in the world is the human brain? The human brain works like a programmable control system because it can reshape itself. You can change the physical characteristics of the brain by teaching it new things.

A human brain under a closed loop control system.

Although, in the world of computers and electronics, control systems are not very flexible. And flexibility is not a requirement for complex operations. You can think of control systems as complex miniature mechanical devices. For instance, if you press one button, it will show one value mechanically.

However, control systems are way more complex than mechanical systems. A comparatively small electronic chip can do way more than a mechanical machinery. In addition, a mechanical contraption will become exponentially complex or bigger as we add more and more operations to the design, which would make it practically unfeasible. But that’s not the case with control systems.

Why Don’t We Use Microcontrollers Instead?

Unlike microcontrollers, a control system operates in a parallel fashion where everything happens together. Microcontrollers’ operations take place in a pipeline, where operations happen in discrete cycles. This makes control systems more robust, reliable, and cheaper.

So, what’s the purpose of PIDs (Control systems) in the world of microcontrollers and microprocessors? In fact, MCU can even create a virtual “control system” through a simple program. So why do we use control systems?

It’s because control systems are less complex, extremely cheap and highly robust. For example, If you want to design a system that detects heat and increases the water flow accordingly. Using a microcontroller to accomplish such tasks might be convenient but not cost-effective: Especially for a business that mass produces such devices. It would not only waste a lot of computational power but also increase the production cost of the overall system.

If you plan to do a DIY project, then a microcontroller would suffice, but if you want to produce an electronic gadget, sell it successfully and make a killing in profits — Then you have to design it using a control system.

Transfer function Definition

Transfer Functions: A transfer function is a mathematical function that converts the input signal to the output. For instance, if you have a machine that feeds on potatoes and spits gold, the process/function that converts potatoes into gold is its Transfer function.

A more technical definition of the transfer function is: The transfer function is the ratio of the Laplace transform of the output signal to the Laplace transform of the input signal. Assuming the initial boundary condition (The value of arbitrary variables) as zero.

Or it is the ratio of the output signal and input signal in the frequency domain.

A Simple Design Overview.

Designing a control system is simple.

1. First, know what you want your control system to accomplish.
2. Then determine the input parameters the system will need to accomplish the task.
3. Then calculate a transfer function, as well as determine the boundary conditions.

A control system can be a closed-loop CS or an open-loop CS. A closed-loop control system has a feedback mechanism. The feedback is incorporated with input signals to calibrate the transfer function. In simple words, the machine can correct itself over time.

This principle is used in adaptive filters and machine learning algorithms. The following diagrams will clear your doubts.

The input shown below is not u(t). It is r(t) which stands for reference input.

Two basic Types of Control Systems

A Simple Design of a Control system

Let’s design a simple control system. Consider this scenario:

Let’s say that we want to build a closed-loop control system that measures the air pressure and adjusts the RPM of the rotary wings to keep the helicopter at a certain altitude.

To achieve this, we’d need the following as input variables:

1. Barometer to measure the current height of the helicopter. (Because the atmospheric pressure changes with altitude)
2. Current RPM of the wing.

Here is a block diagram that explains how the control flow would look like:

Control system block diagram.

The variables and blocks are explained further below.

The transfer function should produce an output (output-error) that increases or decreases the RPM of the rotary wings until the helicopter reaches the desired height.

A step-by-step approach to solving the problem.

Let’s discuss what’s happening on each step.

Figure 1 shows that we have two variable A0 and A1. A0 is the current height of the helicopter and A1 is where the helicopter must go.

In figure 2, we determined the error function e(T) so we know how high we must go to reach the desired altitude.

Figure 3 shows a graph of how that error function will change over time. Since we’re calibrating and moving toward the desired altitude, the error function value will naturally decrease over time (as shown). And because we have a degradation graph, we can model it as the equation written beside it (in yellow).

e(t) = Ax * e^(-at²)

Where the value of e is 2.7183.

Figure 4 shows a simple closed-loop control system diagram of this process.

Transfer function would be a simple linear formula that would calculate the RPM of the helicopter motor. We can optimize this by varying the error steps and reducing it as we approach the local minima (The desired position). If the helicopter overshoots the desired altitude, the error function will change signs as well as reduce the error steps. The error function would then look like this (Image shown below). The varying time-step function would make this control system non-linear.

Error function with varying time-step function.

Characteristics of a Control System:

We usually study LTI systems. LTI stands for “linear time-invariant” control systems. Control systems have either of the following characteristics.

1. Linear or non-linear
2. Time variant or time invariant
3. Causal or non-causal
4. SISO or MIMO: “single Input single Output” or “Multiple Input Multiple Output”.

We’ll discuss these characteristics in great detail in the upcoming post on control systems and engineering. You’ll also learn how we can convert a mathematical function (transfer function) into an electronic circuit.

Using control theory, you’ll be able to work on cheap yet amazing projects. You’d also be able to monetize your control systems by solving problems or making life more convenient for your customers!

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