## CONTROL SYSTEM

Have you ever thought of how control systems are involved in our day to day life? An Air conditioner functions depending on the temperature of the room and the desired temperature, which is set by us using a remote. The temperature of the room is being sensed by a sensor, and the error will be given as an input to the Air conditioner. According to the received error signal, it will work. Thus the room temperature is being controlled by the Air conditioner.

To control means to regulate, to direct, or to command. Hence a control system is an arrangement of different physical elements connected in such a manner to regulate, direct or command itself or some other system. In other words, the Control system is a system of devices, whichmanages, commands, directs, or regulates the behavior of the system to achieve desired results.Now let us have a look at the various systems involved in Control system.

## Open-loop system :

A system in which output is dependent on input but controlling action is entirely **independent of the output** of the systemis called an open-loop system. A **traffic control system** that operates througha signal on a time basis is one of the examples of an open-loop control system.

Consider a** bread toaster** with a pre-selected timer knob setting. The control objective is to toast the bread to the desired color (usually light brown). This is also an example of an open control system.

### Advantages

- Such systems are
**simple**in construction - These are easy from the
**maintenance**point of view - These are simple to
**design**and hence**economical**

### Disadvantages

- The open-loop system give
**inaccurate**results if there are variable in the external environment - Similarly, they cannot sense
**internal disturbances**in the system, after the controller stage

To overcome all the above disadvantages, generally, in practice, closed-loop systems are used.

## Closed-loop system

A system in which the controlling action is somehow **dependent on the output** is called a closed-loop system.To have a dependence of input, on the output, such a system uses the feedback property.** Feedback** is a property of a system by which it permits the output to be compared with the reference input to generate an error signal based on this appropriate controlling action will be decided.In these systems, a part of the output is fedback to the input for comparison with reference input applied to it.

The best example of a closed-loop control system is a **human being**. If a person wants to reach a book on the table, the position of the book is given as the reference. The feedback signal from the eyes compares the actual position of hands with the reference position. An error signal is given to the brain. Brain manipulates this error and givesa signal to the hands. This process continues until the positions of the hands get achieved appropriately

### Advantages

- Accuracy of the system is always very high because the controller modifies and manipulates the
**actuating signal**such that error in the system will be zero. - This system sense environmental changes, as well as
**internal disturbances**and accordingly, modifies the error.

### Disadvantages

- Systems are
**complicated**and**time-consuming**from the design point of view and hence costlier. - Due to feedback, the system may try to overcorrect the error cause
**oscillations**. This leads to system instability and must be taken care of while designing the system.

## Transfer function

The transfer function is a ratio of the output of a system to the input of the system in the Laplace domain with zero initial conditions. This function models the system.

## Frequency response

The frequency response of a control system can be carried by various graphical techniques like **bode plot, polar plot, and Nicholas plot.** The frequency response plots are used to determine the frequency specifications to study the stability of the systems.

*Bode plot*

*Bode plot in MATLAB*

### Polar plot

The polar plot of a transfer function G(s) is a plot of the **magnitude of G(jw) versus the phase angle of G(jw) on polar coordinates **as w varies from 0 to infinity. This polar plot is also called a Nyquist plot.

### Nicholas plot

The Nicholas plot is a frequency response plot of the given transfer function. The Nicholas plot is a **graph between the magnitude of G(jw) in decibels and phase of G(jw) in degrees.**

### Root locus

The path taken by the roots of the system when any system parameters are varied is called root locus

## Time response

The time response of a system is defined as the output of a system as a function of time.

*Step Response*

*Step response in MATLAB*

## Compensator

It is necessary to introduce additional devices or components in the system **to alter the behavior and to meet the desired specifications**. Such a device inserted into the system to satisfy the specification is called a **compensator**

## Why do we need compensator?

The main reason for designing a control system is for obtaining the desired output. So, the control systems are designed to perform specific tasks. The requirements are usually related to accuracy, stability, and response speed.

In the time domain, the specifications are given in terms of **rise time, maximum overshoot, settling time**. In the frequency domain, the specifications are given in terms of **Gain margin and Phase margin.**

The first step in design is the adjustment of gain to meet the desired specifications. In some cases, adjustment of gain alone is insufficient to meet the given specifications. In many cases, increasing the gain may lead to instability.

In such cases, it is necessary to introduce additional devices or components in the system. Such an addition of a device or component is called **compensation**. The compensator introduces pole/zero in the open-loop transfer function to modify the system to meet the design requirements.

## CONTROL SYSTEM DESIGNER TOOLBOX

Using this toolbox, we can directly get the plots like Bode, Nyquist, Nicholas, root locus, pole-zero map, and also response for unit step and impulse inputs directly **without writing any program **as mentioned above for bode plot and unit step response.

We can **design a compensator** for the given transfer function. Here compensator is used for manipulating the system transfer function for meeting the required design parameters.

We should add these requirements in step response by right-clicking on the step response window. After adding, the graph should be in the **white color space** in the window for meeting the required parameters.

So we should tune the compensator for getting the step response within the white-colored space, which will ultimately meet the required output.

- We can tune the compensator
**graphically**by tuning the poles and zeros on design plots, such as Bode and root locus.

- This can be done by right-clicking on the root locus plot and selecting the add pole/zero or delete pole/zero

- We can tune the compensator using
**automated design methods**, such as PID tuning, IMC, and LQG

We can visualize and validate the step response which will dynamically update with respect to the changes made.

*Tuning compensator graphically*

*Tuning compensator using automated tuning methods*

*Internal Model Control (IMC) Tuning*

### Conclusion :

For designing a control system, the Bode plot and the step response are crucial. We saw the program for drawing the Bode plot and step response for the given transfer function. The Control System Designer Toolbox made it so simple. By opening the toolbox itself, the bode plot, step response, and root locus are coming. This is just like a drop in the ocean. There are a lot more that can be done using this toolbox. We can design a control system with a tunable compensator for the given design requirements. This tuning can be done graphically and automatically (using PID, LQG, and IMC). After designing the complete system, we can either export the complete system to Simulink or export the values of the blocks in the system to MATLAB workspace. This is the complete overview of the Control System Designer Toolbox.

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Excellent very useful session.

Thanks