# Types of Control Systems | Linear and Non Linear Control System

A control system is a device scheme that controls, orders, guides or controls other devices ' conduct in order to obtain a required outcome. In other words, it is possible to simplify the concept of a control system as a scheme that regulates other devices to attain a required state. There are different kinds of control schemes that can be widely categorized as either

**linear control**or

**non-linear control**

**systems**. The following are discussed in detail about these kinds of control schemes.

### Linear Control Systems

We should first comprehend the concept of superposition in order to comprehend the linear control system. The superposition theorem concept involves two significant characteristics and is described below:

Homogeneity: A system is said to be homogeneous, if we multiply input with some constant A then the output will also be multiplied by the same value of constant (i.e. A).

Additivity: Suppose we have a system S and we are giving the input to this system as a1 for the first time and we are getting the output as b1 corresponding to input a1. On the second time we are giving input a2 and correspond to this we are getting the output as b2.

Additivity: Suppose we have a system S and we are giving the input to this system as a1 for the first time and we are getting the output as b1 corresponding to input a1. On the second time we are giving input a2 and correspond to this we are getting the output as b2.

Now suppose this time we are giving input as a summation of the previous inputs (i.e. a1 + a2) and corresponding to this input suppose we are getting the output as (b1 + b2) then we can say that system S is following the property of additivity. Now we are able to define the linear control systems as those types of control systems which follow the principle of homogeneity and additivity.

#### Examples of Linear Control System

Consider a network with a steady DC source that is strictly resistive. This circuit follows the homogeneity and additivity principle. All undesired effects are ignored and assuming that each component in the network has an optimal conduct, we conclude that we will receive linear voltage and present characteristics. This is a linear control system instance.

### Non-linear Control Systems

We can simply describe a nonlinear control system as a control system that does not follow the homogeneity principle. All control schemes are non-linear systems in actual lives (linear control systems are theoretically only available). The feature description is an estimated method to analyze certain issues of nonlinear control.

#### Examples of Non-linear System

A well-known instance of a nonlinear system is a curve of magnetization or a DC machine's no load curve. Here we will briefly discuss the no-load curve of DC machines: no load curve gives us the relationship between the air gap flux and the field winding mmf. From the curve provided below, it is very evident that there is a linear connection between curling mmf and air gap flux in the start, but after that, saturation has arrived that demonstrates the curve's nonlinear behavior or the nonlinear control system's features.

### Analog or Continuous System

We have a continuous signal as the system entry in these kinds of control schemes. These indications are time's ongoing feature. We may have a variety of ongoing input signal sources such as sinusoidal signal input source, flat signal input source type; the signal may be in the shape of constant triangle, etc.

### Digital or Discrete System

We have a separate signal (or signal in the shape of pulse) as the scheme entry in these kinds of control schemes. These signals have a discrete time interval. Using the shift, we can transform multiple constant input signal sources such as sinusoidal signal input source, square signal input source sort, etc. into a separate shape.

Now the analog scheme has different benefits of a separate or digital system and these benefits are listed below:

- Nonlinear control systems can be handled more efficiently by digital schemes than by analog systems.
- In the case of a discrete or digital system, the power requirement is lower than that of analog systems.
- Digital system has a greater precision level and can readily execute different complicated computations relative to analog systems.
- Digital system reliability is more like an analog system. They have a tiny, compact size as well.
- Digital system operates on logical operations that multiply their precision.
- Losses are less opposed to analog systems in particular in the event of discrete structures.

### Single Input Single Output Systems

These are also referred to as system type SISO. In this, the scheme has a single output input. Various examples of this type of scheme may include control of temperature, control of location, etc.

### Multiple Input Multiple Output Systems

These are also referred to as system type MIMO. In this, for various inputs, the device has various outputs. Different examples of this sort of scheme may include device type PLC, etc.

### Lumped Parameter System

The multiple active and passive components are presumed to be focused at a stage in these kinds of control structures, and this is why they are called system type lumped parameter. It is very simple to analyze this sort of scheme, which involves differential equations.

### Distributed Parameter System

In these kinds of control structures, it is presumed that the different active parameters (such as inductors and capacitors) and inactive parameters (resistor) are spread evenly along the path and that is why they are called distributed circuit type parameters. It is mildly hard to analyze such sort of scheme, which involves partial differential equations.