- Control Systems Overview: A control system is a device or set of devices that manage and regulate the behavior of other devices to achieve desired results.
- Linear Systems: Linear control systems adhere to principles of homogeneity and additivity, ensuring consistent and proportional responses.
- Non-Linear Systems: Non-linear control systems do not follow linear rules, often resulting in behavior that varies significantly with different inputs.
- Digital vs Analog: Digital systems provide improved accuracy, reliability, and efficiency over analog systems, especially in handling non-linear control systems.
- System Types: Control systems range from simple SISO systems to complex MIMO systems, each suited to different applications.
A control system is a system of devices that manages, commands, directs or regulates the behavior of other devices to achieve a desired result. In other words, the definition of a control system can be simplified as a system which controls other systems to achieve a desired state. There are various types of control systems, which can be broadly categorised as linear control systems or non-linear control systems. These types of control systems are discussed in detail below.
Linear Control Systems
To grasp linear control systems, it’s essential to understand the principle of superposition theorem, which is based on two critical properties explained 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.
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 purely resistive network with a constant DC source. This circuit follows the principle of homogeneity and additivity. All the undesired effects are neglected and assuming ideal behavior of each element in the network, we say that we will get linear voltage and current characteristic. This is the example of a linear control system.
Non-linear Control Systems
A non-linear control system is one that doesn’t adhere to homogeneity. Practically, all real-world control systems are non-linear, although linear ones are theoretically possible. The describing function serves as a method to approximate analysis of these non-linear issues.
Examples of Non-linear System
A well-known example of a non-linear system is a magnetization curve or no load curve of a DC machine. We will discuss briefly no-load curve of DC machines here: No load curve gives us the relationship between the air gap flux and the field winding mmf. It is very clear from the curve given below that in the beginning, there is a linear relationship between winding mmf and the air gap flux but after this, saturation has come which shows the nonlinear behavior of the curve or characteristics of the nonlinear control system.
Analog or Continuous System
In these types of control systems, we have a continuous signal as the input to the system. These signals are the continuous function of time. We may have various sources of continuous input signal like sinusoidal type signal input source, square type of signal input source; the signal may be in the form of continuous triangle etc.
Digital or Discrete System
Digital systems use discrete, often pulsed signals with specific time intervals. These systems can convert continuous signals like sinusoidal or square waves into discrete forms through switching.
Now there are various advantages of discrete or digital system over the analog system and these advantages are written below:
- Digital systems can handle nonlinear control systems more effectively than the analog type of systems.
- Power requirement in case of a discrete or digital system is less as compared to analog systems.
- Digital system has a higher rate of accuracy and can perform various complex computations easily as compared to analog systems.
- Reliability of the digital system is more as compared to an analog system. They also have a small and compact size.
- Digital system works on the logical operations which increases their accuracy many times.
- Losses in case of discrete systems are less as compared to analog systems in general.
Single Input Single Output Systems
These are also known as SISO type of system. In this, the system has single input for a single output. Various example of this kind of system may include temperature control, position control system, etc.
Multiple Input Multiple Output Systems
Known as MIMO systems, these have multiple outputs for multiple inputs. Examples include Programmable Logic Controllers (PLC) among others.
Lumped Parameter System
In these types of control systems, the various active and passive components are assumed to be concentrated at a point and that’s why these are called lumped parameter type of system. Analysis of such type of system is very easy which includes differential equations.
Distributed Parameter System
In these types of control systems, the various active (like inductors and capacitors) and passive parameters (resistor) are assumed to be distributed uniformly along the length and that’s why these are called distributed parameter type of system. Analysis of such type of system is slightly difficult which includes partial differential equations.
