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# Introduction to Classical Control Theory

### Towards A Scalable Theory Of Control

If we look back into the history of control theory, James Clerk Maxwell introduced the control theory in the 19th century. Later on, Edward Routh, Charles Sturm, and Adolf Hurwitz initially gave the control theory. In the whole seminar, we understand the class of network control issues for which scalable distributed controllers can be provided to get the best performance level. The whole criteria will be understood through the examples of controlled system and processes at a huge level.

Theory of control in a control system engineering deals with dynamic processes and machines. The main objective of the theory of control is to design a controlled sculpt for controlling the various systems by using optimal methods to maintain the stability. For this purpose, a well-functioned controlled system with the indispensable functionality is needed the most. This specific kind of system controller is used to supervise the main process variable and then compares it with the set point.

There exists a huge dissimilarity among the definite and required assessment of the specific progression variables, known as an error signal. Also known as, setting point-progression variable error is used as a response to produce the controlled system. There are also other factors such as controllability and observability. On the basis of these advanced features of automation that are being used for manufacturing purpose, aircraft, communications and other industries.

However, a most important function of the control theory is being used in controlled system engineering fields that are specially designed to monitor the process control system of industries. As being a universal hypothesis, the theory is at the top of rank where the feedback is required. According to the control theory, it consists of two major kinds of the controlled loop such as unlock loop and locked loop. The locked loop is called feedback control as well and the theory is based on the locked-loop. If we take the example of the unlocked loop, the control action does not rely on the results of the theory. It can be easily understood with the example of the heating boiler, which is controlled, with the help of a specific timer. Due to this fitted timer, heat can be provided for a specific period.

Control action in the whole process of heat boiler is responsible to switch on and off the boiler. In locked-loop control or feedback control, the control action totally depends on the feedback from the end of the process. In heating boiler scenario, a locked loop will be consisting of a thermostat, which is being used to compare the building temperature with the thermostat temperature. A control loop consists of feedback loop, which is used to process the setting and another point of the controller. Because of this fact, a locked loop is known as feedback loop as well. A huge list of examples occurs in the result of the theory.

To deal with the boundaries of the unlocked loop, the theory set up a feedback loop. A locked loop controller utilizes these feedback loops to handle the output of dynamic systems. Locked-loop controllers have the following benefits as compared to the unlocked loop controllers such as

• The rate of disturbance and ambiguity decreases simultaneously
• Guaranteed performance and efficiency of the systems even due to the occurrence of model improbabilities.
• An unstable system can be stabilized through the functionality of locked loop.
• Reduced the level of sensitivity among the various controlled system.
• Improved and enhance the performance of various controlled tracking systems.

Locked loop and unlocked loop are being used together at the same time in some controlled systems and in these types of systems, the unlocked loop is commonly known as feed forward. Moreover, the most common factor to be considered about the architecture of locked-loop controller is the PID controller.

Term PID is known as the proportional-integral-derivative controller is a method that is specifically designed to control various techniques in the control system. PID controller is used to calculating the error value, which is a difference between set point and the process variable. However, the classical theory is not enough to define the compatibility of large control systems such as power systems and chemical reaction networks. To deal with this situation, new approaches and methods need to be identified. These new technologies and methods will not only compatible with the analysis and synthesis of the controller but also used for the modelling and verification purposes.

Classical control theory is a branch of control theory that directly deals with the response of dynamic systems. The objective of classical theory is to control a system, which is often known as plant and its output factor will be a control signal known as a reference that may consist of fixed or changing values. For this purpose, the controller is designed and manufactured which especially monitors the output and later on compares it with the reference.