Closed Loop Control

Controller design entails constructing a controller to meet the specification. Often the first issue to address is whether to use open- or closed-loop control. In an open-loop control system the output is neither measured nor feedback for comparison with the input. In a closed loop control system the actuating error signal, that is the difference between the input signal and the feedback signal, is fed into the controller so as to reduce the error and bring the output of the system to a desired value (Boulet, 2006).

Closed loop control systems are often referred to a feedback control system. In practice, the term feedback control and closed loop control are used interchangeably. A system that maintains a prescribed relationship between the output and the reference input by comparing them using the difference as means of control is called a feedback control system (Phillips & Harbor, 2000) as shown graphically in Figure 1.

Figure. Feedback control system

In analyzing and designing control system, we must have a basis comparison of performance of various control system. The basis may be set up by specifying particular test input signals and by comparing the responses of various systems to these input signals, where to use these typical input signals for analyzing system characteristic may be determined by the form of the input that the system will be subjected to most frequently under normal operation; if a system is subjected to sudden disturbances, a step function of time may be a good test signal (Ogata, 2008).

Once a control system is designed on the basis of test signals, the performance of the system in response to actual inputs is generally satisfactory. The use of such test signals enables to compare the performance of all systems on the same basis. Performance of various control system can be analyzed by concentrating time response. The time response of a control system consists of two parts: the transient response and the steady – state response. By transient response, we mean the one which goes from the initial state to the final state. By steady – state response, we mean the manner in which the system output behaves as t- time approaches infinity.

Figure2. Transient and Steady-state response analyses

The transient response of a practical control system often exhibits damped oscillations before reaching steady state. In specifying the transient-response characteristics of a control system to a unit-step input, it is common to specify the following Boulet (2006), Phillips & Harbor (2000) and Ogata (2008):

• Delay time

• Rise time

• Peak time

• Maximum overshoot

• Settling time

These specifications are defined in what follows and are shown graphically in Figure 2.

1. Delay time: The delay time is the time required for the response to reach half of the final value in the very first time.

2. Rise time: The rise time is the time required for the response to rise from 0% to 100% of its final value.

3. Peak time: the peak time is the time required for the response to reach the first peak of the maximum overshoot.

4. Maximum (percent) overshoot: The maximum overshoot is the maximum peak value of the response curve measured from the unity. The amount of the maximum (percent) overshoot directly indicates the relative stability of the system.

5. Settling time: The settling time is the time required for the response curve to reach and stay within a range about the final value of size specified by absolute percentage of the final value, usually 2% or 5% (Ogata, 2008). The settling time is related to the largest constant time of the control system. Percentage error criterion to use may be determined from the objectives of the system design in question.