Open loop control is the most rudimentary form of control. We have a system and a desired goal location. We give commands to the system to reach this goal location. If life were as easy as giving commands and getting correct results right away, then neither would this notion page nor would classical control theory exist. The open-loop approach to control is fundamental and doesn't account for noise. It does consider the environment as well. The system will perform better if we add a feedback mechanism to this controller.
The idea of feedback is very intuitive. As the name suggests, we receive feedback from external devices such as sensors and correct our current trajectory to meet our goal position. The correction could be steering more or reducing velocity.
Let's look at feedback control more in-depth. We can see that the input signal ($x_t$) is a function of the output ($y_t$) and disturbance, $e_t$ is an error ($x_{des} - x_t$), $u_t$ is the control signal based on the error and the system actuates by $u_t$ based on its previous position ($x_t - 1$) with some error $ϵ_t$.
The task is to go to the desired position and stop there. At each time instance, we give a control signal and receive a control output that influences the following control signal. Now we look at different controller types to achieve this effect.
The Proportional controller or P controller is very simple. The control law is as follows:
$$ u_t = K_p(x_{des} - x_t) $$
We will have to tune the Proportional gain value ($K_p$). This controller cannot account for the entire kinematics of the system and hence overshoots. To compensate for the overshoot, it goes down to the desired signal but overshoots in the opposite direction. The result of a pure P controller is an oscillator response.
