**4. Control strategies**

The most significant component of the control system is the controller. It is in charge of the control system's performance. It is a mechanism or method that works to keep the amount of the process variable at a predetermined level.

Based on the input(s), a control method can direct its output(s) to a specific value, complete a sequence of events, or execute an action if the terms are met. The controllers are useful for a variety of purposes, including:


In this section, we'll go through the most prevalent path-following control schemes and algorithms. The algorithms are divided into subsections and compared qualitatively. Several control techniques have been implemented due to the CA's dynamics. Fuzzy logic, LQR (LQG), NN, Proportional Integral Derivative (PID), Sliding Mode Control (SMC), and other control systems can be employed [31, 32]. To deal with parameterized uncertainties and external disturbances, robust control systems are extensively developed. Several methods for CA or unsupervised robot path planning have been proposed in recent years. CA translational and rotational restrictions are rarely taken into account by these methods, hence they are rarely useful in practise [33]. Population-based genetic operators have made significant progress recently as a result of developments of swarm intelligence technology [34], and they continue to have a strong ability to find the best answer in a somewhat more efficient and adaptable manner. Using this strategy, an increasing number of researchers have focused on CA path planning. Artificial bee colony approach (ABC), ant-colonyapproach (ACO), genetic-algorithm (GA), and particle swarm algorithm are the most often utilised algorithms (PSO) [35]. The necessity about a robust nonlinear controller in multirotor CAs is dictated by uncertainties originating through propeller rotation, blade flap, shift in propeller rotational speed, and centre of mass position [36]. Each control system, as one might imagine, has certain set of advantages and disadvantages. There were both linear as well as non-linear control designs employed.

One of the control techniques is linear (LQG), whereas the other two are nonlinear (Dynamic feedback and dynamic n-version having nil-dynamics stabilisation provide perfect linearization and non-interacting control [37]). There are several similarities made between these control strategies.

#### **4.1 PID**

A diverse variety of controller applications have used the PID-controller. It is, without a doubt, the most widely used controller in industry. The traditional PID linear controllers has the advantages of being easy to alter parameter gains, being simple to construct, and having strong resilience. However, non-linearity connected with both the precise mathematical and the imprecise character of the model to determine to unmodeled or faulty mathematical modelling of a few of the dynamics are two of the CA's key issues [38]. As a result, using a PID-controller on the CA reduces its performance. The attitude stabilisation of a CA was done with a PIDcontroller, while the altitude control was done with a Dynamic-Surface-Control (DSC). Researchers were able to verify that all CA signals were uniformly ultimately confined using Lyapunov stability criteria. This signified that now the CA was sturdy enough to hover. The PID-controller, on the other hand, appears to been performed better in pitch angle tracking, although substantial steady-state errors were noted in roll angle tracking [39], according to the model and the experimental plots. The PIDcontroller was successfully used to the CA, however with significant limitations, according to the literature.

**Figure 3.** *Depicts the PID-controller bock diagram.*

Tuning the PID-controller might be difficult because it must be done around the equilibrium position, which would be the hover point, in order to achieve better results (**Figure 3**).

The time domain outcome of such a PID controller, that is equivalent to the control signal to the plant, is computed from the feedback inaccuracy as follows:

$$u(t) = K\_p e(t) + K\_i \int e(t)dt + K\_d \frac{de}{dt} \tag{5}$$

First, using the diagram shown above, examine how the PID controller operates in a closed-loop system. The tracking error is represented by the variable (*e*), which is the gap between the actual actual output (*Y*) and the desired output (*r*). This error signal (*e*) is sent into the PID controller, which computes for both derivative and integral of the error function with respect to time. The proportional gain (*Kp*) times of the magnitude of the difference adds the integral gain (*Ki*) repeats the integration of the error in addition of the derivative gain (*Kd*) times of the derivative for error equals the control signal (*u*).

The plant receives this control signal (*u*) and produces the new output (*Y*). The new output (*Y*) is then sent back into the loop and evaluated to the reference signal to determine a new error amplitude (*e*). The controller uses the new error signal to update the control input. This process continues as long as the controller is active.

The Laplace transform of Expression (5) is used to calculate the transfer function for such PID controller.

$$K\_p + \frac{K\_i}{s} + K\_d s = \frac{K\_d s^2 + K\_p s + K\_i}{s} \tag{6}$$

#### **4.2 LQR**

By minimising a suitable cost function, the LQR optimal-control method manages a dynamic system. Boubdallar and colleagues tested the LQR-algorithm on a CA and compared it to the PID-controller's performance. The PID been used on the CA's simplified kinematics, whereas, LQR is used on the entire model. Both of approaches produced not so good results, but it seemed evident, the LQR strategy performed better attributed to the reason that it has been implemented to a more comprehensive dynamic model [40]. Upon the comprehensive dynamic system of the CA, a basic trail *Robust Control Algorithm for Drones DOI: http://dx.doi.org/10.5772/intechopen.105966*

**Figure 4.** *Schematic representation of a CA's LQG controller.*

LQR controller was deployed. Despite the existence of gust and other disturbances, accurate pathway following been demonstrated using simulation utilising of optimal real-time trajectory (ies). After evading a barrier, the controller appeared to lose track. Its effectiveness in the face of several challenges was still being studied.

The LQR technique becomes the Linear-Quadratic-Gaussian (LQG) when combined including a Linear-Quadratic-Estimator (LQE) as well as a Kalman Filter. Considering systems having Gaussian noise and partial state information, this approach is used. In hover mode, the LQG using integral action was used to stabilise the inclination of a CA with good results. The upside of the whole LQG controller is that it can be implemented without having entire state information (**Figure 4**).

If output is to reflect reference r, therefore adding an integrator and specifying error state (*e*) is integrator output, with is difference between system input and output:

$$\begin{aligned} \dot{\mathbf{x}} &= D\mathbf{x} + E\mathbf{u} \\ \mathbf{y} &= \mathbf{G}\mathbf{x} \\ \mathbf{u} &= -\mathbf{K}'\mathbf{x} + \mathbf{k}'\_I \mathbf{e} \\ \dot{\mathbf{e}} &= r - \mathbf{y} = r - \mathbf{G}\mathbf{x} \end{aligned} \tag{7}$$

Equation (7) describe a dynamic system.

$$
\begin{bmatrix} \dot{\mathbf{x}} \\ \dot{e} \end{bmatrix} = \begin{bmatrix} D & \mathbf{0} \\ -\mathbf{G} & \mathbf{0} \end{bmatrix} \begin{bmatrix} \mathbf{x} \\ e \end{bmatrix} + \begin{bmatrix} E \\ \mathbf{0} \end{bmatrix} u + \begin{bmatrix} \mathbf{0} \\ I \end{bmatrix} r \tag{8}
$$

#### **4.3 Linearization of feedback**

Through a change in variables, feedback-linearization control scheme convert a complex nonlinear model into more of an equivalent linear-system. The reduction of granularity due to linearization and the need for a specific set for implementation are two drawbacks of feedback-linearization [41]. On a CA with having dynamic changes in its centre of gravity, feedback-linearization was used as an adaptive control approach for stabilisation and trajectory tracking. When the CA's centre of gravity shifted, the controller proved able to stabilise and reorganise it in real time [42, 43]. In order to develop a path-following controller, feedback-linearization as well as input dynamic inversion had been used. This allowed the designer to describe the control performance and yaw angle as more of a function as displacement anywhere along path. Two simulation scenarios were evaluated, with the CA cruising at varying speeds throughout the course. The airspeed and yaw angle convergence was seen in both circumstances. In, adaptable sliding mode control was compared to feedbacklinearization [14, 44]. The feedback controller proved very vulnerable to sensor noise but not robust, even with simplified dynamics. Under noisy conditions, the SMC operated effectively, and adaptability was able to anticipate uncertainty including ground effect [17]. As a result, nonlinear feedback-linearization control has goodtracking yet poor-disturbance rejection. However, when feed-back-linearization is combined with that another approach that is less sensitive to noise, good results are obtained.
