Dual observer based adaptive controller for hybrid drones

Citation: Dalwadi, N.; Deb, D.; Ozana, S. Dual Observer-Based Adaptive Controller for Hybrid Drones. Drones 2023,7, 48. https:// doi.org/10.3390/drones7010048 Academic Editors:Yu Wu and Liguo Sun Received: 23 November 2022 Revised: 1 January 2023 Accepted: 4 January 2023 Published: 11 January 2023 Copyright: © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). drones Article Dual Observer Based Adaptive Controller for Hybrid Drones Nihal Dalwadi 1, Dipankar Deb 1,* and Stepan Ozana 2 1Department of Electrical Engineering, Institute of Infrastructure Technology Research and Management (IITRAM), Ahmedabad 380026, India 2Department of Cybernetics and Biomedical Engineering, Faculty of Electrical Engineering and Computer Science, VSB-Technical University of Ostrava, 17. Listopadu 2172/15, 708 00 Ostrava-Poruba, Czech Republic *Correspondence: dipankar[email protected] Abstract: A biplane quadrotor (hybrid vehicle) benefits from rotary-wing and fixed-wing structures. We design a dual observer-based autonomous trajectory tracking controller for the biplane quadrotor. Extended state observer (ESO) is designed for the state estimation, and based on this estimation, a Backstepping controller (BSC), Integral Terminal Sliding Mode Controller (ITSMC), and Hybrid Controller (HC) that is a combination of ITSMC + BSC are designed for the trajectory tracking. Further, a Nonlinear disturbance observer (DO) is designed and combined with ESO based controller to estimate external disturbances. In this simulation study, These ESO-based controllers with and without DO are applied for trajectory tracking, and results are evaluated. An ESO-based Adaptive Backstepping Controller (ABSC) and Adaptive Hybrid controller (AHC) with DO are designed, and performance is evaluated to handle the mass change during the flight despite wind gusts. Simulation results reveal the effectiveness of ESO-based HC with DO compared to ESO-based BSC and ITSMC with DO. Furthermore, an ESO-based AHC with DO is more efficient than an ESO-based ABSC with DO. Keywords: biplane quadrotor; extended state observer; nonlinear disturbance observer; dual observer; adaptive backstepping controller; integral terminal sliding mode controller; adaptive hybrid controller 1. Introduction A controller design for Unmanned Ariel Vehicles (UAVs) is the focus of increasing attention because of the wide range of applications in civil, agriculture, military, surveillance, and e-commerce sectors. There are two types of drones: (i) rotary-wing UAVs and (ii) fixed-wing UAVs. Both have pros and cons; rotary-wing UAVs can hover, but fixedwing UAVs cannot, while fixed-wing UAVs have a longer flight duration than rotary-wing ones. A biplane quadrotor is a fusion of a rotary-wing quadrotor and a fixed-wing biplane. The two connected wings in the biplane quadrotor provide an aerodynamic force when switched to fixed-wing mode. Many researchers have developed different hybrid UAVs. For example, Oosedo et al. designed a quadrotor tail-sitter UAV [ 1 ] and a strategy for optimal transition [ 2 ], while a VertiKUL quadrotor tail-sitter UAV with no controlling surface is suitable [ 3 ] for an application of parcel delivery. Swarnkar et al. [ 4 ] present a comprehensive six degrees of freedom mathematical modeling of the biplane quadrotor, which is utilized along with a nonlinear dynamic inverse control design, and a variable pitch flight demo and proof-of-concept [ 5 ]. Phillips et al. [ 6 ] presented the design and development of the biplane quadrotor and tested it successfully in hovering mode for packet delivery. Further, Yeo et al. [ 7 ] show initial results of onboard flow measurement to expand the longitudinal steadiness of a biplane quadrotor under perpendicular gusts. Finally, a varying winglet for a Quadrotor Biplane Tail-sitter (QBiT) to augment the competence within a broad flight envelope is offered [ 8 ]. Finally, Dalwadi et al. [ 9 ] presented BSC with DO for the trajectory tracking of a tail sitter quadrotor, then BSC for trajectory tracking and ABSC Drones 2023,7, 48. https://doi.org/10.3390/drones7010048 https://www.mdpi.com/journal/drones Drones 2023,7, 48 2 of 18 for the payload delivery are designed for the biplane quadrotor [ 10 ]. At the same time, different nonlinear controllers such as BSC, ITSMC, and HC are developed for the biplane quadrotor for autonomous trajectory tracking [ 11 ]. An NDO-based nonlinear controller is designed to handle partial rotor failures despite wind gusts on the biplane quadrotor with slung load [ 12 ]. Further, to cater to a total rotor failure condition, a virtual deflection-based rotor failure compensation strategy is developed [13]. For the trajectory tracking of UAVs with immeasurable states, external disturbances, and parameterized uncertainties, many researchers have developed different controllers with a combination of the different types of observers. Observers estimate the immeasurable states of the system by using the known control input and measurable output to improve closed-loop stability. An extended disturbance observer-based sliding mode controller is proposed for the underactuated system to enhance the overall stability of the system [ 14 ]. At the same time, a higher-order disturbance observer-based robotic system with mismatched uncertainties to estimate lumped disturbances and their derivatives is also proposed [ 15 ]. Rojsiraphisal et al. [ 16 ] developed a disturbance observer-based FTSMC (Fast Terminal Sliding Mode Control) method for steadying underactuated robotic systems in the presence of significant parametric uncertainties as well as external disturbances. Castillo et al. [ 17 ] developed a disturbance observer-based attitude controller and validated it in simulation and experimentally for the quadrotor UAV, where a cascade structure is used to design a controller. An observer technique based on a super twisting sliding mode controller [ 18 ] is designed for accurate trajectory tracking of quadrotor UAVs. Based on the DO, standoff tracking guidance for the multiple small fixed-wing UAVs is presented [ 19 ] where the Lyapunov guidance vector field strategy is used for balancing the effect of the wind and tracking the ground target. Dhaybi et al. [ 20 ] offered a precise instantaneous approximation of the quadrotor UAVs’ supple mass and inertia tensor elements and validated them numerically and experimentally. Boss et al. [ 21 ] proposed a robust feedback controller for trajectory tracking with a high gain observer (EHGO) assessment framework validated by simulation and experimental setup to approximate the unmeasured state of multi-rotor UAVs, modeling error, and external disturbances. Infinite dimensional observer and adaptive time delay estimation are proposed [ 22 ] and numerical simulation validated. Guo et al. [ 23 ] presented MOBADC (Multiple Observer-Based Anti Disturbance Control) algorithms that contain a DO-based controller with ESO for the multiple disturbances acting on the quadrotor UAVs. ESO-based BSC controller is designed for the quadrotor [ 24 , 25 ]. Wang et al. [ 26 ] propose a backstepping sliding mode control with ESO to handle the wind gust disturbances. At the same time, a novel ADRC that requires only an output state information-based controller is designed for the quadrotor UAVs [ 27 ] and based on an anti-wind modeling strategy for a quadrotor, made up of a cascade controller with IESO (Improved Extended State Observer) [ 28 ]. A two-stage control method for fault recognition and fault-tolerant control (FTC) with two observers was proposed by Lien et al. [ 29 ] for the quadrotor UAV suffering from single rotor failure, while Lyu et al. [ 30 ] developed a DO-based H∞ synthesis technique to enhance the hovering accuracy of tail-sitter UAVs under crosswind. Liu et al. [ 31 ] developed a robust nonlinear control method to achieve the desired trajectory without switching the coordinate. Likewise, a Model Predictive Controller (MPC) is proposed for position control of tail-sitters [32]. Researchers have combined two control methods with observers to achieve more accurate trajectory-tracking control problems. For example, a two closed-loop control framework is proposed by Yang et al. [ 33 ] in which ADRC (Active Disturbance Rejection Control) for the inner loop and PD (Proportional-Derivative) controller for the outer loop are used. Lungu et al. [ 34 ] offered a combination of BSC and dynamic inversion control method for the auto landing of fixed-wing UAVs, while Zhou et al. [ 35 ] proposed a hybrid adaptive controller that contains a mass observer and robust controller for the quadrotor UAV. Different adaptive control strategies with observers are developed to adapt to the change in a parameter of the underacted system. ABC with ESO is presented [ 36 ], while Drones 2023,7, 48 3 of 18 the adaptive integral terminal sliding mode method [ 37 ] for the trajectory tracking problem for the quadrotor subject to the disturbances like parametric uncertainties, actuator faults, and wind gusts and an optimal adaptive sliding mode controller (ASMC) tuned by the particle swarm optimization (PSO), is presented [ 38 ] for the quadrotor UAV with parameter uncertainties. This paper presents a dual observer-based control architecture for biplane quadrotor UAVs, where ESO and DO help estimate states and external disturbances. There are three nonlinear controllers: (i) BSC, (ii) ITSMC, and (iii) HC, where ITSMC is for position control and BSC is for attitude control, designed based on the state estimation by ESO for trajectory tracking in the presence of external disturbances. We also develop adaptive versions of ESO-based BSC and HC controllers with DO to handle the mass changes during the flight and in the presence of the wing gust and compare the results. The rest of the paper is as follows: Section 2presents the mathematical model and the control architecture of the biplane quadrotor. Section 3presents the observers for the controller design, followed by an adaptive controller design and stability analysis for the ESO in Section 4, followed by results and discussions in Section 5, and concluding remarks in Section 6. 2. Mathematical Model and Control Architecture of Biplane Quadrotor The flight envelope of the biplane quadrotor can be divided into three modes: (i) Quadrotor Mode, (ii) Transition mode, and (iii) Fixed-wing mode, as shown in Figure 1 . During the take-off, landing, and hover, the biplane quadrotor is operated in the quadrotor mode. After performing the transition maneuver, it will convert to a conventional fixedwing aircraft that can fly with high velocity. For this simulation study, we assume that the mass of the biplane quadrotor is 12 kg. In general, drone motors are chosen in such a way that the total thrust generated by all motors is about 1.5 times higher than the weight of the drone. We consider this as a physical constraint during the simulation. So maximum thrust generated by the motors is 12 ×1.5 =18 N and torque is 9 N-m. Figure 1. Animated picture of biplane quadrotor. In this simulation study, only the quadrotor mode is considered, where the wings generate no aerodynamic forces and moments, and its dynamics are described the same as Drones 2023,7, 48 4 of 18 the conventional quadrotor, so the state space representation of the dynamics of the biplane quadrotor in the quadrotor model [12] is given as                      ˙ x1 ˙ x2 ˙ x3 ˙ x4 ˙ x5 ˙ x6 ˙ x7 ˙ x8 ˙ x9 ˙ x10 ˙ x11 ˙ x12                      =                       x2 (b1x6+b2x2)x4+b3Lt+b4Nt+dφ x4 b5x2x6−b6(x2 2−x2 6) + b7Mt+dθ x6 (b8x2−b2x6)x4+b4Lt+b9Nt+dψ x8 g−T mcx1cx3+dz x10 −T mUx+dx x12 −T mUy+dy                       , (1) where s(·) = sin(·) and c(·) = cos(·) . To avoid singularities, roll, and pitch are bounded in (−π/ 2 π/ 2 ) for yaw angle (−π π) , [LtMtNt] , T are the moments and thrust, [dφdθdψ] and [dxdydz] are the external disturbance acting on attitude and position subsystem of the biplane quadrotor, g is gravitational force. Ux=sx1sx5+cx1sx3cx5 , Uy=−sx1cx5+cx1sx3cx5 , and inertial constants are         b1 b2 b3 b4 b8 b9         =1 IxIz−I2 xz         (Iy−Iz)Iz−I2 xz (Ix−Iy+Iz)Ixz Iz Ixz (Ix−Iy)Ix+I2 xz Ix         ,   b5 b6 b7 =1 Iy  (Iz−Ix) Ixz 1 . Based on the above, the biplane dynamics control architecture is proposed next. The block diagram of the proposed dual observer based controller is shown in Figure 2. Figure 2. Dual observer-based control architecture. The ESO estimates position, attitude, and linear and angular velocities. The DO estimates the external disturbances based on the estimated state by ESO and known control inputs ( L ). The error signals are generated based on the estimated signals ˆ x and desired signals, further, based on these signals the controller gives a command ( L ) to the variable pitch propulsion system, and the signal U is generated for the four motors. The main advantages of the proposed controller architecture over the existing methods are simple yet efficient, practical, easy to implement on actual hardware, and energy-efficient. ESO is introduced to approximate the linear as well as the angular position and velocity of the biplane quadrotor while it operates in the quadrotor mode. Drones 2023,7, 48 5 of 18 3. Observers for Controller Design The ESO for the second-order system can be intended as ˙ l1=l2, ˙ l2=f(xn) + de+b0Us, where f(xn) is the nonlinear function, n= 1 . . . 12, de is the external disturbance acting on the attitude and position subsystem of the biplane quadrotor, b0 is the controlling factor, and sis [MtNtNtT]. For the above second-order system, ESO is designed as Ek=           em=ζ1ι−xm ˙ ζ1ι=ζ2ι−η1ιem ˙ ζ2ι=ζ3ι−η2ι·l f (em,χ1,µ) + b0Us ˙ ζ3ι=−η3ι·l f (em,χ2,µ), (2) where η1 , η2 , η3 , χ1 , χ2 and µ are the set parameter, ι= [φ θ ψ z x y] and m= [x1x3x5x7x9x11] . l f (exm , χ , µ) is the saturation function that regulates signal chattering, and this function is given by l f (em,χ,µ) = (em µ1−χ,|em| ≤ µ |em|χ·sign(em),|em|>µ. Using this equation, we design ESO for the roll subsystem: ˙ x1=x2, ˙ x2= (b1x6+b2x2)x4+b3Lt+b4Nt+dφ, such that Eφ=           ex1=ζ1φ−x1 ˙ ζ1φ=ζ2φ−η1φex1 ˙ ζ2φ=ζ3φ−η2φ·l f (ex1,χ1,µ) + b0Lt ˙ ζ3φ=−η3φ·l f (ex1,χ2,µ), l f (ex1,χ,µ) = (ex1 µ1−χ,|ex1| ≤ µ |ex1|χ·sign(ex1),|ex1|>µ. The ESO for all states of the biplane quadrotor is designed using a similar procedure. 3.1. Stability Analysis of ESO In this section, we discuss stability analysis [ 27 ], and for that the Lyapunov positive definite function Ve of the Extended State Observer (ESO) is deliberated, and the error dynamics are defined as            es1=ζ−x ˙ es1=es2−η1es1 ˙ es2=es3−η2l f (es1) ˙ es3=−η2l f (es1). (3) Drones 2023,7, 48 6 of 18 We can rewrite the above equation in the matrix format as ˙ es=−Λ(es)es, (4) es= [es1,es2,es3]T,Λ=  η1−1 0 η2ρ0−1 η3ρ0 0  , where ρ=l f (es1)/e1> 0 and it is bounded. Then, the theorem below details an adequate constraint for the stability of the ESO in Equation (3). Theorem 1. In the third order dynamics of the ESO in Equation (3) with the observer gains which satisfy ηi> 0 (i= 1 . . . 3 ) , and η1 , η2>η3 , there exists a matrix Γ in which all main diagonal elements are positive and Γ·Λ is a symmetric non-negative definite matrix such that the zero equilibrium point of the ESO is asymptotically stability [27]. Proof. Matrix Γis chosen as Γ=  γ11 γ12 γ13 −γ12 γ22 γ23 −γ13 −γ23 γ33 . (5) For the analysis simplification, the element’s value of the main diagonal is allocated as γ11 =1, γ22 =γ33 =Π. The Lyapunov function for Equation (4) is defined as Ve=Zt 0(Γ·Λ(es)es,˙ es)dT. (6) If the matrix Γ·Λ is positive definite, then Ve also becomes a positive definite Lyapunov function, and using Equation (4) and (5), the matrix His translated to H=  h11 −1−γ12 h21 γ12 −Π h31 γ13 γ23  , (7) where h11 =η1+γ12η2ρ+γ13η3ρ, (8) h21 =−γ12η1+Πη2ρ+γ23η3ρ, (9) h31 =−γ13η1−γ23η2ρ+Πη3ρ. (10) The elements of matrix Hare defined as h21 =−1, h31 =−γ12,h13 =−Π. (11) By combining Equations (8) and (11) to calculate two elements of matrix Γas γ12 =η2 η1η2−η3 +Π ρ η2 1+η2ρ+η1η3ρ η1η2−η3 −Π(η1+η3ρ), (12) γ23 =1 ρ·1 η1η2−η3 −Π ρ η2 1+η2ρ+η1η3ρ η1η2−η3 , (13) Drones 2023,7, 48 7 of 18 since ηi> 0, i= 1, 2, 3 and η1η2>η3 , if Π→ 0 + , the principal minor determinant of matrix Hare calculated as h11 =η1+η2ρ(−Πη1+η2 1+Πη2 1+Πη2ρ+Πη1η2ρ η1η2−η3 )−Πη3ρ =η1+η2 2ρ η1η2−η3 −Π ρ(η1η2+η3) + ρ2η2η3−η2 2ρη2 1+η2ρ+η1η3ρ η1η2−η3! ≈η1+η2 2ρ η1η2−η3 >0. (14)  h11 −1 h21 γ12 =h11 ·γ21 −1 = (η1+η2ρ η1η3−η3 −σ1)(−Πη1+η2 1+Πη2 1+Πη2ρ+Πη1η2ρ η1η2−η3 )−1 ≈(η1+η2 2ρ η1η2−η3 )η2 η1η2−η3 −1=η3+η3 2ρ η1η2−η3 >0. (15)  h11 −1−γ12 h12 γ12 −Π h31 γ13 γ23  =h11(γ12γ23 −Π2)−2Πγ12 −γ23 −γ3 12 ≈h11γ2 23η2ρ−γ23 −(γ23η2ρ)3 =h11 η2 (η1η2−η3)2ρ−η2 η1η2−η33 −1 (η1η2−η3)ρ=η3 (η1η2−η3)2ρ>0. (16) Using (8)–(16), we observe that the principal minor determinants of H are positive, resulting in a symmetric positive definite matrix H . Therefore, there is a matrix Γ that fulfills Theorem 1. Replacing matrix Γinto (6), we have Ve=Zt 0−(Λ(es)es)TΓΛ(es)esdT =Zt 0−(η1es1−es2)2−Π(η2l f (es1)−es3)2−Π(η3l f (es1))2dT. (17) Based on the above equations, the time derivative is ˙ Ve=−(η1es1−es2)2−Π(η2l f (es1)−es3)2−Π(η3l f (es1))2≤0. (18) The above analysis only depends on the central diagonal component of Γ , and ˙ Ve is nonpositive semi-definite. So, if Ve(es1 , es2 , es3) is bounded, then the errors es1 , es2 , and es3 are bounded, and then we can say that ˙ Ve is also bounded which proves that the stability requirement of ESO. Next, we design DO to estimate external disturbances. Some assumptions are required for simplicity and effectiveness in the nonlinear disturbance observer design [9] such that || ˙ dp(t)|| ≤ Dp,|| ˙ do(t)|| ≤ Dot>0. For the position subsystem of a biplane quadrotor [9], a DO is given as ˙ np=−Lpnp−LpLp˙ P+G+1 ma Up, ˆ dp=np+Lp˙ P, (19) Drones 2023,7, 48 8 of 18 where Up=R(O)E3U1 , ˆ dp is the disturbance approximation, is the observer state vector np, tunable gain matrix Lp>0 and G= [0 0 −g]T. Next, we design a nonlinear controller based on the BSC and ITSMC, and the block diagram of the controller design is shown in Figure 2where the controller is designed based on the states and external disturbances estimated by the ESO as well as DO in the quadrotor mode. 3.2. Backstepping Controller Design For ease of calculation, we divide biplane quadrotor dynamics into six subsystems. First, let us take the roll subsystem as ˙ ζ1φ=ζ2φ, ˙ ζ2φ= (b1ζ2ψ+b2ζ2φ)ζ2θ+b3Lt+b4Nt+dφ. (20) As in (19), a DO for the roll subsystem is designed as ˙ nφ=−Lφ(nφ+Lφ˙ ζ1φ+ (b1ζ2ψ+b2ζ2φ)ζ2θ+b3Lt+b4Nt), ˆ dφ=nφ+Lφζ2φ. (21) Differentiating ˆ dφ, we get ˙ ˆ dφ=˙ nφ+Lφ˙ x2=−Lφnφ−Lφ(Lφ˙ ζ1φ+ (b1ζ2ψ+b2ζ2φ)x4+b3Lt+b4Nt) +Lφ((b1ζ2ψ+b2ζ2φ)ζ2θ+b3Lt+b4Nt+dφ)−Lφ(nφ+Lφζ2φ) + Lφdφ, =−Lφ˜ dφ, (22) where ˜ dφ=dφ−ˆ dφ is the estimation error, and ˆ dφ is the estimated disturbance and Lφ> 0 is a tunable gain. Stability analysis of the DO is available in our previous work [ 9 ], and so in this work, we only focus on the overall stability analysis and control law design. Let us define error in the roll angle as e1=ζ1φ−x1d with ζ1φ as the estimated roll angle and x1d as the desired roll angle. Based on the error, a positive definite function is given as V1=1 2e2 1and the time derivative is ˙ V1=e1˙ e1=e1(˙ ζ1φ−˙ x1d) = e1(ζ2φ−˙ x1d). A virtual control signal x2d=˙ x1d−k1e1where k1>0 is designed so that ˙ V1=e1e2−k1e2 1, (23) and the error in roll angle rate become e2=ζ2φ−x2d=ζ2φ−˙ x1d+k1e1 . In the next stage, to improve the function V1 with error in the roll angle rate e2 , the error dynamics ˙ e2=˙ x2−¨ x1d+k1˙ e1 and again based on this error term, Lyapunov positive definite function is given as V2=V1+1 2e2 2, and the time derivative is given as ˙ V2=e1e2−k1e2 1+e2((b1ζ2ψ+b2ζ2φ)ζ2θ+b3Lt+b4Nt+ˆ dφ). (24) Using (22) and (24), a control law is designed for the roll subsystem as Lt=1 b3 (−e1−e2k2+¨ x2d−k1˙ e1−b1ζ2ψ−b2ζ2φζ2θ−b4Nt−ˆ dφ), (25) Drones 2023,7, 48 9 of 18 such that ˙ V2=−k1e2 1−k2e2 2≤ 0, k1 , k2> 0 which ensure that error becomes zero. Using similar calculations, the control laws for the remaining subsystems are Mt=1 b7 (−e3−k4e4+¨ x3d−˙ e3k3−b5ζ2φζ2ψ+b6ζ2 2φ−ζ2 2ψ−ˆ dθ), (26) Nt=1 b9 (−e5−k6e6−˙ e5k5−(b8ζ2φ−b2ζ2ψ)ζ2θ−b4Lt−ˆ dψ+¨ x5d), (27) T=m cζ1φcζ1θ (e7+k8e8−¨ x7d+˙ e7k7+g+ˆ dx−k7˙ e7), (28) Ux=m Te9+k10e10 −¨ x9d+ˆ dx+˙ e9k9, (29) Uy=m Te11 +k12e12 −¨ x11d+ˆ dy+˙ e11k11. (30) where ki>0, i=3, . . . , 12 are tunable gains. 3.3. ITSMC Controller Design Due to the integrator action, there is a reduced chattering phenomenon in the ITSMC, less than SMC and TSMC. A second-order sliding controller which uses the first derivative of the control signals rather than the actual control as control [ 39 ] can eliminate chattering. However, for the present application, reduced chattering is adequate. Let us define the sliding function [11,40] as S=˙ eI+Zω˙ eb/a+τeb 2a−1dt. (31) In addition, the reaching law is carefully chosen as ˙ S=−∇S−εsign(S), (32) where 0 <b/a< 1, ω , τ , ε , ∇> 0. and eI is a state tracking error term. Now let us consider the altitude subsystem (1): ˙ ζ1z=ζ2z, ˙ ζ2z=g−T mcζ1φcζ1θ+dz. (33) As shown in the block diagram (Figure 2), the error in the z axis is given by ez=ζ1z−zd where ζ1z is the estimated z axis position by the ESO. Based on this, a Lyapunov positive definite function is defined as Vz=1 2S2 z. Now, its time-derivative using (33) is ˙ Vz=Sz¨ ζ1z−¨ zd+ωz˙ ebz/az z+τze bz 2az−1 z, =Szg−T mcζ1φcζ1θ+ˆ dz−¨ zd+ωz˙ ebz/az z+τze bz 2az−1 z. (34) The control law is designed using (34) as T=m ζ1φcζ1θ (g+ˆ dz−¨ zd+ωz˙ ebz/az z+τze bz 2az+bz z+∇zSz+εzsign(Sz)). (35) such that ˙ Vz=−∇zS2 z−εz|Sz| ≤ 0, where ∇z,εz>0. Drones 2023,7, 48 16 of 18 DO. The ESO-based AHC with DO responds better than the ESO-based ABSC with DO while tracking the roll and pitch angle. In addition, yaw angle tracking by the ESO-based AHC with DO generates lesser error than the ESO-based ABSC + DO. Figure 9. Altitude tracking by the ESO-based ABSC and AHC and DO. Figure 10. Attitude tracking by the ESO-based ABSC and AHC with DO. 6. Conclusions In this paper, simulation is carried out using MATLAB Simulink to evaluate the ESObased controllers with and without DO for trajectory tracking and ESO-based adaptive controllers with DO for mass adaptation during the mission. The results of these controllers reveal that • ESO estimates the position, altitude, and velocity using only position and attitude signals, and DO estimates the disturbance signal applied on a biplane quadrotor. •x axis trajectory tracking by the ESO-based BSC with DO has a faster response, but overshoot is significant in comparison. ESO-based ITSMC with DO has a sluggish response, but ESO-based HC + DO has a faster response than the ESO-based ITSMC + DO, and less overshoot than the ESO-based BSC + DO. • The ESO-based HC + DO is the faster and most effective controller among these three controllers. • In altitude tracking, ESO-based ITSMC + DO has less overshoot than the other two controllers. • Attitude tracking by the ESO-based HC + DO is better than ESO-based BSC, and ITSMC with DO. • ESO-based ABSC + DO generates a steady-state error in the altitude, while ESO-based AHC with DO can track the altitude efficiently. A large overshoot is generated by the Drones 2023,7, 48 17 of 18 ESO-based ABSC + DO during the x axis trajectory tracking, and a steady-state error of 0.044 m is generated in the yaxis trajectory tracking. • Dual observer-based adaptive hybrid controller tracks the desired altitude trajectory in the presence of the wind gust and mass change. The proposed control architecture is effective. Author Contributions: Conceptualization, N.D. and D.D.; methodology, N.D. and D.D.; software, N.D.; validation, N.D. and D.D.; formal analysis, N.D., D.D. and S.O.; writing—original draft preparation, N.D. and D.D.; writing—review and editing, D.D. and S.O.; supervision, D.D.; funding acquisition, S.O. All authors have read and agreed to the published version of the manuscript. Funding: This work was supported by the project SP2023/009, "Development of algorithms and systems for control, measurement and safety applications IX" of Student Grant System, VSB-TU Ostrava. 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