Abstract
In this chapter, the application of the methodology is extended to marine and aerial vehicles. Here, three representative systems are considered to show that the Linear Algebra-Based Control Design (LAB CD) methodology can be applied to systems of different nature. First, a model of a marine vessel is considered. It is interesting to note that the reference for all the sacrificed variables is not always needed. As a second class of unmanned vehicles, two aerial autonomous devices are considered. First, the control of a planar vertical take-off and landing aircraft is developed. Finally, the control of a quadrotor is considered. The LAB CD methodology is applied, and excellent results are obtained.
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Appendix 5.1: Simulink Diagram for the Control of the Marine Vessel Described in Sect. 5.1
Appendix 5.1: Simulink Diagram for the Control of the Marine Vessel Described in Sect. 5.1
The implementation of the model on the Simulink platform is shown below. The general scheme of the implementation is shown in Fig. 5.18. As it can be seen, the connection of the blocks is carried out, following the LAB control structure. The subsystem vessel model, which is specified in Fig. 5.19, outputs the value of the state variables to the LAB controller block. The disturbance block is displayed in Fig. 5.20. This block allows the generation of the disturbances introduced into the ship model. The LAB controller block contains the embedded “controller.m” file, where the linear algebra methodology designed to follow a predefined trajectory is programed.
Implementation of the general scheme for the ship model
Block connection for the implementation of the vessel model
Disturbance block subsystem implementation
The controller is programed in LAB_CONTROLLER.m file:
function [yc]=controlador(entrada) global tpc per1 per2 p m11c m22c m23c m32c m33c d11c d22c d23c d32c d33c b11c b32c Ts xdeseado ydeseado titadeseado rr uu OMrr i vd kx ky kOM ku kr k1 k2 OMref tu tr errx erry global xan yan uan ran van OMan; i=i+1; Ts=0.1; ui = entrada(1); vi = entrada(2); ri = entrada(3); xi = entrada(4); yi = entrada(5); OMi = entrada(6); tiempo = entrada(7); OMrr(i)=OMi; OMrr=unwrap(OMrr,pi); %% --------------------kinematic-------------------------------------------- xd= (xdeseado(i+1) - kx∗(xdeseado(i)-xi) - xi)/Ts; yd= (ydeseado(i+1) - ky∗(ydeseado(i)-yi) - yi)/Ts; titadeseado(i)=atan2(ydeseado(i+1)- ydeseado(i), xdeseado(i+1)- xdeseado(i)); aux = [xd + vi∗sin(OMi) ; yd - vi∗cos(OMi) ]; OMref(i+1)= atan2(aux(2) , aux(1)) ; OMref=unwrap(OMref,pi); OMref(i+1)=(OMref(i+1)+ (Tf1/Ts)∗OMref(i))/(1+Tf1/Ts); rr(i+1)= (OMref(i+1) - kOM∗(OMref(i)-OMrr(i)) - OMrr(i)) / Ts; uu(i+1)=pinv([cos(OMref(i+1));sin(OMref(i+1))])∗aux; udeseado=uu; rdeseado=rr; ud=(udeseado(i+1) - ku∗(udeseado(i)-ui) - ui)/Ts; rd=(rdeseado(i+1) - kr∗(rdeseado(i)-ri) - ri)/Ts; if i==0 van=0; end vd(i)=-1/m22c∗( m23c∗rd + m11c∗ui∗ri + d22c∗vi+ d23c∗ri ); %% --------------------dynamic-------------------------------------------- A=[b11c 0;0 b32c]; f1= m11c∗ud - m22c∗vi∗ri - m23c∗ri^2 + d11c∗ui; f2= m23c∗vd(i) + m33c∗rd + m22c∗vi∗ui + m23c∗ri∗ui - m11c∗vi∗ui + d32c∗vi + d33c∗ri; b=[f1;f2]; yc=pinv(A)∗b; %% -------------------- CONTROL ACTION end
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Scaglia, G., Serrano, M.E., Albertos, P. (2020). Application to Marine and Aerial Vehicles. In: Linear Algebra Based Controllers. Springer, Cham. https://doi.org/10.1007/978-3-030-42818-1_5
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DOI: https://doi.org/10.1007/978-3-030-42818-1_5
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