Fa2004 16.33311-5 Altitude controller Figure 6: Altitude controller time response for more complicated input The gain Kh must be kept very small since the low frequency poles are heading into the rhP Must take a different control approach to design a controller for the full dynamics Must also use the throttle to keep tighter control of the speed Example in Etkin and Reid, page 277. Simulink and Matlab code for this is on the Web page
Fall 2004 16.333 11–5 0 50 100 150 200 250 300 −20 0 20 40 60 80 100 120 Altitude controller height time h c h Figure 6: Altitude controller time response for more complicated input. • The gain Kh must be kept very small since the low frequency poles are heading into the RHP. ⇒ Must take a different control approach to design a controller for the full dynamics. – Must also use the throttle to keep tighter control of the speed. – Example in Etkin and Reid, page 277. Simulink and Matlab code for this is on the Web page
Fa2004 16.33311-6 Figure 7: Simulink block diagram for implementing the more advanced version of the altitude hold controller. Follows and extends the example in Etkin and Reid page 277
Fall 2004 16.333 11–6 Altitude Controller Completes Figure 8.17 in Etkin and Reid use with altit_simul.m T=alt(:,1);u=alt(:,2);w=alt(:,3); q=alt(:,4);theta=alt(:,5);h=alt(:,6); dele=alt(:,7);delt=alt(:,8);href=alt(:,9); K_h*Khn(s) Khd(s) height Lead alt To Workspace Sum4 Signal 2 Signal Builder Signal Generator Scope1 Scope Saturation Sat Ramp Mux Mux Mux Dele Delt u w q theta h all Longitudinal Model -KK_u K_th K_q Kun(s) Kud(s) Engine Lead JNt(s) JDt(s) Engine Dynamics JNe(s) JDe(s) Elevator Lag 0 Constant1 0 Clock u u_ref Figure 7: Simulink block diagram for implementing the more advanced version of the altitude hold controller. Follows and extends the example in Etkin and Reid, page 277
with q and theta FB to 8 Fa2004 16.33311-7 0.94 -3 Figure 8: Root loci associated for simulation(a, 6 to de) wth u FB to Figure 9: Root loci associated with simulation (u to dt). There is more authority in the linear control analysis but this saturates the nonlinear simulation igure 10: Root loci associated with simulation(h to de). Lead controller
Fall 2004 −3 −2.5 −2 −1.5 −1 −0.5 0 −3 −2 −1 0 1 2 3 0.82 0.66 0.52 0.4 0.28 0.18 0.09 3 0.52 0.4 0.28 0.18 0.09 0.94 0.5 0.82 0.66 2 2.5 0.94 1.5 1 1 2 1.5 0.5 2.5 3 with q and theta FB to δ e Real Axis Imaginary Axis 16.333 11–7 Figure 8: Root loci associated for simulation (q, θ to δe). −2 −1.8 −1.6 −1.4 −1.2 −1 −0.8 −0.6 −0.4 −0.2 0 −2 −1.5 −1 −0.5 0 0.5 1 1.5 2 0.94 0.82 0.66 0.52 0.4 0.28 0.18 0.09 0.94 0.66 0.52 0.4 0.28 0.18 0.09 1.75 0.25 2 0.82 1 0.5 1.25 0.75 1.25 0.75 1.5 1.5 1 0.5 1.75 2 0.25 with u FB to δ t Real Axis Imaginary Axis Figure 9: Root loci associated with simulation (u to δt). There is more authority in the linear control analysis, but this saturates the nonlinear simulation. −1 −0.9 −0.8 −0.7 −0.6 −0.5 −0.4 −0.3 −0.2 −0.1 0 0.1 −2 −1.5 −1 −0.5 0 0.5 1 1.5 2 0.82 0.6 0.42 0.31 0.22 0.16 0.1 0.045 0.6 0.31 0.22 0.16 0.1 0.045 1.75 0.82 2 0.42 0.75 0.25 1.25 0.5 1 0.75 1.5 1.25 0.25 0.5 1 2 1.5 1.75 with h FB to δ e command Real Axis Imaginary Axis Figure 10: Root loci associated with simulation (h to δe). Lead controller
Fa2004 16.333118 Initial Condition response to 90m altitude error. E-FB 5*U Initial Condition response to 90m altitude error 208, input Figure 11: Initial condition response using elevator controller. Note the initial ele- vator effort and that the throttle is scaled back as the speed picks up
Fall 2004 16.333 11–8 0 2 4 6 8 10 12 14 16 18 −20 0 20 40 60 80 100 Initial Condition response to 90m altitude error. E−FB H 5*U θ deg 0 2 4 6 8 10 12 14 16 18 −20 −15 −10 −5 0 5 10 15 20 Commands (degs) Initial Condition response to 90m altitude error δ e input 20*δ t input Figure 11: Initial condition response using elevator controller. Note the initial elevator effort and that the throttle is scaled back as the speed picks up
Fa2004 16.33311-9 DO 100 150 250 Figure 12: Command following ramps up and down. offset, but smooth transitions deg 250 200 Figure 13: Elevator controller -Overall response and inputs
Fall 2004 16.333 11–9 0 50 100 150 200 250 300 0 200 400 600 800 1000 1200 1400 1600 time height Altitude controller: elevator FB h c h Figure 12: Command following ramps up and down. Offset, but smooth transitions. 0 50 100 150 200 250 300 −5 0 5 Linear Response − elevator−FB U α deg θ deg 0 50 100 150 200 250 300 −3 −2 −1 0 1 2 3 δ e 10*δ t Figure 13: Elevator controller – Overall response and inputs