直升飞机模型

This example uses an 8-state helicopter model at the hovering trim condition. The state vectorx = [u,w,q,theta,v,p,phi,r]consists of

The controller generates commandsds,dc,dTin degrees for the longitudinal cyclic, lateral cyclic, and tail rotor collective using measurements oftheta,phi,p,q, andr.

Control Architecture

The following Simulink model depicts the control architecture:

open_system('rct_helico')

The control system consists of two feedback loops. The inner loop (static output feedback) provides stability augmentation and decoupling. The outer loop (PI controllers) provides the desired setpoint tracking performance. The main control objectives are as follows:

We use lowpass filters with cutoff at 40 rad/s to partially enforce the second objective.

Controller Tuning

You can jointly tune the inner and outer loops with thesystunecommand. This command only requires models of the plant and controller along with the desired bandwidth (which is function of the desired response time). When the control system is modeled in Simulink, you can use theslTunerinterface to quickly set up the tuning task. Create an instance of this interface with the list of blocks to be tuned.

ST0 = slTuner('rct_helico',{'PI1','PI2','PI3','SOF'});

Each tunable block is automatically parameterized according to its type and initialized with its value in the Simulink model (for the PI controllers and zero for the static output-feedback gain). Simulating the model shows that the control system is unstable for these initial values:

Mark the I/O signals of interest for setpoint tracking, and identify the plant inputs and outputs (control and measurement signals) where the stability margin are measured.

addPoint(ST0,{'theta-ref','phi-ref','r-ref'})% setpoint commandsaddPoint(ST0,{'theta','phi','r'})% corresponding outputsaddPoint(ST0,{'u','y'});

Finally, capture the design requirements usingTuningGoalobjects. We use the following requirements for this example:

% Less than 20% mismatch with reference model 1/(s+1)TrackReq = TuningGoal.StepTracking({'theta-ref','phi-ref','r-ref'},{'theta','phi','r'},1); TrackReq.RelGap = 0.2;% Gain and phase margins at plant inputs and outputsMarginReq1 = TuningGoal.Margins('u',5,40); MarginReq2 = TuningGoal.Margins('y',5,40);% Limit on fast dynamicsMaxFrequency = 25; PoleReq = TuningGoal.Poles(0,0,MaxFrequency);

You can now usesystuneto jointly tune all controller parameters. This returns the tuned versionST1of the control systemST0.

AllReqs = [TrackReq,MarginReq1,MarginReq2,PoleReq]; ST1 = systune(ST0,AllReqs);

Final: Soft = 1.12, Hard = -Inf, Iterations = 75

The final value is close to 1 so the requirements are nearly met. Plot the tuned responses to step commands in theta, phi, r:

T1 = getIOTransfer(ST1,{'theta-ref','phi-ref','r-ref'},{'theta','phi','r'}); step(T1,5)

The rise time is about two seconds with no overshoot and little cross-coupling. You can useviewGoalfor a more thorough validation of each requirement, including a visual assessment of the multivariable stability margins (seediskmarginfor details):

figure('Position',[100,100,900,474]) viewGoal(AllReqs,ST1)

Inspect the tuned values of the PI controllers and static output-feedback gain.

showTunable(ST1)

Block 1: rct_helico/PI1 = 1 Kp + Ki * --- s with Kp = 1.04, Ki = 2.11 Name: PI1 Continuous-time PI controller in parallel form. ----------------------------------- Block 2: rct_helico/PI2 = 1 Kp + Ki * --- s with Kp = -0.111, Ki = -1.32 Name: PI2 Continuous-time PI controller in parallel form. ----------------------------------- Block 3: rct_helico/PI3 = 1 Kp + Ki * --- s with Kp = 0.144, Ki = -2.24 Name: PI3 Continuous-time PI controller in parallel form. ----------------------------------- Block 4: rct_helico/SOF = D = u1 u2 u3 u4 u5 y1 2.247 -0.3153 -0.003408 0.786 -0.01543 y2 -0.1808 -1.249 0.01881 -0.07823 -0.1181 y3 -0.01772 -0.01091 -1.904 0.005976 0.06484 Name: SOF Static gain.

Benefit of the Inner Loop

You may wonder whether the static output feedback is necessary and whether PID controllers aren't enough to control the helicopter. This question is easily answered by re-tuning the controller with the inner loop open. First break the inner loop by adding a loop opening after theSOFblock:

addOpening(ST0,'SOF')

Then remove theSOFblock from the tunable block list and re-parameterize the PI blocks as full-blown PIDs with the correct loop signs (as inferred from the first design).

PID = pid(0,0.001,0.001,.01);% initial guess for PID controllersremoveBlock(ST0,'SOF'); setBlockParam(ST0,...'PI1',tunablePID(“C1”,PID),...'PI2',tunablePID('C2',-PID),...'PI3',tunablePID('C3',-PID));

Re-tune the three PID controllers and plot the closed-loop step responses.

ST2 = systune (ST0 AllReqs);

Final: Soft = 4.94, Hard = -Inf, Iterations = 66

T2 = getIOTransfer(ST2,{'theta-ref','phi-ref','r-ref'},{'theta','phi','r'}); figure, step(T2,5)

The final value is no longer close to 1 and the step responses confirm the poorer performance with regard to rise time, overshoot, and decoupling. This suggests that the inner loop has an important stabilizing effect that should be preserved.