Pseudo-Control of a Helicopter PDF

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Pseudo-Control of a Helicopter Laboratory Report...

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Control of a Pseudo-Helicopter – Laboratory Report: Spring Term 2019 –

Academic responsible: Department: Course: Module: Academic year: Student: Personal Tutor: CID: Date:

Dr Eric Kerrigan Department of Aeronautics H410 MEng in Aeronautics AE3-417 Experimental Methods 2018/2019 Robert Atanasiu Dr Rafael Palacios 01198290 March 18, 2019

Abstract: The aim of this report is to understand the physical limitations of the Simulink provided models, whilst testing the accuracy of Q-weights chosen in the Pre-laboratory phase. It has been opted for a new set of values which provided a stable behaviour of the real system and plots describing the behaviour of the real set-up with the reference input are presented. The motor voltage input is analyzed side-by-side with the performance of the system, highlighting the integrator’s limit importance. Lastly, manual control has been analyzed with emphasis put on the difference between closed/loop systems, explaining how feedback easens the job of a pilot.

Control of a Pseudo-Helicopter

Robert Atanasiu

Open-loop System Figure 1 shows the differences between the results obtained during the laboratory and the ones using the provided Simulink models. A close-up for the first 10 seconds was created and can be seen in the down right hand side of the plot; this plot highlights the difference in magnitude between the simulations and the real system. The first difference comes due to the fact that the model responses are not bounded. No damping factor is imposed such that the elevation angle is constrained to a fix interval, thus its magnitutde just increases for the whole period of the simulation. Since there is no feedback, there is no error generation before the controller. This is equivalent to a controller which is not able to understand the concept of deviation in output. But in reality, due to physics and manufacturing constraints, the elevation angle can not exceed a value higher than ± 30◦ . Linear NonLinear Real

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Figure 1: Comparison between the simulated linear and nonlinear model step responses with the linear real system

For the real system, another noticeable "feature" in Figure 1 is represented by the delay between userinput(voltage supplied to the motor) and system response. This is highlighted in the close-up, where it can be observed that the Simulink models spike almost instantly, whereas the real system responds after a longer time interval.

Closed-loop System - Pre-lab Performance The 4 pre-lab designs have been tested in the laboratory and the main findings are as follows: the weights set to give out the best Travel and Overall performance have triggered the "Safety Overall" dial, whereas the other two performed as expected. Thus, in order to best highlight why the pre-lab choice of weights should be modified, two plots describing the elevation and travel behaviour of the "Best Overall" system have been computed. Even though a large majority of Q-values used for the "pure" Elevation case have been used for the overall case, the magnitude of the travel weights influenced the behaviour of the real system such that it does not follow the reference as the "pure" case does. It can be observed that after the system

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Best Overall - Elevation Comparison

Best Overall - Travel Comparison

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Figure 2: Best overall [Q] values comparison

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Control of a Pseudo-Helicopter

Robert Atanasiu

covers the first two profiles, a big overshoot at T = 20s happens, after which the system becomes flat. On the other hand, the system does not follow the travel reference at all and after approximately 25 seconds the response starts to increase unbounded. This is certainly a reflection of the instability of the system which also translates into an unbounded decrease in pitch values. The large errors are mainly due to the poor choice of the set of Q weights, but in reality it might also come as a result of the state space model which can not capture the dynamics of the system accurately. As described in the handout, a linear system was assumed, but this is not accurate to a certain extent. The reasons for this can be mostly identified within the context of the system’s inherent non-linearity. Trying to keep the system bounded, the actual damping would not be linear due to effects of aerodynamic damping and friction in the bearings. Moreover, gravity contributions would be non-linear due to terms such as cos θ and sin θ arising from changes in the frame of reference.

Close-loop System - Pre-lab Improvements The design changes are presented in table 1. Some important design modification include the significant increase qR λ in order to approach zero steady state error, while not creating an oscillatory regime. Table 1: Comparison between Q weights choices

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qρ

qλ

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Figure 3: Best overall [Q] values comparison

Now, the system did not trigger the "Safety Override" dial, while also ensuring pretty accurate tracking for both cases. For Elevation case, the simulation predicted an overshoot, whereas in reality, the system barely reached the 10◦ threshold; this is a consequence of chosing too small of a qǫ term. On the other hand, for the travel case a tradeoff between stability and accuracy was made. Even though the rising time was precise, the overshoot was almost 100%, reflecting yet again that the non-linearities of the dynamic model largely influence the behaviour of the real system.

Closed-loop System - Dynamic Response The two inputs are different throughout the experiment, and assuming the motors are identical, one will always produce a larger thrust than the other one. Thus, the dynamics of the model will be affected: the TRMS was constrained such that yaw motion was impeded and the pitch response of the system with feedback control was tested. Feedback control stabilised the system, as expected, i.e. when perturbed the TRMS returned to its equilibrium point (set at 0◦ ). The response of the system to perturbations was observed to be slightly underdamped with very few oscillations exhibited, and satisfactory Rise Time.

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Control of a Pseudo-Helicopter

Robert Atanasiu

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Figure 4: Motor voltage and dynamic response

If particular attention is casted on the response of the system, small-amplitude oscillations can be noticed, but these are most likely due to the ‘noise’ that derivative control introduces. Lastly, here, saturation is considered a nonlinear effect since the input-output relationship changes depending on the value of the input (this is why the system is assumed linear). Thus, observing the oscillatory regime registered throughout the experiment it can be deducted that the level of saturation is high. The voltage is spiking quite often, trying to go out of bounds to match the instantaneous required power to perform the state transformation; at the same time the limits of the integrator act, keeping the voltage in its "supposed" boundaries.

Manual Control Figure 5 shows the comparison in altitude and pitch for the two systems. The first noticeable aspect about the 2 subplots is the oscillatory regime of the open-loop system. This translates into the experience as a pilot, as a small perturbation in the open-loop destabilizes the aircraft which does not have a tendancy to return to a equilibrium position. The joystick is mostly vibrating, signaling that the state of the aircraft is perturbed; on the other hand, the closed-loop provides a smoother control when piloting the aicraft, always reverting any input to a equilibrium position, avoiding at all costs any oscillatory motion. 20

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(b) Pitch Figure 5: Manual Control Comparison

In the particular case of the Twin Rotor System, open-loop control proves to be difficult due to three main reasons: response lag, cross-coupling of the system’s dynamics and non-linearity. The TRMS exhibits a noticeable lag between user-input (voltage supplied to the motor) and system response. This lag makes it inherently difficult for a ‘pilot’ to stabilise the TRMS after a perturbation. It arises due to the motor’s electro-magnetic time response, and accounting for this in a dynamic model of the system is difficult.

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