CLOSED-LOOP VIBRATION CONTROL EXPERIMENTS ON

A ROTOR WITH BLADE MOUNTED ACTUATION

Eric F. Prechtl: Research Assistant, Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, 77 Massachusetts Ave. Cambridge, MA 02139-4307 USA

Steven R. Hall: Associate Professor; Associate Fellow, AIAA, Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, 77 Massachusetts Ave. Cambridge, MA 02139-4307 USA

Keywords: Helicopter, Rotor Blade, Active control, Servo-flap, X-Frame piezoelectric actuator, Hover Test, Controller, Harmonic Vibration

ABSTRACT

A Mach-scaled CH-47 model rotor blade with an actively controlled servo-flap near the tip was designed, manufactured, and tested. The servo- flap was powered by an “X-Frame" piezoelectric actuator. Using hover test data, the transfer function of the rotor (from servo-flap deflection to vertical hub shear) was determined. The servo- flap produces significant control authority, especially near the 3/rev frequency that would be important for the CH-47. Closed-loop feedback control was experimentally applied to the model rotor system. Both single frequency and combined frequency controllers were implemented on the rotor, and produced significant reduction in the vibration level. Most significantly, simultaneous control of 1/rev, 3/rev, 4/rev, 5/rev, and 6/rev harmonic vibration was successfully demonstrated. The peak vibrations were eliminated at each frequency, as well as the vibrations over a small bandwidth surrounding each peak. Comparison of continuous-time and discrete-time controllers was made. Continuous-time controllers were shown to produce more effective vibration reduction.

INTRODUCTION

The normal operation of a helicopter rotor in forward flight typically results in vibration and noise. The source of these effects is the unsteady aerodynamic environment experienced by the rotor blades, including blade/vortex interaction, retreating blade stall, blade/fuselage interaction, and atmospheric turbulence [12]. The forces generated by the unsteady aerodynamics on the blades are then transmitted through to the hub, and are felt as vibration in the fuselage. Generally, the forces on the blades are harmonics of the rotor frequency W, since the rotor aerodynamics are (nearly) periodic. Of these harmonics, only those that are multiples of the blade passage frequency (NΩ, where N is the number of blades) are transmitted to the fixed frame, due to the symmetry of the rotor. In contrast, there is no filtering of the noise generated by the rotor blades. Thus, the entire spectrum of rotor noise must be considered when addressing the noise control problem.

Helicopter rotor control may be used to reduce noise and vibration. A number of experimental studies have demonstrated the benefits of using active control for vibration and noise control [16, 18, 22, 14, 15, 25]. The control methods proposed can be grouped into two classes: higher harmonic control (HHC), and individual blade control (IBC). In HHC, the rotor is actuated harmonically in response to harmonic vibrations in the fixed frame. In IBC, the blades are actuated individually in response to motion of the blades themselves. In both methods, the challenge is to actuate the blades with enough authority and bandwidth to generate useful aerodynamic forces. Traditionally, active rotor control is achieved by using actuators mounted either at the swashplate, or on the pitch links to superimpose high frequency actuation signals on top of the primary collective and cyclic commands. This results in rigid-body pitch actuation of the blades.

Other research has demonstrated the benefits of using actuation near the rotor blade tip to produce spanwise varying blade displacements. Separate analyses by Lemnios et al. [17], Garcia and Hall [6], and Millott and Friedmann [19] have shown that blade mounted actuation using a trailing edge servo-flap can provide substantial improvement in HHC performance. In addition, a study by Hall et al. [11] showed that creating a spanwise varying pitch distribution on the rotor blade can improve the aerodynamic efficiency of the rotor significantly.

The use of blade mounted actuation may have other benefits. The use of blade mounted actuators for vibration control can help reduce the loads encountered by rotor components, reducing stress levels, and improving component lifetime and lowering maintenance costs. If the actuation levels are high enough, 1/rev actuation can be used for maneuvering control, and could even lead to the elimination of the swashplate.

A number of researchers have proposed using a discrete actuator to power a trailing edge servo-flap near the blade tip [24, 2, 8, 1, 3, 7, 13, 26, 5]. One of the challenges to such an approach is developing an actuator suitable for embedding in a rotor blade. The actuator must be powerful enough and have a large enough bandwidth to control the servo-flap. It must also fit within the blade profile, and should be light (relative to the blade mass) so that the blade loads are not significantly increased.

A new actuator that meets these requirements, the X-Frame actuator, has been developed by the authors [21, 20]. In this paper, we report on the testing of an active rotor using the X-frame actuator. The paper is organized as follows: First, the design of the active rotor blade and MIT Hover Test Facility are briefly described, focusing on instrumentation used to measure actuator performance. Next, the open-loop transfer function from flap deflection to vertical hub shear is presented. This transfer function is critical to vibration control, since it determines the control authority available to reduce vibration, and determines the stability and performance of any control system used for vibration control. Finally, the closed-loop control tests are presented, focusing on the design of the controller and the results from the single harmonic and multi-harmonic controller tests. The paper concludes with a brief comparison between the performance of continuous-time and discrete-time control.

ACTIVE ROTOR BLADE DESIGN

The active rotor concept was tested at MIT on a 1/6-scale model of the CH-47 Chinook rotor. The two-bladed rotor is operated at the full-scale tip Mach number, and has one active blade that incorporates an X-Frame actuator to control a trailing edge servo-flap. This section addresses the design, manufacturing, and bench-tests of the active blade.

The design of the active blade is based on model rotor blades used by Boeing Helicopters. Modifications were
made to the blade design and manufacturing procedure to incorporate the actuator and servo-flap. For the most part, the actuation system was designed to be decoupled from the overall blade structure. This allowed the majority of the design effort to be expended on the actuation system.

The design of the entire system assembly was done through the use of the solid modeling software program, ProEngineer (ProE). A rendering of the ProE model of the actuator and trailing edge control system is shown in Figure 1. Note that the skin of the servo-flap is rendered with a slight transparency to highlight the presence of the flap horn, keymount, and pre-stress wire in the interior of the flap.

One prototype active rotor blade was manufactured at MIT. The assembled active rotor blade is shown in Figure 2.

A close-up of the actuator mounted in the spar is shown in Figure 3.

Clearly seen in this figure are the strain gage attached to the center of the actuator frame and the magnets bonded to the inboard end of the inner frame. As will be described below, these magnets are used in concert with a Hall effect transducer, mounted to the bay wall, for the primary measurement of actuator and servo-flap deflection.

The predicted and manufactured properties of the active blade are collected in Table 1. The predicted blade properties were obtained through a combination of the ProEngineer model of the active blade and from input from Boeing Helicopters on the blade design. Center of gravity measurements of the manufactured active blade were not performed.

Property	Measured	Predicted
Total Blade Mass	1.96 lbm	2.01 lbm
Actuation System Mass^a	0.165 lbm	0.157 lbm
Actuation System LE Weight Mass	0.088 lbm	0.088 lbm
Actuation System Radial CG	NED	BS 45.950
Actuation System Chordwise CG^a	NED	2.003" from LE
Blade Ib^b	NED	0.511 slug ft^2
Average blade mass per span^c	NED	0.0303 lbm/in
Blade Pre-Twist	NED	-12 deg

Table 1: Properties of active rotor blade. Note that entries where there is no experimental data are labeled as “NED".

^a Without leading edge weights

^b About flapping hinge line, excluding pitch shaft assembly mass

^c Away from actuator/flap locations

It is useful to separate the mass of the components supporting the actuator and servo-flap from the total mass. These components are identified as those drawn in Figure 1, and will be referred to as the “Actuation System" components. Because these components represent a prototype design, it is expected that through future design iterations, their mass can be reduced. Also note that the mass of the leading edge weights used to balance the actuation system components about the blade quarter chord is also called out as “Actuation System LE Weight Mass". Again, it may be possible to move the CG of the system forward, reducing or eliminating the need for these weights.

HOVER TEST FACILITY

The active rotor blade was tested in air at the MIT Hover Test Facility. The facility was developed as part of the overall research effort to evaluate the effectiveness of blade mounted actuation schemes at Mach scaled rotor speeds. The hover stand was sized for 1/6 scale CH-47 (Chinook) rotor blades. The properties of the rotor and support structure are given in Table 2. Because of the concentrated actuator mass located near the tip of the rotor blades, the inertia of this active blade was much higher than that of a blade with a more uniform cross-section. For example, the Lock number of a full-scale CH-47 blade is 9.37, compared to 7.49 for the model rotor. The difference between these Lock numbers is due solely to the difference in the blade mass moments of inertia.

Property	Value
Radius	60.619 in (5.05 ft)
Hover Speed	1336 RPM
Max Motor Power	150 hp
Lowest Stand Elastic Mode	> 150 Hz
Number of Blades	2
Flap Articulation	BS 1.734 (0.0286R)
Feathering Degree of Freedom	Clamped at BS 4.078 (0.0673R)
Lag Articulation	BS 9.093 (0.15R)
Ib of Pitch Shaft Assemblies	0.0213 slug ft^2
Mass of Pitch Shaft Assemblies	6.437 lbm
Lock Number of Blade/PSA Structure	7.49
Blade Chord (nominal)	5.388
Full Scale to Model Scale Geometric Factor	5.939:1

Table 2: Properties of MIT Hover Test Facility hardware.

A 150 HP motor is used to power the hover test-stand. The motor drives the rotor via a 3 inch diameter steel shaft that is about four feet long. The top of the shaft interfaces with a 6-axis load transducer through a two inch thick coupling flange. The rotor hub is mounted to the top of this sensor through a second, two inch thick flange. The blades are connected to the hub via pitch shaft assemblies, which allow for free articulation of the flap and lag degrees of freedom. However, the blade is clamped at a particular angle of attack for each test.

A passive rotor blade was supplied by Boeing Helicopters to balance the active blade during hover testing. The passive blade has the same planform as the active blade, except that its chord tapers linearly to 1.625 inches from blade station 54.557 inches out to the tip. The passive blade was balanced spanwise against the active blade by incorporating extra steel masses on the pitch shaft assembly of the passive blade. The blades are attached to the lag hinge of the pitch shaft assemblies with a 0.5 inch diameter steel pin.

After connecting the blade to the pitch shaft assemblies, the signal and high voltage blade connectors are attached to the slipring connectors inside the lead shell. The blade wire bundles are then tie-wrapped at several locations on the pitch shaft assemblies and other hub components to support them in the centrifugal field in the rotating frame. A picture of the blades mounted to the spin stand is shown in Figure 4.

Two cameras were used to record all rotor tests. One non-rotating frame camera was mounted near the floor pointing up at the stand and rotor. It served primarily as a safety of flight monitor of the stand during testing. An image from this camera during a rotor test is shown in Figure 5. A second camera was mounted in the rotating frame above the hub, pointed along the active blade. It is shown in Figure 4. The signal from this camera was transmitted via radio frequency to a receiver mounted between the bellmouth and containment ring. This camera picked up blade and servo-flap motion during testing.

The active blade was instrumented with a collection of strain gage sensors to measure blade response; two Hall effect transducers, used to measure flap deflection; and one resistance temperature detector (RTD) to monitor the thermal environment inside the bay. A slipring was used to transfer signals between the non-rotating and rotating frame. In this paper, however, only the data from two sensors are used. The first sensor is the bay-mounted magnet/Hall effect transducer pair used to measure actuator/servo-flap deflection. The second sensor is the z (vertical) component of the hub-mounted six-axis load transducer, mentioned above.

During a rotor test, all sensor signals were stored to the computer through a National Instruments SCXI-1001 data acquisition box using 1120/1320 modules to store direct analog signals and 1121/1321 modules to provide strain gage excitation and conditioning. An analog circuit was built to provide current excitation and differential amplification for the Hall effect transducer sensors.

A “stream-to-disk" LabView virtual instrument (VI) was written to control the data acquisition process during testing. A nominal scan rate of 1000 points per second on all channels was used for all rotor tests. Signal processing techniques to average and smooth the acquired data were applied off-line to identify transfer functions and evaluate performance.

OPEN-LOOP HOVER TEST TRANSFER FUNCTION

Hover tests were conducted to measure the performance of the active blade. Most of the rotor data was collected at a blade angle of attack of 8 deg. This included tests where the rotor speed and actuation voltage was varied to study the effects of parametric changes to operating conditions. A full set of 4 deg angle of attack data was collected at 1336 RPM and 800V_{p_p} actuation to help understand the sensitivity of the performance to angle of attack. Table 3 shows the nominal thrust, coefficient of thrust, blade loading, and maximum torque measured at the six-axis load transducer while in hover (1336 RPM) for the two angles of attack. The coefficient of thrust and solidity are given by:

(1)

(2)

respectively.

Angle of Attack (deg)	Thrust (lbf)	CT		Mz (ft-lbf)
4	153.6	0.00161	0.0285	59.38
8	317.6	0.00333	0.0589	111.34

Table 3: Thrust, blade loading and rotor torque for angle of attack tests.

The modal structure of the rotor blade was identified by examining transfer functions from flap deflection to the blade torsion and bending strain gages as a function of speed. Table 4 lists the mode type and frequencies of the various blade modes within the testing bandwidth. The experimentally determined modal frequencies were compared to the modal frequencies predicted by a simple model of the blade dynamics, using one-dimensional blade properties determined by Boeing Helicopters. The experimental results agree closely with the theoretical predictions. One anomaly is that the chordwise bending frequency is higher than predicted. This is most likely due to extra unmodeled composite embedded near the trailing edge to support the servo-flap components. Note that the elastic flap bending modes are at (non-dimensional) frequencies lower than would be expected at full scale, because the pitch shaft assemblies are heavier than they should be to match the full-scale dynamics.

Mode Type	Frequency
	(Hz)	(per rev)
1st Flap Bending	55.2	2.48
2nd Flap Bending	86.5	3.88
1st Torsion	94.3	4.24
3rd Flap Bending	143.1	6.43
1st Lag Bending	157.0	7.05

Table 4: Rotor modes in hover (1336 RPM).

The flap to hub thrust transfer function is shown in Figure 6, with the peaks due to the various structural blade modes identified. This transfer function response was obtained at hover, for 8 deg angle of attack and 1200 V_{p_p} actuation.

Both the magnitude and phase of this transfer function are important for rotor control. There is a significant amount of phase roll-off with frequency in the transfer function. This is probably due to non-minimum phase dynamics associated with the fact that the actuator (the servo-flap) and the sensor (hub shear sensor) are a non-collocated pair. This will have important implications for the controllability of the system. In terms of the magnitude, at low frequencies the flap has little effect on rotor thrust. This is unexpected, because the servo-flap was designed to operate primarily in reversal, creating twisting moments on the rotor blade near the tip, leading to changes in lift. Quasi-statically, the flap should act like the trim tab on a conventional helicopter blade. The ineffectiveness of the flap at low frequencies indicates that, in hover, the flap is very close to the aileron reversal point, i.e., where the change in lift due to the flap deflections is exactly canceled by the cumulative change in lift caused by the servo-flap induced twisting of the rotor blade.

As the actuation frequency increases, the servo-flap begins to excite the dynamic modes of the rotor blade. These modes are labeled in the figure. As may be seen, the mechanism governing the effectiveness of the servo-flap in controlling hub thrust is based on aeroelastic excitation of the blade modes by the servo-flap. The resultant deformations of the rotor blade affect the lift generated.

From the response it is clear that the servo-flap is most effective in creating hub shear through the excitation of the first torsion mode and the first two flapwise bending modes between 50 Hz and 90 Hz. The physics governing how the excitation of the torsion mode leads to changes in hub thrust are relatively straightforward: the servo-flap induces a twisting moment near the tip that leads to an overall twist, changing the angle of attack of the blade over its entire length, which has a substantial effect on the lift generated. The mechanism through which excitation of the flapwise bending modes leads to changes in rotor thrust is more complicated. The thrust generated is nearly proportional to the flapwise angle of the blade at the horizontal pin. Therefore, excitation of the flap modes through the direct lift effect of the flap will lead to changes in rotor thrust. When acting alone, as in the case of the third flap bending mode in Figure 6, the flapwise modes have a small effect on the thrust generated. However, when acting in concert with the first torsion mode of the blade, as is the case for the first and second bending modes, the modes interact to provide a great deal of authority. It is uncertain just what combination of torsional and bending excitation of the rotor lade will maximize the authority of the system in controlling hub shear. Adjusting flap position, e.g., moving it towards the tip and using a smaller chord flap, will trade the amount to which the flap excites blade torsion versus blade bending. Optimizations of the entire rotor system over such variables should be done in future active blade designs to maximize the effectiveness of the system in performing the designed task.

The active blade is most effective in controlling hub shear between 50 Hz and 90 Hz. By coincidence, this is an ideal range to have maximum effectiveness because the highest level of vibration for a 3-bladed CH-47 is at 3/rev, which corresponds to 66.8 Hz at model scale. The servo-flap has a great deal of authority in affecting hub vertical shear at three per rev. At 1200 V actuation, the system produces a vibratory hub shear of ±39 lbf at this frequency. If these results are scaled to a full-sized Chinook with six identical active blades, this represents an induced vibration of ±8400 lbf at 3/rev. The maximum gross weight of the Chinook is 50,000 lbf, so this prototype actuation system is capable of inducing vibratory hub shear that represents a large fraction of the vehicle weight.

A zero in the transfer function occurs near the 2/rev frequency, 44.5 Hz. The zero near 2/rev is most likely due to an interaction between the rigid flap mode and the first elastic bending mode of the rotor blade. Fortunately, for rotors with three or more blades, the effectiveness at 2/rev is not very important for vibration control. In fact, 2/rev control is ideal for improving rotor induced power losses, so one can imagine a controller designed for vibration control at higher harmonics and induced power control at 2/rev.

CLOSED-LOOP ROTOR VIBRATION CONTROL

One of the primary goals of this research was to develop an actuation system that, through the use of closed-loop control, is capable of significantly reducing the vibration transmitted from the rotor blades to the helicopter fuselage. To test the effectiveness of the prototype active rotor blade in achieving this goal, closed-loop rotor tests were performed. This section describes the development of the closed-loop controller and the implementation of that control strategy to reduce the rotor vibrations at both single and multiple harmonics.

The purpose of the feedback control experiments performed in this research was to demonstrate the effectiveness of the actuation system in canceling the hub vertical shear vibration typically encountered in rotor operation. The aerodynamic disturbances caused by normal rotor operation are due primarily to interactions between the blades and shed vortices in the rotor wake, while the helicopter is in forward flight. Because of the periodic nature of rotor operation, these interactions result in disturbances at frequencies very close to the harmonics of rotor speed.

For the current hover tests, while there was an aerodynamic disturbance present, it differed slightly from that associated with normal helicopter operation. The disturbances generated in these tests were caused by the aerodynamic turbulence within the rotor inflow due to the asymmetry of the testing room and not from interactions with the vortices in the rotor wake. The disturbances in these tests do occur at frequencies close to harmonics of rotor speed, but the peaks in vibration spectrum are broader than those seen in a normal helicopter. The width of these peaks has a major effect on the achievable performance, as will be explained in describing the closed-loop performance results below.

Figure 7 shows the open-loop power spectral density of the hub vertical shear vibration, F_z, while operating the rotor in hover at a blade loading of

In this work, the power spectral density (PSD) of the signal x(t) is defined as:

(3)

where F_xx is the autocorrelation function of x(t). The factor of 2 in front of the integral is used so that the PSD, P_xx, satisfies

(4)

where the units of frequency are in Hz.

(Note that the power spectral density functions, , calculated using the Matlab (Version 5.3) function psd, is related to the functions, P_xx, presented in this paper by the formula P_xx = , where N_p is the number of points in the calculated power spectral density, and ∆f is the change in frequency between points.) For reference, the open-loop rms value of vibration given by integrating under the spectrum of Figure 7 is 17.2 lbf. Note that because the rotor is two-bladed, most of the vibration is centered around the 2/rev (44.5 Hz) and 4/rev (89.1 Hz) harmonics.

The goal of higher harmonic control (HHC) is to cancel the vibration at the multiples of rotor speed, where it dominates. In particular, because only those vibrations that are multiples of the blade passage frequency (NW) are transmitted to the fixed frame, standard HHC algorithms are usually only concerned with reducing those particular vibrational harmonics. However, to verify the performance of the actuation system over a wide bandwidth, vibration cancellation at each of the first six harmonics of rotor speed was addressed in these tests. The first tests that were performed involved continuous-time vibration cancellation at individual rotor harmonics. Follow on tests were performed on simultaneously reducing vibration at multiple rotor harmonics, also using continuous-time control. Finally, discrete-time control was implemented to highlight the change in performance between using discrete-time and continuous-time control. The implementation and resulting performance from these tests are discussed in the following three sections.

The HHC algorithm adopted for these tests is based on one suggested by Shaw et al. [23, 22]. The block diagram of the controller used for these tests is shown in Figure 8. The “plant" represents the active rotor blade system. The input to the plant is the commanded voltage to the high voltage amplifier that drives the X-Frame actuator and the output is the vertical hub shear in the rotating frame, i.e., the z-component of force measured by the six-axis load transducer at the hub. In the model, quasi-steady, linear time invariant assumptions are made about the rotor dynamics which allows the system to be represented by a control response matrix, T. The control response matrix is a 2 x 2 matrix relating the cosine and sine components of the input to the cosine and sine components of the output. Note that this quasi-steady assumption does not hold in reality and the variation in phase and gain of the plant will determine the stability margins and resultant performance of the system. This is discussed in more detail below. The vibratory disturbance (Figure 7) is modeled by adding it at the output of the plant.

The compensator in Figure 8 is designed to eliminate disturbances at a specific frequency. The components of the compensator are located within the dashed box of the figure. The cosine and sine components of the performance signal, z(t), are identified by multiplying that signal by a cosine and sine at the particular harmonic targeted by the controller and multiplying that signal by an integrator and a gain, given by . Multiplying these components by –T^-1 gives the cosine and sine components of the control necessary to cancel the vibration at that particular frequency. These signals are re-modulated by the cosine and sine signals of the appropriate frequency, added together, and fed back to the amplifier.

Hall and Wereley [9, 10] showed the algorithm in Figure 8 to be equivalent to the classical control system shown in Figure 9, where

(5)

(6)

(7)

The feedback controller was implemented in the MIT Hover Test Facility using Simulink. A dSpace real time control system, based on a TMSC40 Processor from Texas Instruments, was used to convert the Simulink code to C, compile it, and download to the digital signal processor. A/D and D/A cards were used to connect this controller to the (thrust) input and (actuator voltage) output signals. This controller architecture was used for all single harmonic continuous-time tests. Only the cosine and sine frequencies and the gain of the matrix T were adjusted between each case. Modifications to this controller were made to implement the multiple harmonic and discrete-time controllers, as explained below.

As was discussed in the previous section, there are a number of rotor blade dynamic modes located within the control bandwidth, and the gain and phase of the plant vary greatly between each harmonic. Because of this, the quasi-steady assumption made in the control law development does not hold. If the quasi-steady assumption did hold, the controller given by Equation (5) would have 90 degrees of phase margin and infinite gain margin. However, the variation of plant phase with frequency violates this assumption and lowers the stability margins of the resultant system.

In order to check the system stability margins before implementation, the loop gain, which is the product of the identified plant transfer function (Figure 6) and the designed compensator, is examined in the frequency domain. For example, Figure 10 shows a Bode plot of the loop gain for the 4/rev controller. There exists a chance for instability at the frequencies where the gain of the loop transfer function exceeds unity. Because this particular controller has an infinite weighting at 4/rev, the gain of the loop transfer function goes to infinity at 89.1 Hz and exceeds unity over a narrow bandwidth centered about this frequency. The variation of phase within this region determines the stability of the controller.

A useful method for checking controller stability is to look at the Nichols plot of the loop transfer function. A Nichols plot contains the same information as a Bode plot. The difference is that instead of plotting the gain and phase separately as a function of frequency, in the Nichols plot, the gain is plotted against the phase and the frequency information is not displayed explicitly. The data from Figure 10 is plotted in such a manner in Figure 11. The stability of the system is ensured if there are no encirclements of the critical point (unity magnitude at 180 degrees of phase). This point is shown by the small circle in Figure 11. Contours of constant disturbance rejection (or amplification), given by the relation

(8)

are also plotted on the Nichols chart. The closed contours around the critical point represent levels of vibration amplification. The thicker, U-shaped contour represents the 0 dB boundary, where no vibration rejection or amplification is achieved. The other contours indicate how much amplification or rejection (in dB) results for the corresponding loop gain GK.

To aid in interpreting the level of vibration amplification or reduction a particular controller causes at a certain frequency, the magnitude of Equation (8) as a function of frequency is plotted in Figure 12. As the frequency approaches 4/rev, the gain increases, affecting the disturbance rejection. Slight amplification of the vibration results at the frequencies surrounding the targeted harmonic. The amount of amplification present is related to the stability margins of the control system.

Using the Nichols plot, the gain and phase margins are easily identified by measuring the proximity of the contour to the critical point when the phase equals 180 degrees or the gain equals unity, respectively. The gain margin for this controller is approximately 6.4, and the phase margin is 50 degrees.

Before implementing each controller, its Nichols plot was generated to verify stability. If the margins were not acceptable, the matrix –T^-1 was modified to improve stability.

Once acceptable stability margins for a controller were achieved, the controller was tested by implementing it in a hover test. All of the closed-loop control tests performed in this research were done at 1336 RPM and at 8 deg angle of attack. Each controller test consisted of spinning the rotor to 1336 RPM, and accumulating at least 2 minutes of data. The first minute was taken with the controller turned on. During the second minute open-loop data was acquired to provide a direct comparison with the closed-loop data. The closed-loop in comparison to the open-loop performance of the 4/rev controller discussed above is shown in Figure 13. The data in each case corresponds to an 8192 point power spectral density of one minute of F_z data, taken at a sampling rate of 1000 points per second. The Matlab psd command (using an 8192 point Bartlett window) was used to calculate the power spectral densities.

As shown, because of the infinite controller gain precisely at 4/rev, the vibration there is virtually eliminated. In addition, the vibration over a small bandwidth surrounding the harmonic was also reduced. The change in performance due to the control can be quantified by comparing the open-loop and closed-loop root mean square values over small frequency bands centered at the controlled harmonic. For example, the change in performance over a 1 Hz window, expressed in decibels, is given by:

(9)

where P_cl and P_ol are the closed- and open-loop power spectral densities of the vibration signal, F_z, and f₁ = (89:067 - 0:5) Hz and f₂ = (89:067 + 0:5) Hz. A negative change corresponds to vibration reduction. Similar calculations are made for the performance over windows spanning 3 Hz, 10 Hz, and over the entire spectrum. All of these performance values are shown in Table 5. Also shown in Table 5 are the controller gain and phase adjustments, k_fix and F, and the open- and closed-loop rms value of the vibration, F_z, over the entire frequency bandwidth. Note that the performance improvement is very good near the rotor harmonic being controlled, but as the width of the frequency band increases to the full spectrum, very little change in performance is seen. As was noted above, the vibrational spectrum present during the current tests is broader with frequency than the spectrum typically seen in an operational helicopter. Because of this, it is expected that better performance over the entire spectrum will be achieved in an operational helicopter.

Hrm	D Gain kfix	D Phase Ø (deg)	Change in Performance (dB)				OL rms Fz (lbf)	CL rms Fz (lbf)
			1 Hz	3 Hz	10 Hz	spect
1	1	0	-5.26	-2.74	0.997	-0.148	15.3	15.1
3	1	0	-11.8	-7.82	-2.99	-0.190	16.0	15.7
4	½	30	-15.9	-10.6	-5.95	-0.919	16.9	15.2
5	¼	0	-6.91	-4.78	-3.05	-0.252	17.0	16.5
6	1	60	-15.3	-7.52	-4.56	-1.49	17.5	14.7

Table 5: Experimental performance of continuous-time single harmonic controllers. This table shows the change in closed-loop performance for each single harmonic controller implemented. Performance was evaluated by taking the ratio of closed- to open-loop rms vibration levels over 1 Hz (±0:5 Hz), 3 Hz (±1.5 Hz), and 10 Hz (±5 Hz) bands as well as over the entire frequency spectrum. Also shown are the open- and closed-loop rms levels of vibration for the spectrum.

In Figure 13, some amplification is seen at the edges of the bandwidth. These local peaks in vibration are a natural artifact of the controller design. The size of these peaks is related to the stability margins of the controller as discussed above in relation to Figure 12. The heights of the peaks can be reduced by lowering the gain of the controller. However, this would also reduce the bandwidth over which vibration reduction is achieved. Therefore, there is a trade-off between the width of vibration reduction achieved and the level of vibration amplification incurred at the edges of the control envelope.

Identical controller development was implemented at each of the first six rotor harmonics. The best performance for each of these continuous-time, single harmonic controllers is listed in Table 5.

Successful implementation was achieved at each harmonic except at 2/rev. The presence of a zero in the transfer function near that harmonic reduced the authority of the system there. In addition, a large portion of the disturbance is centered around

2/rev. As a result, attempts at performing 2/rev feedback control led to actuator saturation. To further complicate the situation, this particular zero becomes non-minimum phase as the angle of attack drops from 8 deg to 4 deg. The presence of a non-minimum phase zero at the frequency of interest severely limits the achievable performance. Fortunately, for helicopters with more than two blades, most of the vibration occurs at frequencies greater than 2/rev, where the actuator has a great deal of control authority.

The algorithm used for the single harmonic controllers was extended to test the ability of the actuator in simultaneously reducing multiple harmonics of vibration. Three separate multiple harmonic controllers were implemented in these tests. One controller was designed to simultaneously reduce the vibration at 3, 4, and 5/rev, a second was designed to reduce 4, and 6/rev vibrations, and the last targets the 1, 3, 4, 5, and 6/rev harmonics. These three controllers are referred to as the multiharmonic I, II, and III controllers, respectively.

The block diagram of the multiharmonic controller is similar to that shown in Figure 8, except multiple copies of the controller (contained in the dashed box), one for each harmonic controlled, are wired in parallel. Separate matrices T_i are specified for each harmonic. After the compensated signals at each harmonic are generated, they are added together and fed back to the plant.

Just as in the single harmonic case, the multiple harmonic controller is subject to the same stability margin concerns. Thus, the Nichols plot of each of these combined controllers were checked to ensure adequate margins before implementation. Figure 14 shows the Nichols plot for the multiharmonic III controller. This plot is similar to Figure 11 except that now the magnitude of the loop gain exceeds unity in five separate regions, corresponding to the vibration suppression being performed at the five different rotor harmonics. The gain and phase margins for this controller can be identified as in Figure 11. In this case, we see that the one contour passes within the 6 dB vibration amplification boundary. This contour corresponds to the frequencies near 4/rev and indicates that there will be some amplification of the vibration at the frequencies near that harmonic.

Each of the multiharmonic controllers were implemented as in the single harmonic control experiments. Figure 15 shows the open- and closed-loop results for the multiharmonic III controller, which is the most sophisticated controller implemented in these tests. As shown, the control system is effective in the simultaneous elimination of the peak vibration at each harmonic. The bandwidth of control around each peak was not as large as in the single harmonic control tests, due to actuator saturation. As expected from examination of the Nichols plot in Figure 14, there is some non-trivial amplification of the vibration near the 4/rev frequency in Figure 15. This could be reduced by lowering the gain at that particular harmonic, if desired.

The exact performance numbers for all of the multiharmonic controllers are given in Tables 6 and 7.

Multi-Hrm Controller	OL rms Fz (lbf)	CL rms Fz (lbf)	D Perf (dB)
I	15.7	14.3	-0.793
II	15.5	15.4	-0.067
III	20.5	19.3	-0.528

Table 6: Wide-band experimental performance of continuous-time multi-harmonic controllers. For each multiharmonic controller, this table gives the open- and closed-loop rms vibration levels, and their ratio over the entire frequency spectrum.

	D Gain	D Phase	Change in Perf (dB)
Hrm	kfix	Ø (deg)	1 Hz	3 Hz	10 Hz
I-3	1/8	-20	-0.46	0.73	0.67
I-4	1/2	30	-15.3	-8.8	-4.8
I-5	1/16	0	-7.4	-4.3	-2.4
II-4	1/2	30	-15.7	-9.6	-4.8
II-6	1/2	50	-8.7	-4.1	-2.2
III-1	1/10	0	-11.4	-7.5	-4.6
III-3	1/8	-20	-11.9	-7.4	-4.2
III-4	1/2	30	-16.5	-10.7	-3.8
III-5	1/16	0	-10.8	-7.4	-4.1
III-6	1/2	50	-9.4	-5.1	-2.5

Table 7: Narrow band experimental performance of continuous-time multi-harmonic controllers. This table shows the change in closed-loop performance for each multiple harmonic controller implemented. Performance was evaluated by taking the ratio of closed- to open-loop rms vibration levels over 1 Hz (±0.5 Hz), 3 Hz (±1.5 Hz), and 10Hz (±5 Hz) bandwidths.

As in the single harmonic control cases, very good performance was achieved in a narrow window around the rotor harmonics, but less improvement is apparent over a broader window. As in the single harmonic case, because of the broad disturbance spectrum present for these tests, the improvement should be more dramatic in an actual helicopter.

The final closed-loop control tests were designed to determine if using discrete-time or continuous-time control is more effective for vibration control. Discrete time implementation of the higher harmonic control algorithm differs from the continuous-time approach by the addition of a sample-and-hold, as shown in Figure 16, which operates with a period equal to that of the rotor.

The effect the sample and hold has on the discrete controller behavior is that the control signal is only updated once per revolution. In contrast, the continuous-time controller updates continuously during operation, thus making use of the entire measured vibratory signal.

As might be expected, the use of a sample and hold step adds an effective delay to the control loop, and thus reduces the performance. The sample and hold is approximately equal to a delay of one-half the period of the hold. The effect on the loop transfer function is a pure phase delay, represented by e^-jwT/2 [4]. This increased phase loss leads to lower stability margins in the controller and thus should worsen the performance of the system. Thus, we expect the continuous-time controller to yield better performance than the discrete-time case [9, 10].

To test this theory, continuous and discrete controllers were implemented with identical T matrices and nearly identical controller bandwidths. The open- and closed-loop performance for these systems is compared in Figure 17. Because of the large controller gain, there is a low gain margin in both cases, leading to large peaks in the response at the edges of the control bandwidth. However, it is clear that, as predicted, the continuous-time controller out-performs the discrete-time controller.

CONCLUSIONS

A model scale CH-47D active rotor blade incorporating the X-Frame actuator to power a trailing edge servo-flap was designed and manufactured at MIT. The active blade was hover tested on the MIT Hover Test Facility. Data was collected at 4 and 8 degree angles of attack as a function of rotor speed and applied voltage. The servo-flap actuation system performed as expected with rotor speed. Analysis of the test data also shows that the actuation system benefits from aeroservoelastic excitation of the blade modes by the servo-flap. This leads to strong actuator authority over frequencies from 50 hz to 90 Hz. If a similar actuation system were implemented in each of the six blades of a CH-47D helicopter, the combined actuation could produce as much as ±8400 lbf at the 3/rev frequency, which should be more than adequate for control of 3/rev vibration.

Closed-loop feedback control was implemented with a frequency weighted controller used in previous studies on rotor HHC. Controllers were successfully implemented at the individual frequencies of 1/rev, 3/rev, 4/rev, 5/rev, and 6/rev and in various combinations thereof. The most significant result was simultaneous control at all five harmonics. Control at 2/rev was impossible to achieve due to the combination of a zero in the transfer function at that frequency and a large disturbance present at 2/rev. An experimental comparison was made between the achievable performance of continuous-time and discrete-time control. The results from these tests verify that continuous-time control leads to better closed-loop performance.

ACKNOWLEDGMENTS

The authors would like to acknowledge the following people for their contributions to this research: (at MIT) Dr. John Rodgers, Paul Bauer, Dr. Mauro Atalla, Mads Schmidt, Jerry Wentworth, and Professor Mark Drela; (at Boeing) Rich Bussom, Douglas Weems, Robert Derham, and Dan Podgurski. We would also like to acknowledge Terry Deane, Dave Belt, and all the machinists at Advanced Machining and Tooling, Inc. for machining the model scale actuation system components for the active blade. This research was supported by DARPA under Contract Number F49620-95-2-0097 and MDA972-98-3-0001, monitored by Bob Crowe, Bill Coblenz, and Ephrahim Garcia. Additional support was provided by the Army Research Office, under contract DAAH04-95-0104, monitored by Gary Anderson.

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