Reference no: EM133146964
ENAE 432 Control of Aerospace Systems - Design Project
Analysis Part I - System Identification
To obtain a linearized model of the nonlinear bare-airframe dynamics about the reference flight condition, that block was detached from the rest of the simulation, special excitations were applied to the elevator control surface deflection input, outputs were recorded, and a system identification analysis was performed. Frequency responses were computed from the elevator deflection in rad to the true airspeed (TAS) V in ft/s, angle of attack at the center of mass α in rad/s, pitch rate q in rad/s, pitch angle θ in rad, and vertical accelerometer at the center of mass az in g units. These frequency response data are supplied in the file frf bair.mat, where the variable w is the vector of frequencies in rad/s and frf are the corresponding frequency response evaluations. Note that these frequency responses are only for the bare-airframe dynamics, and do not include the effects of the actuators or sensors. As frequency responses represent a linear model, they are only valid for small perturbations about the reference flight condition.
Use the provided frequency response data to obtain a transfer function model for the elevator to pitch rate dynamics, q(s)/δ(s). Although the other frequency response data are not necessarily needed, they may be helpful in more quickly or easily extracting some of the modal characteristics. Each transfer function contains the same exact poles as the other transfer functions, but in general has a different gain and zeros.
In your documentation, include the following:
1. Your identified transfer function corresponding to Eq. (2c).
2. Your simplified transfer function corresponding to Eq. (3).
3. A bode plot showing the provided frequency response data as well as frequency responses for your two aforementioned elevator to pitch rate transfer functions.
Analysis Part II - Stability Augmentation System Design
As you can see from your identified transfer functions, the short period mode for the HL-20 in this flight condition has very low damping, which would lead to poor handling qualities ratings from the pilot. Using your truncated model for q(s)/δ(s) from Eq. (3), feed back the measured pitch rate to the elevator input with a gain Kq < 0 to increase the closed-loop damping ratio of the short period mode. The gain is negative because of the convention that positive control surface deflections create negative moments on the vehicle. As you increase the damping, make sure the short period mode remains second order (oscillatory) and has a closed-loop damping ratio in the range ζsp [0.3, 1.0] to meet requirements in MIL-STD-1797A [8]. The closed-loop natural frequency of the short period mode will also shift, but should stay within a few rad/s of the original open-loop value. Due to decoupling of the modes and frequency separation, the phugoid mode will generally not be affected by this loop closure.
This type of control law is known as an inner-loop stability augmentation system (SAS), and is used to correct the modal characteristics apparent to the pilot to within generally acceptable levels. A block diagram for the loop is shown in Fig.2. The resulting control law to implement this SAS is
δc(t) = δp(t) - Kqq(t) (4)
where δp is the pilot command. In this configuration, the pilot input still commands the control surface deflection; the feedback just adds additional inputs to move the closed-loop characteristics of the short period mode.
To attenuate the amount of noise injected into the feedback loop, a first-order low-pass filter with the corner frequency around 10 rad/s is commonly used in conjunction with the gain Kq. You may choose to add this filter to your design (and you may certainly adjust the corner frequency), at the cost of added complexity and additional phase lag.
In your analysis model, the SAS loop can be closed to obtain the "augmented system" G(s) (shown as the blue dashed block in Fig.2) using transfer function block-diagram algebra. This G(s) transfer function will serve as the plant model for the control design in the following section. This loop can also be closed using the feedback.m command in MATLAB®. In this latter case, the first argument to the function is the transfer function of the forward path, q(s)/δc(s), and the second argument is the transfer function of the feedback path, Kq and any applied filter. This closed-loop system can be considered an augmented model of the short period dynamics that includes the SAS and elevator actuator. At this point, the pilot still commands the elevator deflection, but there is an extra amount of feedback from the SAS to augment the modes apparent to the pilot, as in Eq. (4).
In your documentation, include the following:
1.The transfer function for your augmented system, G(s), as depicted by the blue dashed block in Fig.2.
2.A screenshot showing your control law implementation in Simulink ®.
Analysis Part III - Pitch-Rate Command System Design
Using your augmented plant dynamics from the previous section, G(s), design an outer-loop pitch-rate command system H(s) to work alongside your inner-loop SAS design. This is shown as a block diagram in Fig.3. In this control mode, the pilot longitudinal stick commands a desired pitch rate yd(t) = qd(t) for which your control law should track with the output y(t) = q(t) with small error e(t) = qe(t). This rate-command type of system is common in fixed-wing aircraft, particularly at low speeds such as during approach and landing, but is also used in rotary-wing aircraft and spacecraft.
In designing your control law for the pitch-rate command system, your design must meet the following specifications:
• The nominal closed-loop system model for q(s)/qd(s) must be stable.
• The associated gain margin must be larger than 6 dB and the phase margin must be larger than 45 deg (both in absolute value). You are free to pick the magnitude crossover frequency, but note that for aircraft it is generally two to three times the largest modal frequency of interest [12] (i.e., the short period frequency), and generally resides between 1 to 10 rad/s.
• The system must follow constant/step inputs from the pilot with zero steady-state tracking error.
• The system must have perfect rejection to constant disturbances, such as steady winds that generate step gust angles of attack αg(t). Note that maneuver Case 2 provided in run hl20.m that will simulate a step change in the angle of attack gust.
• Your design must only use the measured pitch rate q(t) for control, i.e., a derivative-free implemen- tation. Although angular accelerometers exist, they are at the present time relatively noisy and not common in aerospace vehicles.
• Your control law must produce actuator commands that fall within the actuator capability, as quantified by the position and rate limits of the actuator.
A variety of compensators structures and gain values will sufficiently meet these requirements - there is not a single correct design. Determine a simple control law that will do the job, verify your design with the nonlinear simulation, document your results and defend your choices, and then move on. Do not attempt to significantly improve your design over the requirements or optimize your design for a particular set of goals.
In your documentation, include the following:
1.A Nyquist analysis proving your nominal model is stable.
2.A Nichols chart with labeled gain and phase margins.
3.The transfer function for your pitch-rate command system.
4.A plot showing the poles and zeros of your closed-loop transfer function q(s)/qd(s). Label each pole and zero indicating its physical origin. For example, you might add the annotations "actuator pole" and "short period zero."
5.A screenshot showing your control law implementation in Simulink.
6. Demonstrate the required tracking ability to an appropriate doublet input, and demonstrate the re- quired disturbance rejection capability to an appropriate angle of attack disturbance using the nonlinear simulation, with comparisons to your nominal model. Discuss control activity for this case.
7. How does your system contend with model errors in your plant model of G(s)? Do a multiplicative robustness test for your nominal closed-loop design using
(a) The dynamics associated with the phugoid mode, which you identified for Eq. (2c) but neglected in Eq. (3) and the ensuing control designs.
(b) The first structural mode of the vehicle, which based on a ground vibration test (GVT) is expected to contribute the mode/poles [s2 + 1.26s + 3944] to your plant model.
What are the implications of these robustness tests? Note that the pilot can be expected to provide some stabilizing feedback, up to about 10 rad/s, and can even be expected to compensate for slow instabilities. Also note that these test considered model structure error and not parametric modeling error.
Technical Paper Write-Up
Document your results in the form of an AIAA conference paper, to be (hypothetically) presented at the GNC conference held during the SciTech Forum each January. Templates for these conference papers can be found in Ref. [13], formatted in both MS Word and LATEX, by following the links called "Manuscript Tem- plate." A particularly effective and efficient discussion on technical writing is given in Ref. [14], specifically pages 8-15 on organization.
The audience to whom you are writing this paper should include two groups of people. The first group is your instructor, who is looking for the thought process behind your design, your ability to apply skills and concepts from this course, and clear communication. The second group includes peers attending the conference with at least a fundamental understanding of feedback control theory, who may read your paper, listen to your presentation, and ask critical questions of you in front of the live audience.
Here is a brief overview of how to structure your paper:
• Abstract. Give a few sentences summarizing what was done, what was found, and of what use the work may be.
• Nomenclature. Define any symbols not explicitly defined in the text of your paper, including units.
• Introduction. Provide a short introduction, say three paragraphs or so, describing what the paper is about and how it is organized.
• Body. The body of the text may be split into sections and subsections, as you see fit, to document your design choices and results in a logical fashion. This will be the largest part of the paper, and should include several figures and equations to support your narrative discussion.
• Conclusions. Briefly summarize your paper and the main points for the reader, and reflect on the overall work.
• References. Include any references that are relevant to your arguments, are useful to the reader, and that supply further evidence to support your statements.
Attachment:- Control of Aerospace Systems.rar