Development of a Low-cost, Portable Hardware Platform to Support Hands-on Learning in the Teaching of Control and Systems Theory

Abstract

This paper describes the development of a hardware platform designed to support the teaching of a variety of systems engineering concepts to students at all stages of the curriculum. From concept, the hardware was designed to be low-cost, portable and robust allowing sufficient numbers of hardware units to be acquired. This enabled each student on the course to be loaned their own piece of equipment, either to work with in class or for use as a ‘take home lab’. This provided the students with a more flexible, experimental based learning experience than traditional classroom based teaching. The hardware platform consisted of a miniature three degrees-of freedom helicopter that is interfaced to a personal computer (PC) via a National Instruments myDAQ data acquisition module. This was housed in a small, foam-lined carrying case for portability. Details of the course and assessment, based around the hardware platform, are presented, along with feedback received from the students. This feedback was from the first run of a new MSc course in the spring semester of 2013, and indicated that the new hardware was received positively with the students appreciating the hands-on nature of the teaching it provided.

Keywords:

• educational aids
• control education
• control system analysis
• control system design
• multivariable control
• data acquisition
• rapid control prototyping
• hardware-in-the-loop design

Introduction

A recent survey, conducted by the Institute of Electrical and Electronics Engineers (IEEE) Control Systems Society (Cook and Samad 2009), highlighted that universities ‘overrate the quality of their graduate students in terms of satisfying industry’s needs’. The report indicated industry’s desire to see more practical, hands-on learning, but stressed the importance of mathematical modelling of physical systems, particularly for control systems design and evaluation and also hardware-in-the-loop simulation. The report highlighted the need for universities to emphasise these valuable skills in their teaching. This message is of particular importance to UK universities, where the Engineering Institutes are beginning to insist on more practical-based course content to maintain course accreditation.

It is not only industry driving the requirement for more practical hands-on teaching. This message is also evident in the feedback received from students themselves. The 2010 National Student Survey showed that student satisfaction within the School of Electronic and Electrical Engineering at the University of Manchester rose from 67% to 98% within a single year of introducing more practical coursework into their curriculum (National Instruments 2012). These statistics are difficult to ignore, considering the competition between engineering departments in the UK and abroad, to attract the best students.

In the engineering context, practical teaching is generally performed in laboratory sessions, where the ratio of the number of students to the amount of hardware is high, generally because the cost and size of experimental hardware is significant. As a result, the students are often required to operate this equipment in groups.

The time allocated for these sessions, is generally restricted due to time-tabling constraints and issues relating to facility and staff availability. As a result, laboratory exercises are often written in a very prescriptive manner, with only enough time for the students to perform the prescribed tasks, with little time left over to fully explore the equipment in a fashion that best suits their own personal learning styles. Furthermore, students often do not have the time or freedom to familiarise themselves with the hardware they are using, or explore, at first hand, some of the subtleties of the system in question.

During the final years of the controls undergraduate course, (Years 3 and 4), and the later stages of the MSc course, the Department of Automatic Control and Systems Engineering, at the University of Sheffield, provided no hands-on laboratory based teaching, to reinforce the knowledge learned in the lecture courses, but instead relied solely on simulation-based activities. Experiences from Columbia College, in their teaching of computer architecture, (Heise 2006), showed a dramatic improvement in the student engagement on the course, when simulation only exercises were replaced with hardware that the students could use within scheduled laboratory sessions and take home to use in their own time. Heise (2006), reported a significant reduction in incomplete or partially working projects at the end of the course, and that the student test scores showed a marked improvement. The author supports these observations with evidence from the pedagogical literature, such as the important role hands-on experimentation has in engineering education, and how performing computer simulation can never replace the experience gained through real experimentation (Feisel and Rosa 2005).

Motivated by studies such as the one described here, this paper discusses the work that was carried out in the development of a flexible teaching platform to improve the teaching experience for systems engineering students. A low-cost, dynamically-rich hardware platform was developed to enable each student to be loaned their own piece of experimental equipment, for the duration of the course. This hardware platform was engineered such that it was easily portable and safe to operate unsupervised. This allowed the students the freedom to take the equipment away with them after the scheduled classroom sessions, to work with in their own time, either at home or elsewhere on campus. The aim was to encourage the students to explore the system in their own time, allowing them to take control of their own learning to best match their individual learning styles, and hence promote independent learning.

The remainder of this paper is organised as follows: a description of the hardware and its development is discussed in the next section. The third section describes how the hardware was employed as part of the teaching curriculum, and the fourth section discusses the use of the hardware in its first usage as part of a new MSc course on data acquisition and rapid control prototyping. The final section reflects on the approach and provides conclusions and future developments.

Design and description of the hardware

One of the primary concepts of this exercise was to develop a piece of teaching hardware that reinforced the curriculum delivered throughout the systems and controls teaching course. From the inception, it was decided that each student should be given their own piece of hardware to work with. It was perceived that the student would not only use this equipment in the teaching laboratory, but also take the equipment away to be used out of timetabled hours, at home or elsewhere on campus.

The primary requirements for the hardware were as follows:

• Portability: The equipment was required to be small and light enough to be carried by the student between campus and home.

• Robustness: The equipment needed to be sufficiently designed to withstand general mistreatment on the part of the student.

• Safety: It was necessary to design the hardware such that it was safe for the students to operate in an unsupervised environment.

• Cost: It was essential to keep the system component costs to a minimum, such that it could economically be reproduced for 100 students. A component budget of approximately £250 was allocated for each piece of kit.

• Engagement: From the outset of this exercise it was deemed essential that the resulting control platform be a rewarding control challenge for the students. It was decided that the system should be open-loop unstable containing non-linear dynamics, with multiple inputs and outputs. Above all it had to be obvious to the students that improvements to the control performance could be gained by refining the control design.

• Modular design: The design of the system needed to be modular in nature, so elements could be used with different experiments.

After looking at existing commercially available systems on the market it became apparent that there was nothing available to satisfy the above criteria. Broadly speaking, the available products fitted into two categories: Firstly, products offered by companies such as Quanser Inc. and Googol Technologies Ltd, span a wide range of control experiments, but at price points that are prohibitively expensive (typically an order of magnitude or more than the desired budget). Secondly, equipment from such vendors is generally too cumbersome for carrying to and from campus every day.

However, National Instruments have recently brought to the market a range of low-cost ‘miniSystems’, specifically aimed at the educational market. These miniSystems are designed to interface directly with a National Instruments myDAQ module, (a low cost data acquisition module aimed at the educational market), to form a low cost control problem. These systems are generally printed circuit board based, retailing in the region of £100, with the myDAQ module occupying the same price bracket. Examples of these systems include: a miniature power grid; complete with solar panel and power lines, a vibrating platform, and a one-degree-of-freedom helicopter. These miniSystems are new to the market and do not yet appear to be commonplace in mainstream teaching.

There have been a number of reported uses of the myDAQ, mostly in the teaching of electronic and electrical engineering, such as Chestnut and Baker (2011), Meng-Jun (2011), and Walters (2011), with the University of Manchester’s case study (National Instruments 2012) showing that the myDAQ can be used as an effective teaching aid.

However, in terms of the teaching of multivariable and hardware-in-the-loop control, in the context of the control systems engineering curriculum, it was decided that the miniSystems did not provide sufficient dynamic complexity for final-year and masters students. It was desired that the final solution be sufficiently complex to prove too difficult to control using ad hoc/open-loop methods, thus requiring the students to employ model-based feedback control design methodologies. It was therefore decided that a new piece of hardware should be designed and built, based around the myDAQ module, to meet the curriculum requirements for the department’s controls and systems courses. After much discussion, it was decided that a three-degrees-of-freedom, (3-DOF), helicopter, similar to those of Quanser Inc. and Googol Technologies Ltd, should be designed and manufactured. A prototype of this system is shown in Figure 1.

Figure 1 The hardware platform, showing (1) the 3-DOF helicopter body, (2) signal conditioning and fan driver interface, (3) National Instruments myDAQ module, (4) control PC, (5) LabVIEW Data acquisition teaching module.

The helicopter is designed to ‘mimic’ the dynamics of a chinook-type twin rotor helicopter, where the rotors of the helicopter are emulated by two fans, linked by a short arm to represent the body of the helicopter. The fans do not provide sufficient lift to raise the helicopter, so a counter weighted boom arm is used to provide mechanical assistance. The short link arm, between the fans, is allowed to freely rotate about its mid-point, in-line with the boom arm. The boom arm itself is allowed to rotate with two degrees of freedom in the horizontal and vertical axes, as shown in Figure 2. The fans of the helicopter are individually controlled, allowing it to travel over much of the surface of a sphere, created by the boom arm dimensions.

Figure 2 The coordinate system for the 3-DOF helicopter. The elevation, pitch and travel angles, E(t), Ψ(t), Θ(t), respectively, are shown in their positive sense. The fan thrust vectors, F _a (t) and F _b (t), are also shown.

The travel angle of the helicopter is measured using a digital incremental encoder, mounted in the upright support of the helicopter, and the elevation angle is measured using a rotary potentiometer, mounted at the fulcrum of the boom arm. The feedback signal from the elevation angle encoder and control signals for the fans are transferred to the boom arm joint through a slip-ring mechanism, allowing continuous 360° rotation of the boom arm in the horizontal axis. To reduce the cost and complexity of the helicopter design, it was decided that the pitch angle should not be directly measured, but would be estimated using a Kalman filter state observer.

A National Instruments myDAQ module was used to act as the control interface between the helicopter and the personal computer (PC) running LabVIEW. This configuration was selected to address a number of issues, including:

• The department wished to broaden the teaching of different industrial standard software packages, to address the desire from industry highlighted in the controls Curriculum Survey (Cook and Samad 2009). LabVIEW was introduced into this course to address this need.

• The myDAQ device provided the department with a highly cost effective and versatile method of controlling the helicopter, and used a programming interface, DAQmx, that is widely used within the teaching department, and heavily supported by the wider LabVIEW community.

• The DAQmx is compatible with other software, such as C++ and MATLAB/Simulink, allowing further flexibility for usage of the hardware platform.

The fan control signals were passed from the myDAQ’s digital-to-analogue converters, through a power amplifier on the signal conditioning board to drive the fans. Power amplifiers were required because the myDAQ analogue output channels were not capable of driving the fans directly. The angular sensors were interfaced to the myDAQ module using appropriate signal conditioning circuitry, with connections provided for the students to add an anti-aliasing filter to the elevation axis measurement circuitry. A mains +15 V power supply was used to provide power to the system, since the available power from the myDAQ was insufficient, and a battery solution was deemed impractical.

Where possible, the cabling for the helicopter was routed through the mechanical assembly of the system, to improve the mechanical robustness of the system by reducing the chance of damage to the wiring. The cylindrical base of the helicopter housed the digital rotary encoder for the travel angle and a slip-ring unit that passed the electrical signals to and from the elevation boom arm, allowing continuous 360° rotation. The fan power cables were routed from the slip rings, via the aluminium tubing of the boom arm, and into the pitch arm, through the pitch axis joint. The helicopter base was attached to the signal conditioning and power electronics board via a 15-way D-connector, allowing the base unit to be removed from the signal conditioning board for ease of transportation. Crucially, this allowed other modules to be connected to this interface, such as an extra board used as part of the introductory LabVIEW teaching (discussed later in this paper).

The operating voltage of the system was maintained below +15 V, and the fans were fitted with fan guards, ensuring the system was safe for students to operate unsupervised. The total system was able to be packed into a foam lined carrying case of dimensions 380 mm × 220 mm × 200 mm, with a resulting weight of approximately 2 kg, including case, helicopter, power supply and myDAQ/signal conditioning assembly.

The complete system provided the students with a rich and challenging control problem. The system comprises of a mixture of continuous-time dynamics – the mechanical structure and linkages, and discrete-time dynamics – arising from the use of the myDAQ module, and non-linear dynamic features, such as the friction acting on the rotational linkages.

The maintenance of precise control over the pitch angle is critical to maintaining control of the travel and elevation angles, but this is made challenging for the students by the absence of a pitch angle measurement. To ensure satisfactory performance of the helicopter, students were required to master a number of techniques, including: modelling of the mechanical and electrical systems, state-estimation, and multivariable control. Furthermore, the students encountered a number of often overlooked issues, such as design of the anti-aliasing filters and sample-rate selection.

Course design and delivery

Although possessing sufficient flexibility to support a wide range of teaching activities across the curriculum, the helicopter platform was originally intended to be used as part of a teaching module in data acquisition and rapid control prototyping. The initial teaching module was to run as a one and a half week course and be taught to approximately 70 students, as part of the department’s MSc course in control systems. This course was developed with five hours of introductory lectures and 30-hours of laboratory time, for the students to implement, on real hardware, some of the advanced controls theory that they had learned previously during the MSc controls course. The helicopter hardware provided a multivariable, real-time hardware platform around which the students could perform modelling, simulation and control design; before finally implementing their controller upon the hardware.

The course was aimed at guiding the students through common industrial tasks, based on hands-on experience and learning, using software tools that they may typically experience in industry. The primary learning outcomes for the course were as follows:

• Configure data-acquisition hardware to interface a real-world system to a PC.

• Operate a real-world system using high-level design software (in this case LabVIEW).

• Describe, devise and appraise methods to identify the parameters required to model a real-world system.

• Describe and appraise the differences between, firstly, a real-world system and a simulation model of that system, and secondly, the simulation model and a model used for control system design.

• Describe, devise and evaluate methods to control a real-world system.

The course assumed that the students had no prior experience of LabVIEW, but it was a course prerequisite that the students had prior experience of state-space control methods, (taught previously in the MSc in Control Systems program) and prior knowledge of MATLAB and SIMULINK.

Data acquisition and virtual instrument design

The initial task for the students was to configure the myDAQ module to interface with a separate ‘teaching’ board, shown in Figure 1, that plugged into the top of the signal conditioning and power electronics board, in place of the 3-DOF helicopter. This teaching board contained basic peripherals, such as switches, LEDs and a potentiometer, allowing the students to construct a basic data acquisition platform, based around the teaching board. Once the students had completed the data acquisition tasks, they were set the challenge of configuring the myDAQ module to drive the helicopter fans, in open loop, and reads in angular measurements from the elevation and travel angle sensors. As part of this exercise the students were tasked with designing a graphical user interface, (or ‘virtual instrument’), to provide manual control sliders and display sensor readings from the helicopter hardware. This virtual instrument formed the framework within which the closed-loop controller could be inserted. Controlling the helicopter in an open-loop manner illustrated to the students the motivation for model-based control of the system.

Modelling

Initially, the students were provided with the equations governing the rigid body dynamics of the helicopter, described about the elevation, pitch and travel axes, respectively, as follows:

where J_E, J_Ψ and J _Θ are the moments of inertia about the elevation, travel and pitch axes, respectively, l₁, l₂ and l₃ are the lengths of the pitch arm pivot to the travel axis, the counterweight to the travel axis and the fan centres to the pitch arm pivot, respectively. The masses of the fans and counterweight are m₁ andm₂, whilst k_s and k_d are the spring and damping coefficients, respectively, of the pitch arm. The fan responses were approximated by affine functions of the form: F_a,b = αk_aU_a,b(t) + β, whereU_a,b(t) are the control voltages supplied to the drive electronics, which provide a linear gain k_a over the fan operating voltage range (α and β are fan voltage-thrust coefficients which were obtained from an identification experiment).

The students were initially provided with a SIMULINK model containing the elevation and travel axis dynamics, and were required to implement the pitch axis dynamics. They were also required to populate the model with the physical parameters of the helicopter, such as: component masses, inertias, beam lengths, etc. After completing the model, the students were tasked with simulating the helicopter from various initial conditions, and compare this with their observations of the real hardware. During these exercises the students acquired:

• More practice at using industry standard software, such as MATLAB and SIMULINK, for mathematically solving complex engineering problems.

• An improved understanding of how to derive model parameters through measurement and experimentation.

• Further experience and understanding of the differences between mathematical models and an actual physical system. In carrying out this exercise the students gained a further appreciation that no simulation model of a physical system will ever be perfect, and that it is good engineering practice to question assumptions and methods used when constructing physical system models.

In order to ascertain the degree to which the students had acquired these skills, the course assessments were aligned accordingly.

Control design

After the students had completed the helicopter dynamics model, they moved on to designing a reference tracking controller, to command the helicopter to move to specific travel and elevation angles. As part of this design the students were provided with a performance specification, in terms of overshoot, settling time, steady-state error, and control signal saturation. The time allocated to do this exercise was approximately six days of classroom time, and a three-day weekend in the middle. This meant that the students had considerable time pressure, (similar to that as they may experience in industry), to perform the required tasks, and in so doing, implement much of the theory they had acquired over the course of their degree programme.

The students had free reign over how they implemented the control strategy to meet the performance requirements, but were advised to use a linear multivariable control method they had studied previously during the degree programme, such as linear quadratic Gaussian (LQG) control. At the end of the course the students were orally examined on how they designed their controller, starting from the non-linear model provided. A typical example of the design procedure is summarised as follows:

• Linearisation: The helicopter dynamics were linearised around a steady hover point, using Jacobian linearisation, thus allowing a linear, time-invariant, state-space model to be derived by the students. The students were again asked to discriminate between the simulation model and the real system. Basic stability analysis was then performed by the students and the system was tested for controllability and observability.

• Discretisation: The controller was implemented in LabVIEW, via the myDAQ module acting as the real world interface. As a consequence, the students were required to transform their state-space models into the discrete domain, and determine a suitable sample rate for the system, by considering the dynamics of the helicopter and the limitations of the myDAQ module.

• Observer Design: A critical element in the controller operation was good estimation of the pitch angle of the helicopter. Therefore, the students were required to design a state observer to estimate this angle. The students were provided with a noise model for the required Kalman filter, from data, using the method of Rajamani and Rawlings (2009).

• State Feedback Control: The students designed a linear quadratic regulator (LQR) controller by experimenting with various state and control penalties, and assessed the associated closed-loop performance. Subsequently, the students designed a reference tracking controller by augmenting the state vectors with the integrals of the errors between the elevation and travel angle reference and feedback signals.

The block diagram for the helicopter control system is shown in Figure 3. During the design of the controller and observer, the students were encouraged to use their non-linear and linearised models of the helicopter dynamics to assess and debug their controller and observer designs. The system models were not only used for the design and debugging of the system controller and observer, but the students were also encouraged to use them for further understanding of the system dynamics, and appreciate the effects of the mutual coupling between the axes of rotation. The design of the observer and controller were performed in MATLAB and SIMULINK, then when complete, they were ported to LabVIEW for control of the helicopter hardware.

Figure 3 The block diagram of the system.

Degree-course accreditation was an important consideration whilst developing this course. The following attributes were identified to fit with the criteria specified by the Engineering Council's Standard of Professional Engineering Competence (Engineering Council 2013):

• Ability to identify, classify and describe the performance of systems and components through the use of analytical methods and modelling techniques.

• Ability to apply quantitative methods and computer software relevant to their engineering discipline, in order to solve engineering problems.

• Understanding of and ability to apply a systems approach to engineering problems.

These attributes are in alignment with the tasks described earlier.

Assessment

The assessment of the course was summative throughout its duration. Initially the students were awarded credit for demonstrating the completion of tasks, in the data acquisition and modelling phases of the course. This assessed the student’s basic competence in the LabVIEW programming requirements, and their understanding of the data acquisition tasks.

The control design elements of the course were assessed in two ways. The students were asked to prepare a written report describing the control and modelling aspects of their system. This provided the students an opportunity to practice their report writing skills and provided the course instructors with a means to assess for any instances of plagiarism. At the close of the course, the students were all given an individual viva (lasting 15 minutes). The students were asked to demonstrate their controller design for the helicopter, and were asked a series of questions relating to the design of the controller and operation and dynamics of the helicopter model. Using the viva to assess the students allowed the assessors to probe the answers that the students were providing, and hence their understanding of the core principles of their work, and not just allow them to regurgitate textbook theory. Furthermore, the discussion provided the assessors a method of eliciting answers from the students that were struggling with ‘memory blocks’ during the viva. Furthermore, the viva placed the students under pressure to present a working solution in a timely fashion; a common scenario within industry.

The demonstration of the equipment, during the viva, allowed the assessors to inspect every piece of equipment for damage, and allowed any potentially faulty equipment to be identified for maintenance. This removed the need for the fully functioning equipment to be further inspected after the course had concluded.

The course assessment was heavily weighted towards the control assignment and viva, with only 10% of the marks awarded for the data acquisition tasks, and 90% of the marks being awarded equally between the modelling and control report and the viva.

Reflection on use

The student feedback after the course was very positive. Of the 49 students who returned questionnaires, 96% responded to say that they had enjoyed the course, providing comments such as ‘generally speaking the course was excellent’ and ‘[this module] is one of the most interesting in the MSc course’. Over two-thirds of the students thought the course was well structured, and 94% would actively recommend this course to future students.

All of the students felt that they had learned something useful during the course. Approximately three quarters of the students indicated that they felt better prepared for a career in systems engineering, and that they had a better understanding of control system implementation as a result of the practical nature of the course, and the open access to the hardware.

The majority of students used the hardware outside the scheduled classroom sessions, with two-thirds reporting they had used it elsewhere on campus, and three quarters saying that they had used it at home. A number of students reported that they were able to work through problems with the hardware in a more free and relaxed manner outside the laboratory sessions, where there were fewer distractions.

Those students that indicated that they had not used the equipment at home were asked why this was the case, and their typical responses were either that they had finished the work in the classroom sessions, or they preferred to work elsewhere on campus. However, the portable nature of the equipment was being put to good use in enabling a flexible learning approach.

This course was allocated six days classroom time (two days teaching, followed by a three-day bank holiday weekend, then another four days of teaching time). The small quantity of negative feedback that was received stemmed from the short period of time the students had to work with the equipment, which ‘did not allow [the students] to gain an intuitive understanding’ of the helicopter or build the confidence to fully engage with the experience. However, the students did feel that it was a ‘very worthwhile and interesting course’, which provided an enjoyable application of the material learned previously on the course. The timetabling constraints of the existing MSc course structure preclude greater teaching time for this module. However, the course has now been moved forward to a point in the year where there is no bank holiday, thus enabling students access to an extra day of support from teaching assistants.

No damaged, lost or faulty systems were reported or detected at the end of the course, suggesting that the equipment was sufficiently robust and that the students took proper care of it whilst in their possession.

Assessment of the approach

The development of the equipment has provided a means for the students to implement much of the knowledge they have learned throughout the controls MSc course, in a practical and engaging manner.

Many of the time limitations and issues with laboratory equipment access have been overcome by providing each of the students on the course with their own piece of equipment and allowing them to work with the equipment outside of the allotted laboratory time, either elsewhere on campus or at home.

During the initial run of the MSc course, it was found that the pitch angle observer did not provide estimates of sufficient accuracy to enable fast reference tracking control of the system, owing to model uncertainty and the bandwidth of the pitch axis being significantly higher than that of the elevation and travel axes. Consequently, during the design of the LQR controller, it was found that significant penalties were required to be imposed on the pitch states to maintain the stability of the helicopter. As a result, the controller designs implemented by the students tended to exhibit a degree of overshoot in the travel axis and somewhat sluggish performance. It was also found that the fan control signals were at times quite noisy, again owing to the use of the pitch estimates.

To overcome the problems encountered with the pitch angle estimation, during this initial course, the helicopter modules have been subsequently modified to incorporate a simple pitch angle sensor. The pitch angle sensor was implemented using a hall effect sensor mounted at the end of the boom arm, with a small magnet mounted to the pitch arm joint. The feedback signal from this sensor is non-linear and requires calibration. This will provide the students with a sensor linearisation exercise and a measurement uncertainty issue to overcome in their observer design.

Conclusions and future development

This paper described the development of a 3-DOF helicopter that was designed specifically to be low-cost, robust and portable, thus allowing it to be used as a ‘take home lab’ for a systems engineering course. The helicopter was controlled through a National Instruments myDAQ data acquisition module configured using National Instruments LabVIEW software. System simulation and control design were carried out using MATLAB and SIMULINK, with the controller being ported across to LabVIEW for real-time control of the hardware. Motivation for the development of this hardware was driven by the requirements for providing students with a more stimulating and hands-on experience in the systems and control curriculum, and directed by the course accreditation bodies.

The development of this equipment has proven to be a very worthwhile activity. Not only has it provided a very engaging element to the controls course, as illustrated from the student feedback, but is has also provided the students with an open access hardware platform to practice implementing the knowledge they have learned, throughout the controls MSc course. From a departmental perspective, the 3-DOF helicopter provides a hardware resource that can be integrated into other areas of the teaching curriculum and used as a marketing tool to attract future students into the department.

It is planned that this hardware platform will be further used for the teaching of final year undergraduate students, as part of a semester long teaching course. The extended teaching time, for the semester long course will allow us to encapsulate further engineering concepts, such as hardware-in-the-loop simulation. The modular nature of the hardware platform will allow for further hardware modules to be added in to the teaching courses, such as a fan assembly to perform component level hardware-in-the-loop simulations. Further to this, it is expected that this hardware platform be used to support teaching in other modules in the MSc and undergraduate courses.

Appendix 1. Linearised Helicopter Model

The helicopter dynamics were approximated about the horizontal hover point, (E(t), Ψ(t), Θ(t)) = (0,0,0): With , where ε, ψ and θ are the perturbation elevation, pitch and travel angles. The vector for the perturbation input is defined as: u^T(t) = [u_a(t) u_b(t)]. The matrices defining the system model are: Where is the defined as the voltage that needs to be applied from the myDAQ module to achieve hover.