Inverse modelling and inverse simulation for system engineering and control applications

Following extensive development over the past two decades, techniques of inverse simulation have led to a range of successful applications, mainly in the fields of helicopter flight mechanics, aircraft handling qualities and associated issues in terms of model validation. However, the available methods still have some well-known limitations. The traditional methods based on the Newton-Raphson algorithm suffer from numerical problems such as high-frequency oscillations and can have limitations in their applicability due to problems of input-output redundancy. The existing approaches may also show a phenomenon which has been termed “constraint oscillations” which leads to low-frequency oscillatory behaviour in the inverse solutions. Moreover, the need for derivative information may limit their applicability for situations involving manoeuvre discontinuities, model discontinuities or input constraints. Two new methods are developed to overcome these issues. The first one, based on sensitivity-analysis theory, allows the Jacobian matrix to be calculated by solving a sensitivity equation and also overcomes problems of input-output redundancy. In addition, it can improve the accuracy of results compared with conventional methods and can deal with the problem of high-frequency oscillations to some extent. The second one, based on a constrained Nelder-Mead search-based optimisation algorithm, is completely derivative-free algorithm for inverse simulation. This approach eliminates problems which make traditional inverse simulation techniques difficult to apply in control applications involving discontinuous issues such as actuator amplitude or rate limits. This thesis also offers new insight into the relationship between mathematically based techniques of model inversion and the inverse simulation approach. The similarities and shortcomings of both these methodologies are explored. The findings point to the possibility that inverse simulation can be used successfully within the control system design process for feedforward controllers for model-based output-tracking control system structures. This avoids the more complicated and relatively tedious techniques of model inversion which have been used in the past for feedforward controller design. The methods of inverse simulation presented in this thesis have been applied to a number of problems which are concerned mainly with helicopter and ship control problems and include cases involving systems having nonminimum-phase characteristics. The analysis of results for these practical applications shows that the approaches developed and presented in this thesis are of practical importance. It is believed that these developments form a useful step in moving inverse simulation methods from the status of an academic research topic to a practical and robust set of tools for engineering system design

Resource-aware motion control:feedforward, learning, and feedback

Controllers with new sampling schemes improve motion systems’ performanc

Aeronautical Engineering: A Continuing Bibliography with Indexes

This supplemental issue of Aeronautical Engineering, A Continuing Bibliography with Indexes (NASA/SP-1999-7037) lists reports, articles, and other documents recently announced in the NASA STI Database. The coverage includes documents on the engineering and theoretical aspects of design, construction, evaluation, testing, operation, and performance of aircraft (including aircraft engines) and associated components, equipment, and systems. It also includes research and development in aerodynamics, aeronautics, and ground support equipment for aeronautical vehicles. Each entry in the publication consists of a standard bibliographic citation accompanied, in most cases, by an abstract. Two indexes-subject and author are included after the abstract section

Dynamics and control of flexible manipulators

Flexible link manipulators (FLM) are well-known for their light mass and small energy consumption compared to rigid link manipulators (RLM). These advantages of FLM are even of greater importance in applications where energy efficiency is crucial, such as in space applications. However, RLM are still preferred over FLM for industrial applications. This is due to the fact that the reliability and predictability of the performance of FLM are not yet as good as those of RLM. The major cause for these drawbacks is link flexibility, which not only makes the dynamic modeling of FLM very challenging, but also turns its end-effector trajectory tracking (EETT) into a complicated control problem. The major objectives of the research undertaken in this project were to develop a dynamic model for a FLM and model-based controllers for the EETT. Therefore, the dynamic model of FLM was first derived. This dynamic model was then used to develop the EETT controllers. A dynamic model of a FLM was derived by means of a novel method using the dynamic model of a single flexible link manipulator on a moving base (SFLMB). The computational efficiency of this method is among its novelties. To obtain the dynamic model, the Lagrange method was adopted. Derivation of the kinetic energy and the calculation of the corresponding derivatives, which are required in the Lagrange method, are complex for the FLM. The new method introduced in this thesis alleviated these complexities by calculating the kinetic energy and the required derivatives only for a SFLMB, which were much simpler than those of the FLM. To verify the derived dynamic model the simulation results for a two-link manipulator, with both links being flexible, were compared with those of full nonlinear finite element analysis. These comparisons showed sound agreement. A new controller for EETT of FLM, which used the singularly perturbed form of the dynamic model and the integral manifold concept, was developed. By using the integral manifold concept the links’ lateral deflections were approximately represented in terms of the rotations of the links and input torques. Therefore the end-effector displacement, which was composed of the rotations of the links and links’ lateral deflections, was expressed in terms of the rotations of the links and input torques. The input torques were then selected to reduce the EETT error. The originalities of this controller, which was based on the singularly perturbed form of the dynamic model of FLM, are: (1) it is easy and computationally efficient to implement, and (2) it does not require the time derivative of links’ lateral deflections, which are impractical to measure. The ease and computational efficiency of the new controller were due to the use of the several properties of the dynamic model of the FLM. This controller was first employed for the EETT of a single flexible link manipulator (SFLM) with a linear model. The novel controller was then extended for the EETT of a class of flexible link manipulators, which were composed of a chain of rigid links with only a flexible end-link (CRFE). Finally it was used for the EETT of a FLM with all links being flexible. The simulation results showed the effectiveness of the new controller. These simulations were conducted on a SFLM, a CRFE (with the first link being rigid and second link being flexible) and finally a two-link manipulator, with both links being flexible. Moreover, the feasibility of the new controller proposed in this thesis was verified by experimental studies carried out using the equipment available in the newly established Robotic Laboratory at the University of Saskatchewan. The experimental verifications were performed on a SFLM and a two-link manipulator, with first link being rigid and second link being flexible.Another new controller was also introduced in this thesis for the EETT of single flexible link manipulators with the linear dynamic model. This controller combined the feedforward torque, which was required to move the end-effector along the desired path, with a feedback controller. The novelty of this EETT controller was in developing a new method for the derivation of the feedforward torque. The feedforward torque was obtained by redefining the desired end-effector trajectory. For the end-effector trajectory redefinition, the summation of the stable exponential functions was used. Simulation studies showed the effectiveness of this new controller. Its feasibility was also proven by experimental verification carried out in the Robotic Laboratory at the University of Saskatchewan

Automatic landing control using H[infinity] control and stable inversion

The design of an automatic landing system (ALS) is a challenging task. It is both a robust and a tracking control problem. In this thesis, a method combining H[Infinity] robust control and stable inversion is employed to develop controllers for an automatic landing system. We adopt the linearized longitudinal model of a Boeing 747 commercial airplane to verify this method. The control actuators, wind gust, and wind shear models are also established to simulate the landing process. H[Infinity] control is a robust control method. It can optimize the system performance and provide robust stability against uncertainties in the plant. The stable inversion is a precision tracking approach. We combine these two methods together to satisfy both robust and exact tracking requirements for the automatic landing system. Based on the stable inversion technique, the desired altitude and airspeed trajectories are also designed. The numerical simulation results show that the automatic landing system can meet FAA (Federal Aviation Administration) requirements for Category III precision approach landing. As expected, the integrated system can achieve accurate tracking, in the presence of measurement noise, wind gust, and wind shear with low intensity. Compared with existing approaches in automatic landing systems, the method used in this thesis can achieve higher precision. Finally, this method is particularly well suited for automatic landing systems using Global Positioning System

Coping with Algebraic Constraints in Power Networks

In the intuitive modelling of the power network, the generators and the loads are located at different subset of nodes. This corresponds to the so-called structure preserving model which is naturally expressed in terms of differential algebraic equations (DAE). The algebraic constraints in the structure preserving model are associated with the load dynamics. Motivated by the fact the presence of the algebraic constraints hinders the analysis and control of power networks, several aggregated models are reported in the literature where each bus of the grid is associated with certain load and generation. The advantage of these aggregated models is mainly due to the fact that they are described by ordinary differential equations (ODE) which facilitates the analysis of the network. However, the explicit relationship between the aggregated model and the original structure preserved model is often missing, which restricts the validity and applicability of the results. Aiming at simplified ODE description of the model together with respecting the heterogenous structure of the power network has endorsed the use of Kron reduced models; see e.g. [2]. In the Kron reduction method, the variables which are exclusive to the algebraic constraints are solved in terms of the rest of the variables. This results in a reduced graph, the (loopy) Laplaican matrix of which is the Schur complement of the (loopy) Laplacian matrix of the original graph. By construction, the Kron reduction technique restricts the class of the applicable load dynamics to linear loads. The algebraic constraints can also be solved in the case of frequency dependent loads where the active power drawn by each load consists of a constant term and a frequencydependent term [1],[3]. However, in the popular class of constant power loads, the algebraic constraints are “proper”, meaning that they are not explicitly solvable. In this talk, first we revisit the Kron reduction method for the linear case, where the Schur complement of the Laplacian matrix (which is again a Laplacian) naturally appears in the network dynamics. It turns out that the usual decomposition of the reduced Laplacian matrix leads to a state space realization which contains merely partial information of the original power network, and the frequency behavior of the loads is not visible. As a remedy for this problem, we introduce a new matrix, namely the projected pseudo incidence matrix, which yields a novel decomposition of the reduced Laplacian. Then, we derive reduced order models capturing the behavior of the original structure preserved model. Next, we turn our attention to the nonlinear case where the algebraic constraints are not readily solvable. Again by the use of the projected pseudo incidence matrix, we propose explicit reduced models expressed in terms of ordinary differential equations. We identify the loads embedded in the proposed reduced network by unveiling the conserved quantity of the system