DISCRETE-TIME VARIABLE STRUCTURE CONTROLLER FOR AIRCRAFT FLIGHT ANGLE TRACKING

The paper presents the longitudinal, short-period aircraft dynamics and its application on the climb angle tracking. For the aircraft flight angle tracking the stable system centre technique is developed for controlling the output in a discrete-time non-minimum phase causal system using the sliding mode control. The developed discrete-time stable system centre technique transforms the output tracking problem to a corresponding state variable tracking problem by asymptotically identifying the ideal internal dynamics for the unstable internal states of a discrete-time system. A numerical simulation example is given to show the effectiveness of the method

On Limitations to the achievable path following performance for linear multivariable plants

In this paper, we consider a problem termed “path following”. This differs from the common problem of reference tracking, in that here we can adjust the speed at which we traverse the reference trajectory. We are interested in ascertaining the degree to which we can track a given trajectory, and in characterizing the class of paths for which we can generate an appropriate temporal specification so that the path can be tracked arbitrarily well in an L2 sense.We give various bounds on the achievable performance, as well as tight results in special cases. In addition, we give a numerical procedure based on convex optimization for computing the achievable performance. The results demonstrate that there are situations where arbitrarily good L2 performance may be achieved even though the origin is not in the convex hull of the positive limit set of the path to be followed

DISCRETE-TIME VARIABLE STRUCTURE CONTROLLER FOR AIRCRAFT FLIGHT ANGLE TRACKING

The paper presents the longitudinal, short-period aircraft dynamics and its application on the climb angle tracking. For the aircraft flight angle tracking the stable system centre technique is developed for controlling the output in a discrete-time non-minimum phase causal system using the sliding mode control. The developed discrete-time stable system centre technique transforms the output tracking problem to a corresponding state variable tracking problem by asymptotically identifying the ideal internal dynamics for the unstable internal states of a discrete-time system. A numerical simulation example is given to show the effectiveness of the method

On Limitations to the achievable path following performance for linear multivariable plants

In this paper, we consider a problem termed “path following”. This differs from the common problem of reference tracking, in that here we can adjust the speed at which we traverse the reference trajectory. We are interested in ascertaining the degree to which we can track a given trajectory, and in characterizing the class of paths for which we can generate an appropriate temporal specification so that the path can be tracked arbitrarily well in an L2 sense.We give various bounds on the achievable performance, as well as tight results in special cases. In addition, we give a numerical procedure based on convex optimization for computing the achievable performance. The results demonstrate that there are situations where arbitrarily good L2 performance may be achieved even though the origin is not in the convex hull of the positive limit set of the path to be followed

Implementation of Nonlinear Model Predictive Path-Following Control for an Industrial Robot

Many robotic applications, such as milling, gluing, or high precision measurements, require the exact following of a pre-defined geometric path. In this paper, we investigate the real-time feasible implementation of model predictive path-following control for an industrial robot. We consider constrained output path following with and without reference speed assignment. We present results from an implementation of the proposed model predictive path-following controller on a KUKA LWR IV robot.Comment: 8 pages, 3 figures; final revised versio

Guidance of Nonlinear Nonminimum-Phase Dynamic Systems

The first two years research work has advanced the inversion-based guidance theory for: (1) systems with non-hyperbolic internal dynamics; (2) systems with parameter jumps; (3) systems where a redesign of the output trajectory is desired; and (4) the generation of recovery guidance maneuvers

Continuous-Time Reinforcement Learning: New Design Algorithms with Theoretical Insights and Performance Guarantees

Continuous-time nonlinear optimal control problems hold great promise in real-world applications. After decades of development, reinforcement learning (RL) has achieved some of the greatest successes as a general nonlinear control design method. However, a recent comprehensive analysis of state-of-the-art continuous-time RL (CT-RL) methods, namely, adaptive dynamic programming (ADP)-based CT-RL algorithms, reveals they face significant design challenges due to their complexity, numerical conditioning, and dimensional scaling issues. Despite advanced theoretical results, existing ADP CT-RL synthesis methods are inadequate in solving even small, academic problems. The goal of this work is thus to introduce a suite of new CT-RL algorithms for control of affine nonlinear systems. Our design approach relies on two important factors. First, our methods are applicable to physical systems that can be partitioned into smaller subproblems. This constructive consideration results in reduced dimensionality and greatly improved intuitiveness of design. Second, we introduce a new excitation framework to improve persistence of excitation (PE) and numerical conditioning performance via classical input/output insights. Such a design-centric approach is the first of its kind in the ADP CT-RL community. In this paper, we progressively introduce a suite of (decentralized) excitable integral reinforcement learning (EIRL) algorithms. We provide convergence and closed-loop stability guarantees, and we demonstrate these guarantees on a significant application problem of controlling an unstable, nonminimum phase hypersonic vehicle (HSV)

Relay Feedback and Multivariable Control

This doctoral thesis treats three issues in control engineering related to relay feedback and multivariable control systems. Linear systems with relay feedback is the first topic. Such systems are shown to exhibit several interesting behaviors. It is proved that there exist multiple fast relay switches if and only if the sign of the first non-vanishing Markov parameter of the linear system is positive. It is also shown that these fast switches can appear as part of a stable limit cycle. A linear system with pole excess one or two is demonstrated to be particularly interesting. Stability conditions for these cases are derived. It is also discussed how fast relay switches can be approximated by sliding modes. Performance limitations in linear multivariable control systems is the second topic. It is proved that if the top left submatrices of a stable transfer matrix have no right half-plane zeros and a certain high-frequency condition holds, then there exists a diagonal stabilizing feedback that makes a weighted sensitivity function arbitrarily small. Implications on control structure design and sequential loop-closure are given. A novel multivariable laboratory process is also presented. Its linearized dynamics have a transmission zero that can be located anywhere on the real axis by simply adjusting two valves. This process is well suited to illustrate many issues in multivariable control, for example, control design limitations due to right half-plane zeros. The third topic is a combination of relay feedback and multivariable control. Tuning of individual loops in an existing multivariable control system is discussed. It is shown that a specific relay feedback experiment can be used to obtain process information suitable for performance improvement in a loop, without any prior knowledge of the system dynamics. The influence of the loop retuning on the overall closed-loop performance is derived and interpreted in several ways

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