6 - Design and Performance of Feedback Controllers

The dynamics of a web transport system are coupled and interactive among spans of web and rolls/rollers. As the process speed or variation of the speed is high, system friction and inertia of rotation of rolls could cause problems in implementation of observer techniques for tension estimation and control. In the author's previous study (see IEEE International Conference on Industrial Electronics, Control and Instrumentation, Denver, Colorado, USA (2001)), an observer-based tension feedback controller with friction and inertia compensation was proposed. However, the gains of observer and controller were determined based on the trial-and-error approach. This paper continues the author's previous study and presents an analytical approach for the gain design of observers in the time domain but design of controllers in the frequency domain. The linearization and decentralization techniques are implemented. Design of tension observers and feedback controllers with friction and inertia compensation is studied. Approaches for the gain design are discussed, and summarized procedures are given. The proposed analytical approach for design of tension observers and feedback controllers has been proven to be adequate by experiment.

Circle Condition-Based Robust Feedback Control Against Plant Perturbation

It is well-known that phase-shifting controllers used for active combustion control must be manually adjusted in order to maintain control over a broad range of operating combustor operating conditions. If one assumes that the thermoacoustic instabilities are linearly stabilizable, then what is needed is a method to determine, and ultimately predict, the frequency response of the plant for any range of operating conditions, so the controller design can be automatically updated to track the changing plant gain/phase relationships that are observed with changing heat release. A unique test-based, design process has been proposed to predict the gain/phase characteristics required of a proportional, phase-shifting controller that can stabilize the thermoacoustic instabilities. In this paper, that process is used to automate the design of a fixed-gain feedback controller that limits the amplitudes of any feedback induced instabilities (to some pre-specified level) while providing the best control of the targeted limit cycling pressure oscillations. The paper describes how a neural network was trained, using the suggested design process, to predict the frequency response of the thermoacoustics in a tube combustor at frequencies adjacent to the limit cycle frequency using certain operating conditions that included a sparsely-sampled temperature profile, total air/fuel flow rate, and equivalence ratio. The neural net training was performed using complex valued, open-loop frequency response function data as the desired signal with the previously mentioned operating conditions as the input signals. (The open loop data was collected for a narrow frequency range surrounding the limit cycle instability by performing a sine dwell at discrete frequencies). Once the neural network was trained, it was used to predict the approximate phase and gain margins as a function of temperature and flow conditions. The margins were then used to automatically update and design a fixed shape feedback controller having the proper phase and magnitude to ensure stability and control in the face of changing operating conditions. A companion paper describes the methodology that underlies the automated design of the feedback controller gain and phase delay.

This article presents a systematic methodology for the design of a feedback controller for a boost-type DC-DC converter based on the foraging behavior of a colony of honey bees. It is shown how bee foraging can be refined and used to construct an optimization algorithm. The new scheme is first tested on a few benchmark test functions, and the results are compared with that obtained using a genetic algorithm. The feedback controller design for a boost-type DC-DC converter is formulated as an optimization problem, and the solution is sought through the new algorithm. Computed and measured results are presented to validate the new dispensation. Further, the new dispensation is shown to be superior to the genetic algorithm.

In this paper, we propose an adaptive fuzzy output feedback control method for trajectory tracking control problem for robotic systems. Using Lyapunov method, we first develop a stable adaptive fuzzy state feedback control algorithm by assuming that the systems output and its derivatives are available for feedback control design. The algorithm combines fuzzy systems with robust adaptive controller. The fuzzy system approximates the certainty equivalent (CE)-based optimal controller while robustifying adaptive control term is used to cope with uncertainties that appeared from the effect of external disturbance, fuzzy approximation errors and other modeling errors. Then, an output feedback form of the position-velocity (state feedback) controller is proposed where unknown velocity signal is replaced by the output of model-free linear estimator. We show via asymptotic analysis that the tracking performance of the output feedback design can recover the performance achieved under the state feedback control design. Finally, the proposed method is implemented and evaluated on a 2-DOF robotic system to demonstrate the theoretical development for the real-time applications.

In this paper, a tracking control problem for the longitudinal model of an airbreathing hypersonic vehicle subject to external disturbances is investigated. Based on the characteristics of the longitudinal model, the model is divided into two subsystems, including an altitude subsystem and a velocity subsystem. A novel ideal is that, for each subsystem, some nonlinear coupling terms are considered to be parts of lumped disturbances, which are estimated by a nonlinear disturbance observer, and a corresponding feedforward design is then implemented to compensate the lumped disturbances. Meanwhile, by using a finite time control technique, a continuous finite time control law is introduced in the feedback control design. Then, a composite control scheme is obtained, which consists of a feedback control law based on the finite time control technique and a feedforward compensator based on the nonlinear disturbance observer technique. This scheme can guarantee stable tracking of the reference trajectories of velocity and altitude. Finally, simulation results are provided to demonstrate the effectiveness of the proposed method. The results show that the control performance of the proposed method in terms of both tracking and disturbance rejection are considerably better than the traditional method.

16 - Design of feedback controls

Feedback control design by Lyapunov's direct method

In this paper we provide a robust feedback controller and observer design to provide a maximum stability radius. The technique would take into account the performance specifications in the design process. This is done by using the linear matrix inequalities (LMI). The technique is illustrated on a feedback controller and observer design of an inverted pendulum

State feedback controller design for the synchronization of Boolean networks with time delays

This paper considers linear time-invariant control systems over fading channels in both continuous-time and discrete-time cases and addresses the design of output feedback controllers that stabilize the closed-loop system in the mean square sense. It is shown that a sufficient and necessary condition for the existence of such controllers can be obtained by solving a convex optimization problem in the form of a semidefinite program. This condition is obtained by reformulating mean square stability as asymptotical stability of a suitable matrix comprising plant, controller, and channel, and by introducing modified Hurwitz and Schur stability criteria.

Over the last couple of decades the demand for high precision and enhanced performance of physical systems has been steadily increasing. This demand often results in miniaturization and complex design, thus increasing the need for complex nonlinear control methods. Some of the state of the art nonlinear methods are stymied by the requirement of full state information, model and parameter uncertainties, mathematical complexity, etc. For many scenarios it is nearly impossible to consider all the uncertainties during the design of a feedback controller. Additionally, while designing a modelbased nonlinear control there is no standard mechanism to incorporate performance measures. Some of the mentioned issues can be addressed by using online learning. Animals and humans have the ability to share, explore, act or respond, memorize the outcome and repeat the task to achieve a better outcome when they encounter the same or a similar scenario. This is called learning from interaction. One instance of this approach is reinforcement learning (RL). However, RL methods are hindered by the curse of dimensionality, non-interpretability and non-monotonic convergence of the learning algorithms. This can be attributed to the intrinsic characteristics of RL, as it is a modelfree approach and hence no standard mechanism exists to incorporate a priori model information. In this thesis, learning methods are proposed which explicitly use the available system knowledge. This can be seen as a new class of approaches that bridge model-based and model-free methods. These methods can address some of the hurdles mentioned earlier. For example, i) a prior system information can speed up the learning, ii) new control objectives can be achieved which otherwise would be extremely difficult to attain using only model-based methods, iii) physical meaning can be attributed to the learned controller. The developed approach is as follows: themodel of the given physical system is represented in the port-Hamiltonian (PH) form. For the system dynamics in PH form a passivity-based control (PBC) law is formulated, which often requires the solution to a set of partial differential equations (PDEs). Instead of finding an analytical solution, the PBC control law is parameterized using an unknown parameter vector. Then, by using a variation of the standard actor-critic learning algorithm, the unknown parameters can be learned online. Using the principles of stochastic approximation theory, a proof of convergence for the developed method is shown. The proposedmethods are evaluated for the stabilization and regulation ofmechanical and electro-mechanical systems. The simulation and experimental results show comparable learning curves. In the final part of the thesis a novel integral reinforcement learning approach is developed to solve for the optimal output tracking control problem for a set of linear heterogeneous multi-agent systems. Unlike existing methods, this approach does not need to solve either the output regulator equation or requires a p-copy of the leader’s dynamics in the agent’s control law. A detailed numerical evaluation has been conducted to show the feasibility of the developed method.

Design of rank-one modification feedback controllers for second-order systems with time delay using frequency response methods

Design of feedback control, for a system with slow and fast eigenvalue modes, using single sampling rate results in either information loss (for a larger sampling period) or increased computations (for a smaller sampling period). This paper contributes to designing multirate state feedback controllers for such systems. In this, it is shown that the feedback control for a linear time-invariant system, having slow and fast eigenvalue modes, can be successfully designed by multirate sampling of states in two stages. Multirate sampling refers to sampling slow- and fast-varying states at different rates, that is sampling slow states at a lower rate than the fast states. Here, two approaches for multirate sampling of states are presented, depending on the sampling sequence. In the first approach, fast subsystem states are sampled initially, and then, slow subsystem states are sampled, whereas in the second approach, slow subsystem states are sampled before sampling the fast subsystem states. As far as the two-stage design is concerned, the first stage of the design of feedback control is initiated just after sampling the first subsystem. Then, the left subsystem is sampled, and the second stage of the design of feedback control is accomplished. It is proved that the feedback controls derived with the multirate sampling of states stabilize the full-order system in both approaches. The design and implementation aspects of both approaches are compared. Finally, the applicability of the proposed control is demonstrated by simulating two examples. Simulations are also compared with other methods proposed in the literature.

This paper deals with the design of robust state feedback controller based on fuzzy logic and its evaluation in adjusting the speed of an induction machine. The basic idea of the proposed controller is similar to the gain scheduling approach. The design is based on a reduced order state space model of the motor drive from which a family of local state space models covering the operating range of the drive system are defined. We then use the state feedback design concept to get a linear state feedback controller for each local model using pole placement topology. The performance of the fuzzy state feedback controller is evaluated under different operating regimes of the drive system.