QFT Based Robust Positioning Control of the PMSM Using Automatic Loop Shaping with Teaching Learning Optimization

Automation of the robust control system synthesis for uncertain systems is of great practical interest. In this paper, the loop shaping step for synthesizing quantitative feedback theory (QFT) based controller for a two-phase permanent magnet stepper motor (PMSM) has been automated using teaching learning-based optimization (TLBO) algorithm. The QFT controller design problem has been posed as an optimization problem and TLBO algorithm has been used to minimize the proposed cost function. This facilitates designing low-order fixed-structure controller, eliminates the need of manual loop shaping step on the Nichols charts, and prevents the overdesign of the controller. A performance comparison of the designed controller has been made with the classical PID tuning method of Ziegler-Nichols and QFT controller tuned using other optimization algorithms. The simulation results show that the designed QFT controller using TLBO offers robust stability, disturbance rejection, and proper reference tracking over a range of PMSM’s parametric uncertainties as compared to the classical design techniques

Stability Analysis and Design of Digital Compensators for Networked Control Systems

Networked Control Systems (NCSs) are distributed control systems where sensors, actuators, and controllers are interconnected by communication networks, e.g. LAN, WAN, CAN, Internet. Use of digital networks are advantageous due to less cost, ease in installation and/or ready availability. These are widely used in automobiles, manufacturing plants, aircrafts, spacecrafts, robotics and smart grids. Due to the involvement of network in such systems, the closed-loop system performance may degrade due to network delays and packet losses. Since delays are involved in NCS, predictor based compensators are useful to improve control performance of such systems. Moreover, the digital communication network demands implementation of digital compensators. First, the thesis studies stability analysis of NCSs with uncertain time-varying delays. For this configuration, both the controller and actuators are assumed as event-driven (i.e. the delays are fractional type). The NCS with uncertain delays and packet losses are represented as systems in polytopic form as well as with norm-bounded uncertainties. The closed-loop system stability is guaranteed using quadratic Lyapunov function in terms of LMIs. For given controller gain the maximum tolerable delay calculated and the resultant stability regions of the system is explored in the parameter plane of control gain and maximum tolerable delay. The stability region is found to be almost same for both the methods for the case of lower order systems (an integrator plant), whereas for higher order systems (second order example system), the obtained stability region is more for the case of polytopic approach than the norm-bounded one. This motivates to use the polytopic modeling approach in remaining of the thesis. Next, design of digital Smith Predictor (SP) to improve the performance of NCS with bounded uncertain delays and packet losses in both the forward and feedback channels is con-sidered. For implementing a digital SP, it is essential that the controller is implemented with constant sampling interval so that predictor model is certain and therefore the controller is required to be time-driven one (sensor-to-controller channel uncertainties are integer type). On the other hand, the actuator is considered to be event-driven since it introduces lesser delay compared to the time-driven case. Thereby, the controller-to-actuator channel delays are fractional type. The system with uncertain delay parameters (packet losses as uncertain integer delays) are modeled in polytopic form. For this system, Lyapunov stability criterion has been presented in terms of LMIs to explore the closed-loop system stability. Finally, the proposed analysis is verified with numerical studies and using TrueTime simulation en- vironment. It is observed that the digital SP improves the stability performance of the NCS considerably compared to without predictor. However, the choice of predictor delay affects the system performance considerably. Further, an additional filter is used along with conventional digital SP to improve the system response and disturbance rejection property of the controller. For this configurations, both the controller and actuators are assumed to be time-driven. The NCS with random but bounded delays and packet losses introduced by the network is modeled as a switched system and LMI based iterative algorithm is used for designing the controller. A LAN-based experimental setup is developed to validate the above theoretical findings.The plant is an op-amp based emulated integrator plant.The plant is interfaced with a computer using data acquisition card. Another computer is used as the digital controller and the two computers are connected via LAN using UDP communication protocol. The effectiveness of the proposed controller design method is verified with this LAN-based experi- mental setup. Three controller configurations (i.e. without and with digital SP as well as the digital SP with filter) are considered for comparison of their guaranteed cost performance. It is shown that the digital SP with filter improves the performance of NCS than with and without simple digital SP based NCS configurations. Finally, design of digital predictor based robust H1 control for NCSs is made in such a way that the effect of randomness in network delays and packet losses on the closed-loop system dynamics is reduced. For the purpose, the predictor delay is chosen as a fixed one whereas variation of random delays in the system are modeled as disturbances. Then quadratic H1 design criterion in the form of LMIs is invoked so that the network jitter effect is minimized. The efficacy of the proposed configurations are validated with the developed LAN based NCS setup. It is seen that the designed controllers effectively regularize the system dynamics from random variations of the network delays and packet losses

Sound and Automated Synthesis of Digital Stabilizing Controllers for Continuous Plants

Modern control is implemented with digital microcontrollers, embedded within a dynamical plant that represents physical components. We present a new algorithm based on counter-example guided inductive synthesis that automates the design of digital controllers that are correct by construction. The synthesis result is sound with respect to the complete range of approximations, including time discretization, quantization effects, and finite-precision arithmetic and its rounding errors. We have implemented our new algorithm in a tool called DSSynth, and are able to automatically generate stable controllers for a set of intricate plant models taken from the literature within minutes.Comment: 10 page

Robust L2–L∞ control of uncertain differential linear repetitive processes

This is the post print version of the article. The official published version can be obtained from the link - Copyright 2008 Elsevier LtdFor two-dimensional (2-D) systems, information propagates in two independent directions. 2-D systems are known to have both system-theoretical and applications interest, and the so-called linear repetitive processes (LRPs) are a distinct class of 2-D discrete linear systems. This paper is concerned with the problem of L2–L∞ (energy to peak) control for uncertain differential LRPs, where the parameter uncertainties are assumed to be norm-bounded. For an unstable LRP, our attention is focused on the design of an L2–L∞ static state feedback controller and an L2–L∞ dynamic output feedback controller, both of which guarantee the corresponding closed-loop LRPs to be stable along the pass and have a prescribed L2–L∞ performance. Sufficient conditions for the existence of such L2–L∞ controllers are proposed in terms of linear matrix inequalities (LMIs). The desired L2–L∞ dynamic output feedback controller can be found by solving a convex optimization problem. A numerical example is provided to demonstrate the effectiveness of the proposed controller design procedures.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, the Nuffield Foundation of the UK under Grant NAL/00630/G, and the Alexander von Humboldt Foundation of Germany

Average-cost based robust structural control

A method is presented for the synthesis of robust controllers for linear time invariant structural systems with parameterized uncertainty. The method involves minimizing quantities related to the quadratic cost (H2-norm) averaged over a set of systems described by real parameters such as natural frequencies and modal residues. Bounded average cost is shown to imply stability over the set of systems. Approximations for the exact average are derived and proposed as cost functionals. The properties of these approximate average cost functionals are established. The exact average and approximate average cost functionals are used to derive dynamic controllers which can provide stability robustness. The robustness properties of these controllers are demonstrated in illustrative numerical examples and tested in a simple SISO experiment on the MIT multi-point alignment testbed

Linear matrix inequality-based nonlinear adaptive robust control with application to unmanned aircraft systems

Unmanned aircraft systems (UASs) are gaining popularity in civil and commercial applications as their lightweight on-board computers become more powerful and affordable, their power storage devices improve, and the Federal Aviation Administration addresses the legal and safety concerns of integrating UASs in the national airspace. Consequently, many researchers are pursuing novel methods to control UASs in order to improve their capabilities, dependability, and safety assurance. The nonlinear control approach is a common choice as it offers several benefits for these highly nonlinear aerospace systems (e.g., the quadrotor). First, the controller design is physically intuitive and is derived from well known dynamic equations. Second, the final control law is valid in a larger region of operation, including far from the equilibrium states. And third, the procedure is largely methodical, requiring less expertise with gain tuning, which can be arduous for a novice engineer. ^ Considering these facts, this thesis proposes a nonlinear controller design method that combines the advantages of adaptive robust control (ARC) with the powerful design tools of linear matrix inequalities (LMI). The ARC-LMI controller is designed with a discontinuous projection-based adaptation law, and guarantees a prescribed transient and steady state tracking performance for uncertain systems in the presence of matched disturbances. The norm of the tracking error is bounded by a known function that depends on the controller design parameters in a known form. Furthermore, the LMI-based part of the controller ensures the stability of the system while overcoming polytopic uncertainties, and minimizes the control effort. This can reduce the number of parameters that require adaptation, and helps to avoid control input saturation. ^ These desirable characteristics make the ARC-LMI control algorithm well suited for the quadrotor UAS, which may have unknown parameters and may encounter external disturbances such as wind gusts and turbulence. This thesis develops the ARC-LMI attitude and position controllers for an X-configuration quadrotor helicopter. The inner-loop of the autopilot controls the attitude and altitude of the quadrotor, and the outer-loop controls its position in the earth-fixed coordinate frame. Furthermore, by intelligently generating a smooth trajectory from the given reference coordinates (waypoints), the transient performance is improved. The simulation results indicate that the ARC-LMI controller design is useful for a variety of quadrotor applications, including precise trajectory tracking, autonomous waypoint navigation in the presence of disturbances, and package delivery without loss of performanc