Design of Low-Order Controllers using Optimization Techniques

In many applications, especially in the process industry, low-level controllers are the workhorses of the automated production lines. The aim of this study has been to provide simple tuning procedures, either optimization-based methods or tuning rules, for design of low-order controllers. The first part of this thesis deals with PID tuning. Design methods or both SISO and MIMO PID controllers based on convex optimization are presented. The methods consist of solving a nonconvex optimization problem by deriving convex approximations of the original problem and solving these iteratively until convergence. The algorithms are fast because of the convex approximations. The controllers obtained minimize low-frequency sensitivity subject to constraints that ensure robustness to process variations and limitations of control signal effort. The second part of this thesis deals with tuning of feedforward controllers. Tuning rules that minimize the integrated-squared-error arising from measurable step disturbances are derived for a controller that can be interpreted as a filtered and possibly time-delayed PD controller. Using a controller structure that decouples the effects of the feedforward and feedback controllers, the controller is optimal both in open and closed loop settings. To improve the high-frequency noise behavior of the feedforward controller, it is proposed that the optimal controller is augmented with a second-order filter. Several aspects on the tuning of this filter are discussed. For systems with PID controllers, the response to step changes in the reference can be improved by introducing set-point weighting. This can be interpreted as feedforward from the reference signal to the control signal. It is shown how these weights can be found by solving a convex optimization problem. Proportional set-point weight that minimizes the integrated-absolute-error was obtained for a batch of over 130 different processes. From these weights, simple tuning rules were derived and the performance was evaluated on all processes in the batch using five different feedback controller tuning methods. The proposed tuning rules could improve the performance by up to 45% with a modest increase in actuation

Optimal Control and Path Following for Industrial Robots

When using industrial robots in production lines both speed and accuracy is of great importance. This thesis investigates how off-line optimization can be used to create references to a control structure with the aim of traversing a given path in as little time as possible, under given input constraints, without deviating from the path. In this thesis Modelica and Optimica is used to formulate and solve minimum time optimization problems. For the purpose of optimization, a model of an ABB IRB140B industrial robot was identified. A control structure known as a Path Velocity Controller has been implemented in Simulink with the objective to control the IRB140B. The implemented controller was then evaluated in simulations

Design of Optimal Low-Order Feedforward Controllers

Design rules for optimal feedforward controllers with lead-lag structure in the presence of measurable disturbances are presented. The design rules are based on stable first-order models with time delays, FOTD, and are optimal in the sense of minimizing the integrated-squared error. The rules are derived for an open-loop setting, considering a step disturbance. This paper also discusses a general feedforward structure, which enables decoupling in the design of feedback and feedforward controllers, and justifies the open-loop setting

Low-order feedforward controllers: Optimal performance and practical considerations

Feedforward control from measurable disturbances can significantly improve the performance in control loops. However, tuning rules for such controllers are scarce. In this paper design rules for how to choose optimal low-order feedforward controller parameter are presented. The parameters are chosen so that the integrated squared error, when the system is subject to a step disturbance, is minimized. The approach utilizes a controller structure that decouples the feedforward and the feedback controller. The optimal controller can suffer from undesirable high-frequency noise characteristics and tuning methods for how to filter the control signal are also provided. For scenarios where perfect disturbance attenuation in theory is achievable but where noise-filtering is needed, the concept of precompensation is introduced as a way to shift the controller time-delay to compensate for the low-pass filtering

Optimal Robot Control using Modelica and Optimica

In this paper, Modelica along with Optimica has been used to formulate and solve a minimum time optimization problem. The problem concerns traversing a given path with a robot in as short time possible under input constraints. Different problem reformulations are discussed that increase the chance of finding optimal solutions. This paper also discusses the use of these optimal solutions for control of industrial robots. A control structure, in which the optimal trajectories are essential, are used on an ABB IRB140B to ensure robustness for model errors and disturbances

A Synthesis Method for Automatic Handling of Inter-patient Variability in Closed-loop Anesthesia

This paper presents a convex-optimization-based technique to obtain parameters for a PID feedback controller, used to control the infusion rate of the anesthetic drug propofol. The controller design is based on a set of identified patient models, relating propofol infusion to an EEG-based conciousness index. The main contribution lies in the method automatically taking inter-patient variability into account, i.e., it guarantees robustness (sensitivity peak) and performance (disturbance rejection) over a set of patient models, without the need for manual intervention. The method is demonstrated using a clinically relevant design example. A controller designed using the proposed method is currently scheduled for clinical evaluation

Diffractive Imaging of Coherent Nuclear Motion in Isolated Molecules

Observing the motion of the nuclear wave packets during a molecular reaction, in both space and time, is crucial for understanding and controlling the outcome of photoinduced chemical reactions. We have imaged the motion of a vibrational wave packet in isolated iodine molecules using ultrafast electron diffraction with relativistic electrons. The time-varying interatomic distance was measured with a precision 0.07 Å and temporal resolution of 230 fs full width at half maximum. The method is not only sensitive to the position but also the shape of the nuclear wave packet

Femtosecond gas phase electron diffraction with MeV electrons

We present results on ultrafast gas electron diffraction (UGED) experiments with femtosecond resolution using the MeV electron gun at SLAC National Accelerator Laboratory. UGED is a promising method to investigate molecular dynamics in the gas phase because electron pulses can probe the structure with a high spatial resolution. Until recently, however, it was not possible for UGED to reach the relevant timescale for the motion of the nuclei during a molecular reaction. Using MeV electron pulses has allowed us to overcome the main challenges in reaching femtosecond resolution, namely delivering short electron pulses on a gas target, overcoming the effect of velocity mismatch between pump laser pulses and the probe electron pulses, and maintaining a low timing jitter. At electron kinetic energies above 3 MeV, the velocity mismatch between laser and electron pulses becomes negligible. The relativistic electrons are also less susceptible to temporal broadening due to the Coulomb force. One of the challenges of diffraction with relativistic electrons is that the small de Broglie wavelength results in very small diffraction angles. In this paper we describe the new setup and its characterization, including capturing static diffraction patterns of molecules in the gas phase, finding time-zero with sub-picosecond accuracy and first time-resolved diffraction experiments. The new device can achieve a temporal resolution of 100 fs root-mean-square, and sub-angstrom spatial resolution. The collimation of the beam is sufficient to measure the diffraction pattern, and the transverse coherence is on the order of 2 nm. Currently, the temporal resolution is limited both by the pulse duration of the electron pulse on target and by the timing jitter, while the spatial resolution is limited by the average electron beam current and the signal-to-noise ratio of the detection system. We also discuss plans for improving both the temporal resolution and the spatial resolution

Femtosecond gas phase electron diffraction with MeV electrons

We present results on ultrafast gas electron diffraction (UGED) experiments with femtosecond resolution using the MeV electron gun at SLAC National Accelerator Laboratory. UGED is a promising method to investigate molecular dynamics in the gas phase because electron pulses can probe the structure with a high spatial resolution. Until recently, however, it was not possible for UGED to reach the relevant timescale for the motion of the nuclei during a molecular reaction. Using MeV electron pulses has allowed us to overcome the main challenges in reaching femtosecond resolution, namely delivering short electron pulses on a gas target, overcoming the effect of velocity mismatch between pump laser pulses and the probe electron pulses, and maintaining a low timing jitter. At electron kinetic energies above 3 MeV, the velocity mismatch between laser and electron pulses becomes negligible. The relativistic electrons are also less susceptible to temporal broadening due to the Coulomb force. One of the challenges of diffraction with relativistic electrons is that the small de Broglie wavelength results in very small diffraction angles. In this paper we describe the new setup and its characterization, including capturing static diffraction patterns of molecules in the gas phase, finding time-zero with sub-picosecond accuracy and first time-resolved diffraction experiments. The new device can achieve a temporal resolution of 100 fs root-mean-square, and sub-angstrom spatial resolution. The collimation of the beam is sufficient to measure the diffraction pattern, and the transverse coherence is on the order of 2 nm. Currently, the temporal resolution is limited both by the pulse duration of the electron pulse on target and by the timing jitter, while the spatial resolution is limited by the average electron beam current and the signal-to-noise ratio of the detection system. We also discuss plans for improving both the temporal resolution and the spatial resolution