A Data-Driven Frequency-Domain Approach for Robust Controller Design via Convex Optimization

The objective of this dissertation is to develop data-driven frequency-domain methods for designing robust controllers through the use of convex optimization algorithms. Many of today's industrial processes are becoming more complex, and modeling accurate physical models for these plants using first principles may be impossible. With the increased developments in the computing world, large amounts of measured data can be easily collected and stored for processing purposes. Data can also be collected and used in an on-line fashion. Thus it would be very sensible to make full use of this data for controller design, performance evaluation, and stability analysis. The design methods imposed in this work ensure that the dynamics of a system are captured in an experiment and avoids the problem of unmodeled dynamics associated with parametric models. The devised methods consider robust designs for both linear-time-invariant (LTI) single-input-single-output (SISO) systems and certain classes of nonlinear systems. In this dissertation, a data-driven approach using the frequency response function of a system is proposed for designing robust controllers with H∞ performance. Necessary and sufficient conditions are derived for obtaining H∞ performance while guaranteeing the closed-loop stability of a system. A convex optimization algorithm is implemented to obtain the controller parameters which ensure system robustness; the controller is robust with respect to the frequency-dependent uncertainties of the frequency response function. For a certain class of nonlinearities, the proposed method can be used to obtain a best-linear-approximation with an associated frequency dependent uncertainty to guarantee the stability and performance for the underlying linear system that is subject to nonlinear distortions. The concepts behind these design methods are then used to devise necessary and sufficient conditions for ensuring the closed-loop stability of systems with sector-bounded nonlinearities. The conditions are simple convex feasibility constraints which can be used to stabilize systems with multi-model uncertainty. Additionally, a method is proposed for obtaining H∞ performance for an approximate model (i.e., describing function) of a sector-bounded nonlinearity. This work also proposes several data-driven methods for designing robust fixed-structure controllers with H∞ performance. One method considers the solution to a non-convex problem, while another method convexifies the problem and implements an iterative algorithm to obtain the local solution (which can also consider H2 performance). The effectiveness of the proposed method(s) is illustrated by considering several case studies that require robust controllers for achieving the desired performance. The main applicative work in this dissertation is with respect to a power converter control system at the European Organization for Nuclear Research (CERN) (which is used to control the current in a magnet to produce the desired field in controlling particle trajectories in accelerators). The proposed design methods are implemented in order to satisfy the challenging performance specifications set by the application while guaranteeing the system stability and robustness using data-driven design strategies

H∞ smith predictor design for time-delayed MIMO systems via convex optimization

A new method for robust fixed-order H∞ controller design for uncertain time-delayed MIMO systems is presented. It is shown that the H∞ robust performance condition can be represented by a set of convex constraints with respect to the parameters of a linearly parameterized primary controller in the Smith predictor structure. Therefore, the parameters of the primary controller can be obtained by convex optimization. The proposed method will be applied to stable MIMO models with uncertain dead-time and with multimodel and frequency-dependent uncertainty. The performance of this method is illustrated by simulation examples of industrial processes

A Robust Data-Driven Controller Design Methodology With Applications to Particle Accelerator Power Converters

A new data-driven approach using the frequency response function (FRF) of a system is proposed for designing robust-fixed structure digital controllers for particle accelerators' power converters. This design method ensures that the dynamics of a system are captured and avoid the problem of unmodeled dynamics associated with parametric models. The H ∞ robust performance condition can be represented by a set of convex constraints with respect to the parameters of a two degree of freedom RST controller. This controller is robust with respect to the frequency-dependent uncertainties of the FRF. A convex optimization algorithm is implemented to obtain the controller parameters. The effectiveness of the method is illustrated by considering two case studies that require robust controllers for achieving the desired performance

A Data-Driven Approach in Designing RST Controllers with H∞ Performance via Convex Optimization

In this paper, a new method for designing robust fixed-order $\mathcal{H}_{\infty}$ discrete-time controllers is presented. The controller structure is a two-degree of freedom polynomial controller of the $RST$ type. A data-driven approach is implemented for the design process in order to capture the unmodeled dynamics that may exist with parametric models. The H infinity robust performance condition can be represented by a set of convex constraints with respect to the parameters of the RST controllers. A convex optimization algorithm can then be implemented to obtain these parameters. The proposed method is applied to a multi-axis torsional system where the goal is to control the position of the disks with variable inertia

On active disturbance rejection based control design for superconducting RF cavities

Superconducting RF (SRF) cavities are key components of modern linear particle accelerators. The National Superconducting Cyclotron Laboratory (NSCL) is building a 3 MeV/u re-accelerator (ReA3) using SRF cavities. Lightly loaded SRF cavities have very small bandwidths (high Q) making them very sensitive to mechanical perturbations whether external or self-induced. Additionally, some cavity types exhibit mechanical responses to perturbations that lead to high-order non-stationary transfer functions resulting in very complex control problems. A control system that can adapt to the changing perturbing conditions and transfer functions of these systems would be ideal. This paper describes the application of a control technique known as “Active Disturbance Rejection Control” (ARDC) to this problem

On Active Disturbance Rejection Based Control Design for Supercomputing RF Cavities

Superconducting RF (SRF) cavities are key components of modern linear particle accelerators. The National Superconducting Cyclotron Laboratory (NSCL) is building a 3 MeV/u re-accelerator (ReA3) using SRF cavities. Lightly loaded SRF cavities have very small bandwidths (high Q) making them very sensitive to mechanical perturbations whether external or self-induced. Additionally, some cavity types exhibit mechanical responses to perturbations that lead to high-order non-stationary transfer functions resulting in very complex control problems. A control system that can adapt to the changing perturbing conditions and transfer functions of these systems would be ideal. This paper describes the application of a control technique known as “Active Disturbance Rejection Control” (ARDC) to this problem

On Active Disturbance Rejection Based Control Design for Supercomputing RF Cavities

Superconducting RF (SRF) cavities are key components of modern linear particle accelerators. The National Superconducting Cyclotron Laboratory (NSCL) is building a 3 MeV/u re-accelerator (ReA3) using SRF cavities. Lightly loaded SRF cavities have very small bandwidths (high Q) making them very sensitive to mechanical perturbations whether external or self-induced. Additionally, some cavity types exhibit mechanical responses to perturbations that lead to high-order non-stationary transfer functions resulting in very complex control problems. A control system that can adapt to the changing perturbing conditions and transfer functions of these systems would be ideal. This paper describes the application of a control technique known as “Active Disturbance Rejection Control” (ARDC) to this problem

A Data-Driven Frequency-Domain Approach for Robust Controller Design via Convex Optimization

The objective of this dissertation is to develop data-driven frequency-domain methods for designing robust controllers through the use of convex optimization algorithms. Many of today's industrial processes are becoming more complex, and modeling accurate physical models for these plants using first principles may be impossible. Albeit a model may be available; however, such a model may be too complex to consider for an appropriate controller design. With the increased developments in the computing world, large amounts of measured data can be easily collected and stored for processing purposes. Data can also be collected and used in an on-line fashion. Thus it would be very sensible to make full use of this data for controller design, performance evaluation, and stability analysis. The design methods imposed in this work ensure that the dynamics of a system are captured in an experiment and avoids the problem of unmodeled dynamics associated with parametric models. The devised methods consider robust designs for both linear-time-invariant (LTI) single-input-single-output (SISO) systems and certain classes of nonlinear systems. In this dissertation, a data-driven approach using the frequency response function of a system is proposed for designing robust controllers with $\mathcal{H}_{\infty}$ performance. Necessary and sufficient conditions are derived for obtaining $\mathcal{H}_{\infty}$ performance while guaranteeing the closed-loop stability of a system. A convex optimization algorithm is formulated to obtain the controller parameters which ensure system robustness; the controller is robust with respect to the frequency-dependent uncertainties of the frequency response function. For a certain class of nonlinearities, the proposed method can be used to obtain a best-linear-approximation with an associated frequency-dependent uncertainty to guarantee the stability and performance for the underlying linear system that is subject to nonlinear distortions. The controller for this design scheme is presented as a ratio of two linearly-parameterized transfer functions; in this manner, the numerator and denominator of a controller are simultaneously optimized. With this construction, it can be shown that as the controller order increases, the solution to the convex problem converges to the global optimal solution of the $\mathcal{H}_{\infty}$ problem. This method is then extended to the 2-degree-of-freedom discrete-time controller where the necessary and sufficient conditions are imposed for multiple weighted sensitivity functions. The concepts behind these design methods are then used to devise necessary and sufficient conditions for ensuring the closed-loop stability of systems with sector-bounded nonlinearities. The conditions are simple convex feasibility constraints which can be used to stabilize systems with multi-model uncertainty. Additionally, a method is proposed for obtaining $\mathcal{H}_{\infty}$ performance for systems with uncertain gains within these sectors. By convexifying the $\mathcal{H}_{\infty}$ problem, the global optimal solution to an approximate problem is obtained. For low-order controllers, the solution to this approximate problem may lead to solutions far from the optimal solution of the true $\mathcal{H}_{\infty}$ problem. Thus two methods are proposed to address this issue for low-order controllers. In one method, a non-convex problem is formulated which optimizes the basis function parameters of a controller while guaranteeing the stability of the closed-loop systems. In another method, a set of convex problems are solved in an iterative fashion to obtain the desired performance (which also guarantees the closed-loop stability of the system). With both methods, the local solution to the $\mathcal{H}_{\infty}$ problem for fixed-structure controllers is obtained. However, the convex problem is computationally tractable and can also consider $\mathcal{H}_2$ performance. The effectiveness of the proposed method(s) is illustrated by considering several case studies that require robust controllers for achieving the desired performance. The main applicative work in this dissertation is with respect to a power converter control system at the European Organization for Nuclear Research (CERN) (which is used to control the current in a magnet to produce the desired field in controlling particle trajectories in particle accelerators). The proposed design methods are implemented in order to satisfy the challenging performance specifications set by the application while guaranteeing the system stability and robustness using data-driven design strategies

Data-Driven Controller Design for High Precision Pulsed Power Converters for Bumper Magnets of the PS Booster

A new data-driven approach using the frequency response function of a system is proposed for designing robust digital controllers for the injection bumper magnet (BSW) power supplies of the PS Booster. The powering of the BSW requires high precision 3.4 kA to 6.7 kA trapezoidal current pulses with 2 ms flat-top and 5 ms ramp-up and ramp-down time. The tracking error must remain within ± 50 parts-per-million (ppm) during the flat-top of the trapezoidal reference, and ± 500 ppm during the ramp-down. The BSW is powered with a four quadrant switch-mode power converter and the current through the magnet is controlled in closed-loop form with a 2-degree-of-freedom controller at a sampling rate of 10 kHz. A convex optimization algorithm is performed for obtaining the controller parameters. The effectiveness of the method is illustrated by designing the controller for a full-scale prototype of the BSW system at CERN, which is in the framework of the LHC Injector Upgrade (LIU) project