FeedNetBack-D04.03 - Design of Robust Variable Rate Controllers

A consequence of the execution of control algorithms on digital distributed platforms is inducing delays, jitter and various limitations in sampling rate from different sources in the control loops. These disturbances should be taken into account in the control algorithms design and tuning. Control systems are often cited as examples of "hard real-time systems" where jitter and deadline violations are strictly forbidden. In fact experiments show that this assumption may be false for closed-loop control. Any practical feedback system is designed to obtain some stability margin and robustness w.r.t. the plant parameters uncertainty. This also provides robustness w.r.t. timing uncertainties: closed-loop systems are able to tolerate some amount of sampling period and computing delays deviations, jitter and occasional data loss without loss of stability or integrity. Hence the design of dependable distributed control systems may rely on robust controllers, i.e. controllers which are slightly sensitive to both process model and execution resource uncertainties, or on controllers which are made adaptive w.r.t. the variations of the control intervals and other implementation induced disturbances. Section 2 provides new results concerning the control of systems with delays. A novel analysis of linear systems under asynchronous sampling is provided. This approach is based on the discrete-time Lyapunov Theorem applied to the continuous-time model of the sampled-data systems. Tractable conditions are derived to ensure asymptotic stability and also to obtain an estimate of the exponential rate of the solutions. Examples show the efficiency of the method and the reduction of the conservatism compared to other results from the literature. Moreover the methodology addresses the stability analysis of systems under several sampling periods. We show that a sampled-data system can be stable even if one of the sampling period leads to instability. This has been treated by a continuous-time approach and allows considering uncertain or time-varying systems. An extension of the method includes transmission delays in the control loop. As the variations of the control intervals can be both a consequence of network induced delays and a control variable to manage the CPU and/or network load, robust variable sampling control design is investigated in section 3. Here it is assumed that the control interval is itself a control parameter, e.g. which can be adapted at run-time by a feedback scheduler to cope with operating conditions in a varying environment. The control design is stated using the formulation of Linear Parameters Varying (LPV) systems, where the sampling interval is considered as a varying and measurable parameters of the system. Previous results using a polytopic model of a discretized plant are recalled. A new design using a Linear Fractional Transform (LFT) is developed, where the control interval is considered as a system's uncertainty. This new approach is expected to be more tractable that the polytopic one when the system has several varying parameters. Both designs are assessed and compared using as testbed the control of Autonomous Underwater Vehicles using scheduled ultrasonic sensors for control and navigation.

D04.05 - Feasibility mock-ups of feedback schedulers

Control and computation co-design deals with the interaction between feedback control laws design and their implementation on a real execution resource. Control design is often carried out in the framework of continuous time, or under the assumption of ideal sampling with equidistant intervals and known delays. Implementation on a real-time execution platform introduces many timing uncertainties and distortions to the ideal timing scheme, e.g. due to variable computation durations, complex preemption patterns between concurrent activities, uncertain network induced communication delays or occasional data loss. Analyzing, prototyping, simulating and guaranteeing the safety of complex control systems are very challenging topics. Models are needed for the mechatronic continuous system, for the discrete controllers and diagnosers, and for network behavior. Real-time properties (task response times) and the network Quality of Service (QoS) influence the controlled system properties (Quality of Control, QoC). To reach effective and safe systems it is not enough to provide theoretic control laws and leave programmers and real-time systems engineers just do their best to implement the controllers. This report first describes, through the detailed design of a quadrotor drone controller, the main features of {\sc Orccad}, an integrated development environment aimed to bridge the gap between advanced control design and real-time implementation. Besides control design and implementation, a real-time (hardware-in-the-loop) simulation has been designed to assess the control design with a simulated target rather than with the real plant. Using this HIL structure, several experiments using flexible real-time control features are reported, namely Kalman filters subject to data loss, control under (m,k)-firm constraints, control with varying sampling rates and feedback scheduling using the MPC approach

Robust Control Design of Gain-scheduled Controllers for Nonlinear Processes

In the chemical or biochemical industry most processes are modeled by nonlinear equations. It is of a great significance to design high-performance nonlinear controllers for efficient control of these nonlinear processes to achieve closed-loop system's stability and high performance. However, there are many difficulties which hinder the design of such controllers due mainly to the process nonlinearity. In this work, comprehensive design procedures based on robust control have been proposed to efficiently deal with the design of gain-scheduled controllers for nonlinear systems. Since all the design procedures proposed in this work rely strongly on the process model, the first difficulty addressed in this thesis is the identification of a relatively simple model of the nonlinear processes under study. The nonlinearity of the processes makes it often difficult to obtain a first-principles model which can be used for analysis and design of the controller. As a result, relatively simple empirical models, Volterra series model and state-affine model, are chosen in this work to represent the nonlinear process for the design of controllers. The second major difficulty is that although the nonlinear models used in this thesis are easy to identify, the analysis of stability and performance for such models using nonlinear control theory is not straightforward. Instead, it is proposed in this study to investigate the stability and performance using a robust control approach. In this approach, the nonlinear model is approximated by a nominal linear model combined with a mathematical description of model error to be referred to, in this work, as model uncertainty. In the current work it was assumed that the main source of uncertainty with respect to the nominal linear model is due to the system nonlinearity. Then, in this study, robust control theoretical tools have been especially developed and applied for the design of gain-scheduled Proportional-Integral (PI) control and gain-scheduled Model Predictive Control (MPC). Gain-scheduled controllers are chosen because for nonlinear processes operated over a wide range of operation, gain-scheduling has proven to be a successful control design technique (Bequette, 1997) for nonlinear processes. To guarantee the closed-loop system's robust stability and performance with the designed controllers, a systematic approach has been proposed for the design of robust gain-scheduled controllers for nonlinear processes. The design procedure is based on robust stability and performance conditions proposed in this work. For time-varying uncertain parameters, robust stability and performance conditions using fixed Lyapunov functions and parameter-dependent Lyapunov functions, were used. Then, comprehensive procedures for the design and optimization of robust gain-scheduled PI and MPC controllers tuning parameters based on the robust stability and performance tests are then proposed. Since the closed-loop system represented by the combination of a state-affine process model and the gain-scheduled controller is found to have an affine dependence on the uncertain parameters, robust stability and performance conditions can be tested by a finite number of Linear Matrix Inequalities (LMIs). Thus, the final problems are numerically solvable. One of the inherent problems with robust control is that the design is conservative. Two approaches have been proposed in this work to reduce the conservatism. The first one is based on parameter-dependent Lyapunov functions, and it is applied when the rate of change of the time-varying uncertainty parameters is a priori available. The second one is based on the relaxation of an input-saturation factor defined in the thesis to deal with the issue of actuator saturation. Finally, to illustrate the techniques discussed in the thesis, robust gain-scheduled PI and MPC controllers are designed for a continuous stirred tank reactor (CSTR) process. A simple MIMO example with two inputs and two outputs controlled by a multivariable gain-scheduled MPC controller is also discussed to illustrate the applicability of the methods to multivariable situations. All the designed controllers are simulated and the simulations show that the proposed design procedures are efficient in designing and comparing robust gain-scheduled controllers for nonlinear processes

DECENTRALIZED ROBUST NONLINEAR MODEL PREDICTIVE CONTROLLER FOR UNMANNED AERIAL SYSTEMS

The nonlinear and unsteady nature of aircraft aerodynamics together with limited practical range of controls and state variables make the use of the linear control theory inadequate especially in the presence of external disturbances, such as wind. In the classical approach, aircraft are controlled by multiple inner and outer loops, designed separately and sequentially. For unmanned aerial systems in particular, control technology must evolve to a point where autonomy is extended to the entire mission flight envelope. This requires advanced controllers that have sufficient robustness, track complex trajectories, and use all the vehicles control capabilities at higher levels of accuracy. In this work, a robust nonlinear model predictive controller is designed to command and control an unmanned aerial system to track complex tight trajectories in the presence of internal and external perturbance. The Flight System developed in this work achieves the above performance by using: 1 A nonlinear guidance algorithm that enables the vehicle to follow an arbitrary trajectory shaped by moving points; 2 A formulation that embeds the guidance logic and trajectory information in the aircraft model, avoiding cross coupling and control degradation; 3 An artificial neural network, designed to adaptively estimate and provide aerodynamic and propulsive forces in real-time; and 4 A mixed sensitivity approach that enhances the robustness for a nonlinear model predictive controller overcoming the effect of un-modeled dynamics, external disturbances such as wind, and measurement additive perturbations, such as noise and biases. These elements have been integrated and tested in simulation and with previously stored flight test data and shown to be feasible

Fast Dynamic 1D Simulation of Divertor Plasmas with Neural PDE Surrogates

Managing divertor plasmas is crucial for operating reactor scale tokamak devices due to heat and particle flux constraints on the divertor target. Simulation is an important tool to understand and control these plasmas, however, for real-time applications or exhaustive parameter scans only simple approximations are currently fast enough. We address this lack of fast simulators using neural PDE surrogates, data-driven neural network-based surrogate models trained using solutions generated with a classical numerical method. The surrogate approximates a time-stepping operator that evolves the full spatial solution of a reference physics-based model over time. We use DIV1D, a 1D dynamic model of the divertor plasma, as reference model to generate data. DIV1D's domain covers a 1D heat flux tube from the X-point (upstream) to the target. We simulate a realistic TCV divertor plasma with dynamics induced by upstream density ramps and provide an exploratory outlook towards fast transients. State-of-the-art neural PDE surrogates are evaluated in a common framework and extended for properties of the DIV1D data. We evaluate (1) the speed-accuracy trade-off; (2) recreating non-linear behavior; (3) data efficiency; and (4) parameter inter- and extrapolation. Once trained, neural PDE surrogates can faithfully approximate DIV1D's divertor plasma dynamics at sub real-time computation speeds: In the proposed configuration, 2ms of plasma dynamics can be computed in $\approx$0.63ms of wall-clock time, several orders of magnitude faster than DIV1D.Comment: Published in Nuclear Fusio