A Python package for the Virtual Reference Feedback Tuning, a direct data-driven control method

In this paper, thepyvrft, a Python package for the data-driven control method known as Virtual Reference Feedback Tuning (VRFT), is presented. Virtual Reference Feedback Tuning is a control designtechnique that does not use a mathematical model from the process to be controlled. Instead, it uses input and output data from an experiment to compute the controller’s parameters, aiming to minimizean H2 Model Reference criterion. The package implements an unbiased estimate of the controller for MIMO (Multiple-Input Multiple-Output) processes using both least-squares and instrumental variabletechniques. The package also provides accessory functions to import data and to perform MIMO systems simulations, together with some examples

Control of flexible joint robotic manipulator using tuning functions design

The goal of this thesis is to design the controller for a single arm manipulator having a flexible joint for the tracking problem in two different cases. A controller is designed for a deterministic case wherein the plant parameters are assumed to be known while another is designed for an adaptive case where all the plant parameters are assumed to be unknown. In general the tracking problem is; given a smooth reference trajectory, the end effector has to track the reference while maintaining the stability. It is assumed that only the output of the manipulator, which is the link angle, is available for measurement. Also without loss of generality, the fast dynamics, that is the dynamics of the driver side of the system are neglected for the sake of simplicity; In the first case, the design procedure adopted is called observer backstepping. Since the states of the system are unavailable for measurement, an observer is designed that estimates the system states. These estimates are fed to the controller which in turn produces the control input to the system; The second case employs a design procedure called tuning functions design. In this case, since the plant parameters are unknown, the observer designed in case one cannot be used for determining the state estimates. For this purpose, parameter update laws and filters are designed for estimation of plant parameters. The filters employed are k-filters. The k-filters and the parameter update laws are given as input to the controller, which generates the control input to the system; For both cases, the mathematical models are simulated using Matlab/Simulink, and the results are verified

Direct data-driven design of LPV controllers with soft performance specifications

If only experimental measurements are available, direct data-driven control design becomes an appealing approach, as control performance is directly optimized based on the collected samples. The direct synthesis of a feedback controller from input-output data typically requires the blind choice of a reference model, that dictates the desired closed-loop behavior. In this paper, we propose a data-driven design scheme for linear parameter-varying (LPV) systems to account for soft performance specifications. Within this framework, the reference model is treated as an additional hyper-parameter to be learned from data, while the user is asked to provide only indicative performance constraints. The effectiveness of the proposed approach is demonstrated on a benchmark simulation case study, showing the improvement achieved by allowing for a flexible reference model.</p

Virtual reference feedback tuning for linear discrete-time systems with robust stability guarantees based on set membership

In this paper we propose a novel methodology that allows to design, in a purely data-based fashion and for linear single-input and single-output systems, both robustly stable and performing control systems for tracking piecewise constant reference signals. The approach uses both (i) Virtual Reference Feedback Tuning for enforcing suitable performances and (ii) the Set Membership framework for providing a-priori robust stability guarantees. Indeed, an uncertainty set for the system parameters is obtained through Set Membership identification, where an algorithm based on the scenario approach is proposed to estimate the inflation parameter in a probabilistic way. Based on this set, robust stability conditions are enforced as Linear Matrix Inequality constraints within an optimization problem whose linear cost function relies on Virtual Reference Feedback Tuning. To show the generality and effectiveness of our approach, we apply it to two of the most widely used yet simple control schemes, i.e., where tracking is achieved thanks to (i) a static feedforward action and (ii) an integrator in closed-loop. The proposed method is not fully direct due to the Set Membership identification. However, the uncertainty set is used with the only objective of providing robust stability guarantees for the closed-loop system and it is not directly used for the performances optimization, which instead is totally based on data. The effectiveness of the developed method is demonstrated with reference to two simulation examples. A comparison with other data-driven methods is also carried out

The internal performance of iterative feedback tuning

Includes bibliographical references (p. 113-115).Under certain conditions Iterative Feedback Tuning (IFT) may produce a controller that cancels the poles of the process and as a result can give a closed loop that has poor internal performance. The disadvantage of this is that the closed loop will have poor input disturbance rejection. A solution for ensuring that IFT does not have poor internal performance is to make sure that the disturbance rejection is adequate. However an adequate input disturbance may lead to other undesirable dynamics in the closed loop performance. These are such as overshoot in the response for setpoint tracking and that for output disturbance rejection. On the other hand the advantage of pole shifting is that for a one degree of freedom control structure all the characteristic equations of the loop transfer functions will be the same. Four methods are proposed for avoiding pole-zero cancellation by concentrating on the input disturbance. These methods are using: a model for input disturbance rejection, time-weighted IFT for disturbance rejection, a setpoint-tracking model with overshoot and approximate pole placement IFT. Approximate pole placement IFT was chosen as the best method. The reason is that the dynamics of the closed loop can be specified with the choice of characteristic equation. This method was then investigated further to establish its feasibility on a physical system. After the evaluation of this method, it was applied on a DC motor for speed control to show that is viable in practice. Multiple experiments were done to show that this method does not produce a controller that cancels the process poles, confirming it as a good solution to prevent poor internal performance

Adaptive Data-Driven Control for Linear Time Varying Systems

In this paper, we propose an adaptive data-driven control approach for linear time varying systems, affected by bounded measurement noise. The plant to be controlled is assumed to be unknown, and no information in regard to its time varying behaviour is exploited. First, using set-membership identification techniques, we formulate the controller design problem through a model-matching scheme, i.e., designing a controller such that the closed-loop behaviour matches that of a given reference model. The problem is then reformulated as to derive a controller that corresponds to the minimum variation bounding its parameters. Finally, a convex relaxation approach is proposed to solve the formulated controller design problem by means of linear programming. The effectiveness of the proposed scheme is demonstrated by means of two simulation examples