Data-Driven Controller Design Based on Response Estimation for Multi-Performance Optimization

The goal of this paper is to study model-free data-driven control evaluation and design strategies for discrete-time linear time-invariant systems, where the system model is unknown. In particular, our main contribution is twofold: 1) new state-input exploration and data collection schemes from experiences; 2) new data-driven linear matrix inequalities and dynamic programming methods for stabilization and optimal control problems. The proposed exploration and data collection schemes theoretically guarantee to acquire sufficient information from the system’s state-input trajectories that can solve the underlying control design problems. We prove that under mild assumptions, as more and more data is accumulated, the collected data can solve the problems with higher probability along with the proposed algorithms.

The paper proposes a linearly parametrized data-driven controller design method based on minimum variance evaluation. The approach updates control parameters that improves disturbance attenuation properties from regulatory control input and output measurements. Most of data-driven controller design methods address model matching problem for improving tracking properties, whereas our previous works proposed data-driven minimum variance controller design that achieves simultaneous update of both a controller and a process model. However, they used the same controller structure as the controller of the minimum variance control, which requires correct order informations on the controlled process model. In contrast, the proposed method uses linearly parametrized controllers, and obtains sub-optimal control parameters based on variance evaluation. The paper shows data-driven cost function and its validity. Comparing with the original cost criterion that represents minimum variance evaluation subject to linearly parametrized controller, the validity is firstly shown by the analytical expansion on the assumption that disturbance model is known. Then, the paper extends the analysis to the unknown disturbance model case by simultaneously estimating disturbance model. Finally, the paper shows the effectiveness of the proposed method through a numerical example.

Data-driven control design is a method to create and tune controllers directly from the initial experimental data without a mathematical model to be controlled. Tracking and disturbance suppression are necessary to control real systems. A two-degree-of-freedom (2DOF) control system is effective to simultaneously enhance the performances of both. This study proposes a direct data-driven tuning method for the controller parameters of a 2DOF control system using only one-shot initial experimental data without mathematical modeling of the controlled object. The proposed approach improves the tracking and disturbance suppression performances by utilizing an estimation method in which the sensitivity function and the closed-loop transfer function are identified after updating the parameters in the time domain. Specifically, the closed-loop response and control input are estimated after updating the parameters, realizing efficient control system design because the control performance can be evaluated prior to implementation. To validate the effectiveness of the proposed method, a simulation for a mechanical system and an experiment for motor control are performed. The proposed method can estimate the response and control input of a 2DOF control system after updating the parameters by offline computations. The optimal control parameters can be obtained to enhance the tracking and disturbance suppression performances.

This paper deals with data-driven control design in a model reference framework for multivariable systems. Based on a single batch of input–output data collected from the process, a fixed structure controller is estimated without using a process model, by embedding the control design problem in the prediction error identification of an optimal controller. This is an extension of optimal controller identification (OCI) for multivariable systems. Even though the multiple-input multiple-output (MIMO) formulation is extended from its single-input single-output version in a natural way, the solution of the optimization problem is rather complex due to the special structure the inverse of the controller assumes in its MIMO version. Comparisons between the OCI and the virtual reference feedback tuning—a well-known data-driven control method—are provided, showing the efficiency of the OCI controller estimate. We also explore the case where the batch of design data is collected in closed loop. Simulated and experimental results show the efficiency of the proposed methodology.

Performance enhancement of hard disk drives through data-driven control design and population clustering

Since most chemical processes exhibit severe nonlinear and time-varying behavior, the control of such processes is challenging. In this paper, we propose data-driven controller design method based on lazy learning for chemical processes. Using a lazy learning algorithm, a local valid linear model denoting the current state of system is automatically exacted for adjusting the PID controller parameters based on input/output data. This scheme can adjust the PID parameters in an online manner even if the system has nonlinear properties. The simulation results on the dynamic model of Continuous Stirred Tank Reactor (CSTR) are provided to demonstrate the effectiveness of the proposed new control techniques.

Data-driven control for discrete-time piecewise affine systems

Estimating the controller's parameters using a data-driven method usually requires to collect data from a specific experiment, which can be a very costly and undesirable task. A possibility to relief this burden is to use routine operating data. However, the blind application of such data may lead to inappropriate tuning and undesirable closed-loop behaviour due to lack of informativity in the data. Therefore, it is necessary to identify the informative subsets within the entire data set. The present paper is an extension of our previous work where two data selection criteria, developed to the system identification framework, were applied to the data-driven control design problem focusing on the case of full-order controllers. In this paper we treat the case of reduced order controllers, and show that only one of those two criteria can be applied to this case. The feasibility and robustness of the proposed solution is presented through Monte-Carlo simulations in a case study.

The L-DDC (Loewner Data Driven Control) algorithm is a data-driven controller design method based on frequency-domain input-output data. The identification of the plant is skipped and the controller is designed directly from the measurements using the Loewner approach, known for model approximation and reduction. However, in the L-DDC method, the identified controller is not guaranteed to be stable and the effect of noise on the identified controller is unknown. In this article, we ensure the stability of the controller and propose a solution to deal with noisy data. The method is validated on a numerical example.

Guest Editorial

Starting in Chap. 5, the particularities of the H 2 cost functions that are minimized in data-driven control design are explored. Convergence to the globally optimal controller is sought in a data-driven control design, so the properties of the cost function are analyzed with respect to this goal. A number of properties of these particular cost functions and of some basic optimization algorithms when applied to them are presented in this chapter. From these properties, guidelines for the optimization are provided, involving the choice of the optimization algorithm and the automatic selection of step sizes. Step size policies that speed up the convergence to the global minimum are presented, and a general choice of optimization algorithm is advocated: start with the steepest descent then switch to the Newton-Raphson method when sufficiently close to the global optimum. A case study is presented to illustrate the convergence properties of the various algorithmic choices. The theoretical results also set the stage for the synthetic procedures to be presented in Chap. 6.

Data-Driven control design by prediction error identification for a refrigeration system based on vapor compression

The goal of this paper is to investigate model-free data-driven control design strategies for unknown systems. In particular, we report new data-driven linear matrix inequalities (LMIs) and dynamic programming (DP) methods. Both continuous-time and discrete-time systems are considered. We consider data transition equations that include complete information on the system model using state-input trajectories. Instead of computing explicit system model, the data transition equations are used to construct data-dependent LMI and DP formulations. The proposed formulations provide additional insights in data-driven control designs. In addition, we regard the proposed methods as a complement rather than replacement of existing methods.

It is well-known that the IMC-PID controller tuning gives fast and improved set point response but slow disturbance rejection. A modification has been proposed in IMC-PID tuning rule for the improved disturbance rejection. For the modified IMC-PID tuning rule, a method has been developed to obtain the IMC-PID setting in closed-loop mode without acquiring detailed information of the process. The proposed method is based on the closed-loop step set point experiment using a proportional only controller with gain Kc0. It is the direct approach to find the PID controller setting similar to classical Ziegler-Nichols closed-loop method. Based on simulations of a wide range of first-order with delay processes, a simple correlation has been derived to obtain the modified IMC-PID controller settings from closed-loop experiment. In this method, controller gain is a function of the overshoot obtained in the closed loop set point experiment. The integral and derivative time is mainly a function of the time to reach the first peak (overshoot). Simulation has been conducted for the broad class of processes and the controllers were tuned to have the same degree of robustness by measuring the maximum sensitivity, Ms, in order to obtain a reasonable comparison. The PID controller settings obtained in the proposed tuning method show better performance and robustness with other two-step tuning methods for the broad class of processes. It has also been applied to temperature control loop in distillation column model. The result has been compared to the open loop tuning method where it gives robust and fast response.

In this paper, a new data-driven model predictive control (MPC), based on bilinear subspace identification, is considered. The system's nonlinear behavior is described with a bilinear subspace predictor structure in an MPC framework. Thus, the MPC formulation results in a fixed structure objective function with constraints regardless of the underlying nonlinearity. For unconstrained systems, the identified subspace predictor matrices can be directly used as controller parameters. Therefore, we design optimization algorithms that exploit this feature. The open-loop optimization problem of MPC that is nonlinear in nature is solved with series quadratic programming (SQP) without any approximations. The computational efficiency already demonstrated with the current formulation presents further opportunities to enable online control of nonlinear systems. These improvements and close integration of modeling and control also eliminate the intermediate design step, which provides a means for data-driven controller design in generalized predictive controller (GPC) framework. Finally, the proposed control approach is illustrated with a verification study of a nonlinear continuously stirred tank reactor (CSTR) system. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society