Compare VRFT with others methods

The problem of designing feedback controllers (usually industrial PID controllers) on the basis of a set of I/O measurements has attracted the attention of control engineers since the 1940s with the pioneering work by Ziegler and Nichols. After the original work by Ziegler and Nichols, many more techniques have been proposed, exploring different directions.

By comparing VRFT with the most commonly used tuning rules for PID controllers, some main differences are worth noticing:

• VRFT aims at finding a solution to a model-reference control problem, while other methods usually try to find a generically "well-working" solutions according to some criterion "built-in" in the method. While this introduces an extra difficulty for the designer (since he/she has to select a suitable reference models), it also adds an important degree of freedom in the definition of the control specifications. It should be noted that the model-reference could as well be chosen to be a very simple transfer function (of degree 1 or 2) in standard applications.

• VRFT is not restricted to PID controllers as it is applicable to any linear controller. Moreover, the idea underlying VRFT can be extended so as to cover non-linear controllers as well.

• The computational effort required in the implementation of VRFT is higher than for standard tuning rules. However, in view of the computational power of modern digital circuits and computers, this does not appear to be a limitation. The real bottleneck in the design of a data-based controller lies in the number of experiments to perform on the real plant, since these experiments are time consuming and often require to halt the normal operation of the system. In this respect, VRFT is comparable to standard tuning rules as it requires a single data set collected from one single experiment on the plant.

 

Compare VRFT with IFT

A design technique is called "direct" when the I/O data collected from the plant are used to directly tune the controller, without passing through a plant identification step. Direct techniques are conceptually more natural than indirect ones (where the controller is designed on the basis of an estimated model of the plant), since they are directly targeted to the final goal of tuning the controller parameters. However, despite the appeal of direct methods, very few genuine direct techniques have been proposed in the literature. In particular, the only genuine "direct" data-based technique which can be compared with VRFT is a method called Iterative Feedback Tuning (IFT), developed and proposed by Hjalmarsson and co-authors. Even if IFT and VRFT belong to the same class of design methods, their peculiar features are quite different:

• IFT: is based on a gradient descent approach and it is therefore an iterative technique. It typically converges to the local minimum closest to the initial condition (it is a "local" optimisation technique). However, it can be shown that, if the initialization is in the basin of attraction of the global minimum, IFT provides an unbiased estimate of the optimal parameter controller. IFT can possibly call for a large number of experiments and, in any case, it requires to perform experiments on the true plant with specific inputs.

• VRFT: is a "one shot" method which searches for the global minimum of the performance index, with no need for iterations nor an initialization. Moreover, it does not require the use of specific inputs. However, the VRFT technique is only near-optimal, in the sense that it provides a controller which is close, but not equal, to the one minimizing the model-reference criterion J.

As we can see, IFT and VRFT are in a sense complementary methods with their own area of applicability. In short, we could say that VRFT provides a good solution with little effort, while IFT points to the optimal solution, but is more demanding.

The main features of VRFT can be summarized as follows:

• requires just a single set of I/O data;
• does not require the identification of a mathematical model of the plant (i.e. it is a direct method);
• determines the controller parameters in one-shot, with no need for iterations;
• the controller complexity can be fixed in the beginning when the controller class is selected. So, no controller complexity reduction is required;
• the controller provided by VRFT is only approximately optimal.