Design of a Data-Driven Control System for a Hydraulic Excavator

PID control schemes have been widely used in most industrial systems. However, it is difficult to achieve the desired control performance for nonlinear systems such as hydraulic excavators by using fixed PID parameters. In order to overcome such a problem, data-driven PID control scheme based on database has been proposed. Moreover, data-driven scheme has a learning method in off-line by using closed-loop data. In this paper, data-driven control scheme is applied to a hydraulic excavator to get desired control performance


Introduction
In most industries, it is very important to get desired control performance by using some control schemes.PID control schemes 1,2 have been widely used because control parameters have a clear physical meaning and control structure is simple.However, it is very difficult to get desired control performance for nonlinear systems such as hydraulic excavators by using fixed PID parameters.In order to overcome such problem, data-driven PID control scheme 3 based on database has been proposed.It is a controller for nonlinear system and it has an off-line learning method by using closed-loop data.In this paper, data-driven control scheme is applied to a hydraulic excavator to improve control performance.The effectiveness of the proposed scheme is numerically verified by using a simulation example.

Schematic Figure of a Hydraulic System
Fig. 1 shows schematic of a hydraulic system 4 .As the system, the motion of system is swing operation.The input should be the direction of flow rate for a hydraulic pump, and the output should be this torque.In the system, the relief valve works in order to prevent increasing hydraulic pressure.Therefore, the hydraulic system is a kind of time-variant system include a derivative element after the relief valve work.That why, it is difficult to get desired control performance by using fixed controller.

Schematic of Data-Driven Control System
Schematic of data-driven control system is shown in fig. 2. The current information of controlled object is stored in a database and suitable control parameters are calculated by historical data in the database.Moreover, off-line learning method is utilized to avoid on-line learning time cost.The specific design procedure of data-driven scheme is described in section 7.

Control law
Hydraulic system in Fig. 1 has derivative element.Therefore, controller with double integral element is needed and PII 2 D controller is defined as follows: where () denotes control error, and   ,   ,   and   respectively are proportional gain, integral gain, derivative gain and double integral gain.Furthermore,  denotes a difference operator.
where  ̃() is reference model output and ( −1 ) is user-specified polynomial.In FRIT, Control parameters are calculated to minimize difference between  ̃() and ().
Here, ( −1 ) is designed based on the reference design as follows: where  is a parameter related to the rise-time and  is a parameter related to the damping oscillation.User set Fig. 1.Schematic of a hydraulic system.(13) ( = 1,2, , ⋯ , )  ̅  () denotes the th element of query  ̅ ().max ̅  () is a maximum th element in database.In contrast, min ̅  () is a minimum th element.In addition, the number of neighbors' data  are selected, which data are based on smallest distance .
[STEP 3] Calculate control parameters.Control parameters are calculated by using the following linearly weighted average (LWA): where   is the weight corresponding to the  th information vector  ̅ () in the selected neighbors.It is calculated by following equation: In order to calculate effective control parameters, a learning method is needed.Therefore, an off-line learning method is described in next section.

Off-line learning method in Data-Driven Control scheme by using FRIT
In this section, an off-line learning method is described by using FRIT.At first, the number of neighbors' data  is selected and   () is calculated by equation ( 14) using closed-loop data  0 () and  0 ().Next, the following steepest descent method is utilized to modify the control parameters: = [  ,   ,   ,   ], where  denotes the learning rate and ( + 1) is defined as following error criterion: () ≔  0 () −  ̃(), (18) The each partial differential of equation ( 16 Therefore, control parameters can be learned off-line by using closed-loop data in equation ( 16) and (19).

Numerical Example
In this section, the effectiveness of the proposed scheme is verified.Table 1 shows the user-specified parameters included in proposed scheme.it cannot be reached to reference signal because the system includes derivative element.In proposed scheme, control performance is better than above control result since control parameters are adjusted.Trajectories of control parameters are show in Fig. 4.   is adjusted largely after  = 4[s] because system has derivative elements.

Conclusion
This paper has proposed a data-driven control system for a hydraulic excavator.Control parameters should be adjusted because a hydraulic excavator is nonlinear system.In this paper, controller has been designed as PII 2 D controller for derivative system.The effectiveness of proposed scheme has been numerically verified by using simulation example.

Fig. 3 .
Fig. 3.Control results by fixed PII 2 D control and proposed scheme.

Table 1 .
User-specified parameters included in proposed scheme.