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This paper presents model and controller design applications to pneumatic actuator embedded system. Two model strategies of position and force are proposed to realize compliance control for stiffness characteristic. Model of the pneumatic actuator system (transfer function) is obtained from system identification (SI) method. Next, combination of predictive functional control with observer (PFC-O) design is selected as a new control strategy for pneumatic system. Performance assessment of the controller is performed in MATLAB and validated through real-time experiments using national instrument (NI) devices and programmable system on chip (PSoC) microcontroller. Result shows that the new controller is adapted to the system and able to successfully control both simulation and real-time experiments.

Pneumatic control systems are widely explored in research and development (R&D) activities by researchers and industry as they offer advantages such as easy and simple maintenance, relatively low cost, self-cooling properties, good power density (power/dimension rate), fast acting with high accelerations, and installation flexibility [

Various researchers proposed modeling and controller design in pneumatic system including system identification model. System identification not only can model the plant but also can realize online identification and control of pneumatic actuator in a real-time environment [

Controller design for pneumatic system to control the position, force, compliance, viscosity, and so forth is a challenging issue for improving its tracking performance. Many controller designs were proposed to control pneumatic system such as proportional-integral-derivative (PID), artificial intelligence, and robust controller. Model predictive control (MPC) is one of the controllers that have been successfully used in both industry and academia for the control of large-scale installations, which are typically described by large-scale models with relatively slow dynamics. The key element in MPC is to repeatedly solve an optimization problem based on available measurements of the current state of the process. The advantages of MPC over classic PID control are its ability to steer the process in an optimal approach while taking proactively desired future behavior into account, to tackle multiple inputs and outputs simultaneously and to incorporate constraints. Among the most popular MPC algorithms are dynamic matrix control (DMC), model algorithm control (MAC), generalized predictive control (GPC), predictive functional control (PFC), and so forth [

In recent years, interest in exploiting several controller designs on embedded systems has grown. Examples of implementing the controller design for embedded system and their advantage were presented by [

The related development of the pneumatic system used in this research is presented in [

Pneumatic system and its parts.

The rest of this paper is organized as follows. In Section

System Identification (SI) technique is proposed to obtain real-time model of the pneumatic system. Two models are proposed, position model, and force model to realize the stiffness characteristic. The plant mathematical models are developed using MATLAB System Identification Toolbox from open-loop input-output experimental data. Through experimental setup, the hardware and Personal Computer (PC) communicate using Data Acquisition (DAQ) card over the MATLAB software. During experimental setup, data will be gathered and analyzed to support system identification model and to observe the system dynamic. The system identification model will go through model estimation, structure selection, and validation for three models. Good parameters identification requires the usage of input signals that are rich in frequencies. There are several methods of generating the signals such as Pseudo Random Binary Sequence (PRBS), sinusoidal, step multi-sine and so forth. For model estimation in position model, square wave input signal is used while pseudorandom binary sequence (PRBS) input signal is used in force models. In this research, a lower sampling time of

There are few structures of parametric model that can be used to represent certain system. An example are Auto-Regressive with Exogenous Input (ARX) model, Auto-Regressive Moving Average with Exogenous Input (ARMAX) model, Output-Error (OE) model, and Box-Jenkins (BJ) model [

All these processes are done through the System Identification Toolbox in MATLAB. The following discrete-time open-loop transfer functions for position model shown in (

Pole-zero plot for the models.

This research proposed the predictive functional control with observer (PFC-O) design for pneumatic system. The formulation of PFC can handle linear and nonlinear processes [

Many literature approaches of PFC and other MPC algorithms are designed based on the state-space (matrix) form of the plant. The state-space form is preferable for several reasons, easy generalization to multivariable systems and easy analysis of the closed-loop properties, and allows online computation [

It is clearly seen from (

As stated earlier, there is only one coincidence point. According to [

Choose the desired time constant,

Do a search for coincidence horizon,

Select the

Simulate the proposed law. Otherwise, reselect

Optimal parameter tuning is an optimization problem, which requires implementation of global optimization strategy such as particle swarm optimization (PSO).

The model states are not related to physical parameters. In such cases and for the real implementation of PFC, an observer must be designed as the state variable

Adding a sufficiently fast observer will not affect the performance of the PFC controller; (

Block diagram of PFC-O for plant model.

The stability test method for this research is done by testing the locations of the closed-loop poles. The stability performance of the closed-loop feedback system is determined primarily by the location of the poles (eigenvalues) of the matrix

The relationship between deflection and force is known as the stiffness or can be assumed as a spring rate. The greater the stiffness, the less the deflection for a given force,

Within its elastic (flexibility) limit, the deflection, ^{2}.

Coil spring illustration.

Before applying to embed algorithm in PSoC programming, all equations need specific data, a simple equation, and rewriting for easier coding. Consider a PFC controller with the following fundamental matrices:

Figure

PFC controller stage.

Figure

Observer stage.

To rewrite the equations for easier coding, the equation for PFC controller and observer stage is now reduced to (

In this research, the control methodology contains force inner loop and position outer loop to obtain the stiffness characteristic objective. By controlling the difference of both sides of the pneumatic actuator, the inner loop enforces the natural stiffness characteristic of the pneumatic actuator. The working function of stiffness characteristic is shown in Figure

Block diagram for control system with stiffness characteristic.

The feedback of output force (signal inner loop) to observer is

The experimental setup for these researches consists of simulation and real-time analysis. The simulation data is acquired using MATLAB Simulink, where (

National instrument (NI) devices connection.

Real experiment setup using NI devices.

Position control or compliance control

Force control

Next, experimental setup to implement the real-time environment using embedded system is a continuation of previous work using the PSoC control board [^{
2}

By applying this methodology, the overall system will be enhanced with the new controller coding such as PFC-O algorithm, simpler connections, and reduced numbers of wires between PC and the actuator. Furthermore, the communication protocol between PC and^{
2}

Embedded system connection.

Pneumatic actuator with mass.

In this research, a new model and a novel embedded process control strategy to design the controller for real-time pneumatic system have been proposed. This section shows the results of model validation and application to embedded system are analyzed and discussed to further evaluate the controller.

Simulation and real-time experiment using national instrument (NI) device analysis were carried out to validate the controller performance. This analysis of the actual situation pneumatic actuator where force maximum and without stiffness characteristics. The results of position control and force control are analyzed before applying the PFC-O controller algorithm to embedded system.

Comparison between the simulation and the experiment result for position step and multistep responses including control signals within 18 s is shown in Figures

Comparison of simulated and experimental performance for position control.

Specifications | Simulation | Experiment |
---|---|---|

Settling time ( |
0.79 s | 1.12 s |

Rise time ( |
0.57 s | 0.80 s |

Percent steady state error (% |
0.01% | 0.03% |

%: percent, s: second.

Position step responses.

Position multistep responses.

Figures

Comparison of simulated and experimental performance for force control.

Specifications | Simulation | Experiment |
---|---|---|

Settling time ( |
0.2788 s | 0.935 s |

Rise time ( |
0.1601 s | 0.3616 s |

Percent steady state error (% |
0.01% | 0.08% |

%: percent, s: second.

Force step responses.

Force multistep responses.

The results for model validation analysis and the position control and force control analysis provide good performance in terms of no overshoot, faster settling time

The control analysis will be done in the simulation and real-time experiment using National Instrument (NI) device environment. Next, all coding in Section

The basic compliance control is presented in (

Stiffness characteristic responses.

Position step responses for difference stiffness.

The second method for compliance control was referred to in (

Comparison of deflection results.

Stiffness parameters, |
Theory | Real-time: NI devices | Real-time: embedded system |
---|---|---|---|

0.5 N/mm | 58.86 mm | 58.23 mm | 57.50 mm |

1 N/mm | 29.43 mm | 29.01 mm | 28.17 mm |

2 N/mm | 14.72 mm | 16.80 mm | 15.94 mm |

N: newton, mm: millimeter.

Deflection analysis responses.

In the analysis of compliance control for an embedded system, stiffness characteristics were successfully applied to give the spring effect. The experimental

Considering the nonlinear characteristics of the pneumatic system for this research scope, the results from the simulation and the both real-time experiments matched closely, and this is considered as a validation of the obtained mathematical model. Controller design for pneumatic actuator is done using PFC-O. Stiffness characteristic is realized using the compliance control. To compare the performance of the PFC-O analysis, several parameters have been identified. The results obtained from the simulation and experiment show that the developed real-time model could be used for various research bases, such as improvement of the controller performance and implementation on embedded systems. Furthermore, this pneumatic system can work well as a robust system and that makes it a suitable controller with good control performance. This research will provide greater opportunities for future work such as development of graphic user interface (GUI) to enhance online communication with more than one actuator and to apply the pneumatic actuator to related applications such as rehabilitation device.

The authors declare that there is no conflict of interests regarding the publication of this paper.

The authors would like to thank the Universiti Teknologi Malaysia (UTM), Ministry of Higher Education (MOHE), Malaysia, under Exploratory Research Grant Scheme (ERGS) no. R.J130000.7823.4L070, Universiti Teknikal Malaysia Melaka (UTeM), and the Okayama University for their support.