Pid Control for Ambulatory Gait Orthosis: Application of Different Tuning Methods

www.seipub.org/aber Advances in Biomedical Engineering Research (ABER) Volume 2, 2014

Pid Control for Ambulatory Gait Orthosis: Application of Different Tuning Methods Ritushree Dutta, Neelesh Kumar and Dinesh Pankaj Biomedical Instrumentation Division, CSIR‐Central Scientific Instrumentation Organization, Chandigarh‐160030, India ritushreegimt@gmail.com; neel5278@gmail.com; dineshpankaj@yahoo.co.in

Abstract Actuating mechanisms of orthotic devices are important aspects of today’s robotic field. Controlling a linear actuator attached in an orthotic limb using PID controller with a suitable tuning method is the main discussion of this paper.

Tuning methods like, Internal Model Control (IMC), Zeigler‐ Nichols and Tyreus‐Lyben are applied in this work and analyzed the response in time domain specification, by considering the aspects of orthotic devices. Since simulation is the best way to testing a design, here we use control and simulation module of LabVIEW to simulate our process.

Simulation results have shown us the improvement of the system performance by the application of different tuning methods and we have found that IMC method is the best for PID controller to control the DC drive in case of an ambulatory gait orthotic.

Key words Orthotic Device; PID; Tuning Method; IMC; Control and Simulation; LabVIEW

Introduction In recent days, the popularity of robotic orthotic devices increases day by day as these are considered as prime devices for gait rehabilitation of stroke or Spinal cord injury patients and assistance of disabled or elderly people by means of upper or lower limb Orthosis (Ruiz, Forner‐Cordero et al. 2006).Orthotic devices are the combination of robotic and mechatronic technologies (Weinberg, Nikitczuk et al.

2007)where a mechanical movement is achieved by means of electrical drives. There are varieties of actuating mechanism of joints on orthotic devices like powered joint mechanism having actuator encompass with motor and shaft to move the joint (Gilbert and Landry 2013).Electric linear actuators are the most demanding solution when system leads to simple, safe and clean movement with accurate and smooth motion control. These are also more cost‐effective and more energy‐efficient power transmission than their hydraulic and pneumatic counterparts. The

44

proportional, integral and derivative mode of controllers are the most commercially used controller in process industries(Shahrokhi and Zomorrodi 2013) [13] for its good performance and easy to obtain good settings (Jeng, Tseng et al. 2013)[14]. Tuning of a controller is done for optimization of the process and minimizes the error between the process variable and its set point. There are many methods are available for tuning of PID controllers such as Close loop Ziegler‐ Nichols method, Open loop Ziegler‐Nichols method, IMC method, C‐H‐R method etc. This paper work represents the analysis of different tuning methods of a PID controller to obtain a good response for a DC motor in case of an orthotic device.

Methods and Material A prototype of orthotic devices is available for our lab work which includes six electrical linear actuators and twelve sensors. The actuators are attached in each limb of prototype to create activity and motion of the device.

The actuator comprises of DC motor and it is analyzed through PID controller.

Mathematical Model of DC Motor The DC motor used in this work is MAXON RE40,which is a 12V permanent magnet DC motor with Gear ratio 81:1,terminal resistant 0.117Ω,terminal inductance‐0.02mH, rotor inertia‐135gcm2, torque constant 16.4mNm/A, motor constant 581 rpm/V and time constant 6ms.

The transfer function of a Permanent Magnet DC motor is shown in equation (1), .

Where KT=Torque constant L=Terminal Inductance J=Effective moment of inertia R=Terminal resistant

(1)

Advances in Biomedical Engineering Research (ABER) Volume 2, 2014 www.seipub.org/aber

The proportional gain (KP) changes the input directly proportional to the control error(Huidang, Yubo et al.

2010)[5].Increased in proportional gain will increase the speed of the control system, but with a very large value of KP ,the process variable will begin to oscillate and controller may not give steady state error performance needed in a system. The integral gain (Ti) changes the input proportional to the integral value of the error and eliminate offset(Huidang, Yubo et al.

2010) [6].The increased in integral response can drive the steady state error to zero. The derivative gain (Td) changes the input proportional to the derivative of the controlled variable and stabilize the system(Huidang, Yubo et al. 2010) [6].The derivative gain leads the system to give faster response.

KE=Motor proportionality constant Considering the feature of Maxon motor, the transfer function of the motor is shown in equation (2), .

. .

.

.

(2)

Controller and System Design Proportional‐Integral‐Derivative (PID) control algorithm is the most commonly used algorithm in the variety of control application for their functional simplicity and robust performance. Proportional, Derivative and Integral are the basic parameters of the PID algorithm which are varied to get optimal response.PID controller is the controller that computes desired actuator output after reading the sensor output by calculating proportional, integral and derivative parameter and the output result is the summing of those three parameters (Ang, Chong et al. 2005).Thus equation of control signal of a PID controller is

Our system consists of three separate DC motor driven linear actuators in each lower limb of the exoskeleton.

The actuators are moved according to the control algorithm and drives are controlled by the PID controller.

(3)

As we shown in the fig1, we have used a real time controller (RTC) with a reconfigurable FPGA (Field Programmable Gate Array) chassis and a PID controller. Controller feed a signal to the actuator and the sensor will send an error signal to the PID controller through FPGA.

The transfer function is expressed as, (4) Or 1

(5)

FEEDBACK SIGNAL

FPGA

RTC

LINEAR PID BLOCK

+

ACTUAT OR

SENS OR

CONTRROLLER FIG 1: BLOCK DIAGRAM OF THE SYSTEM

45

www.seipub.org/aber Advances in Biomedical Engineering Research (ABER) Volume 2, 2014

Tuning of PID Controller

2) Close‐loop Ziegler‐Nichols

Tuning is desirable for the controller to get optimized output by setting the controller parameters. The tuning methods of PID controller are categorized in open loop method and close loop method. In this paper work the following methods are used:

Zeigler‐Nichols method is the simplest and mostly used PID tuning method. It is the oldest close loop tuning method and it gives a rough estimation about the basic parameters of the plant (Drljevic, Perunicic et al. 2007)[10]. The disadvantages of this method are (Shahrokhi and Zomorrodi 2013)[13]:

1. Internal Model Control (IMC) 2. Close Loop Zeigler‐Nichols(CLZN)   

Fast performance(FP) Normal performance(NP) Slow performance(SP)

3. Open Loop Zeigler‐Nichols(OLZN)   

4. Tyreus‐Luyben (T‐L) 1) Internal Model Control (IMC) IMC method, that developed by Morari and his coworkers (Morari 1989)[9] is considered as an adaptive robust controller. The popularity of this method is due to its favorable framework for determining the PID parameter (Rivera, Morari et al. 1986)[7].This control strategy based on the mathematic model of the process to design the controller(Fu, Shi et al. 2009)[8].Two important advantages of IMC method are that it consider the system uncertainty and provide analytical method to the designer to analyze the system robustness ,process changes and modeling error(Shahrokhi and Zomorrodi 2013)[13]. IMC controller is usually designed as the inverse process model in series with a low‐pass filter (Morari 1989)[9] as shown in equation (6), (6) Where n is the order of the filter.

Therefore, GIMc =Gm‐1(s)Gf(s) (7) where Gm is the plant transfer function.

The transfer function of the overall controller is thus, (8)

By solving the above equations we can find the value of PID parameter.

46

2. It may lead the process into a marginally stable condition which is the cause of system instability.

3) Open Loop Zeigler‐Nichols

Fast performance (FP) Normal performance (NP) Slow performance (SP)

1

1. A trial and error method must be performed to determine ultimate gain(Ku) and ultimate period(Pu), therefore close loop Zeigler‐Nichols is considered as a time consuming method.

The open‐loop Ziegler‐Nichols tuning method is a good tuning method for a system with time‐delay (d) and first‐order characteristics (i.e time constant ( )). It is also simple enough and an appropriate starting to get a process under control(Dreinhoefer 1988) [11].The two limitations of the Ziegler‐ Nichols tuning method are First, the control is manual and second, the process must have first order characteristic and time delay (Dreinhoefer 1988)[11].

4) Tyreus‐Luyben Like close loop Zeigler‐Nichols method, Tyreus‐ Luyben method is also dependent on ultimate gain(Ku) and oscillation period(Pu) to compute the PID gains(Kalaiselvan and Tagore 2013)[12].It is the modified form of Z‐N method. But the final controller settings are different.

The summery of different tuning rules proposed for PID controller shown in table1.

TABLE 1: TUNING RULES OF DIFFERENT TUNING METHOD

Method

Kp

Ti

Td

C LZN(NP)

0.25 Ku

0.5Pu

0.12Pu

OLZN(NP)

0.53 /d

4d

0.8d

T‐L

Ku/3.2

2.2Pu

Pu/6.3

Experimental Results The algorithm for control is developed in the LabVIEW using control and simulation module. The benefit of simulation is that we can modify the system parameters to check how the performance of a system changes even when the simulation is running. There is also a simulation time parameter which is used to specify the time interval over which the ordinary

Advances in Biomedical Engineering Research (ABER) Volume 2, 2014 www.seipub.org/aber

Transfer function equation block: It represents the transfer function equation of the model.

differential equation (ODE) solver evaluates the model.

Another benefit of the control and simulation module is that there is a solver method parameter from which we can chose the suitable ODE solver to use to evaluate the model. In our simulation, we have chosen Runga‐Kutta4 method as ODE solver. From PID and Fuzzy logic tool kit of LabVIEW we have a PID palette for PID application, transfer function model block and transfer function equation block.

Simulation Response By setting the value of PID parameters for DC motor using IMC method we get a good response which is shown in fig.2.The output characteristic(OC) has less overshoot with minimum settling time 1.1millisecond(ms).

Less overshoot is desirable in case of orthotic devices where actuators are attached in the joints. Fig.3 shows the response of OLZN for fast, normal and slow performance with =6ms and d=0.7ms. The overshoot is more in case of fast performance than normal and slow performance and settling point is also less in fast performance. But overall response of OLZN has more overshoot than the IMC method. The response of CLZN for fast, normal and slow performance is shown in fig.4.In our experiment Ku=2.5 and Pu=1.5ms. From the output characteristic (OC), slow Performance has lesser overshoot than the normal and fast response, but fast performance has less settling time. The overall performance of CLZN is better than OLZN in our system. The simulation response of T‐L method is almost similar to that of CLZN slow performance which shown in fig.5.

PID block: It consists of several inputs like set point that specifies the desired value of the Process variable that we are controlling. The process variable specifies the current value of the variable. Another input Pid gain consist of proportional gain(Kc),the integral time(Ti)that adjust the effect of the error integral term on the output and the derivative term(Td)that adjust the effect of the error derivative term on the output. It has also an input function of set point range that specifies maximum and minimum value of the set point.

Transfer function model: This block creates a transfer function representation of a system using sampling time, numerator, denominator and delay and specify data in numeric form.

20 15 OC

10

r_IMC

5

r_D

0 ‐5 0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

TIME(ms)

FIG 2: SIMULATION RESPONSE OF PID USING IMC METHOD

30

OC

20

r_S

10

r_N r_F

0 ‐5

‐10

0

5

10

15

20

25

30

35

r_D

TIME(ms)

FIG 3: SIMULATION RESPONSE OF PID USING OLZN FOR FAST, NORMAL AND SLOW PERFORMANCE

47

www.seipub.org/aber Advances in Biomedical Engineering Research (ABER) Volume 2, 2014

30

OC

20

r_F

10

r_N r_S

0 ‐5

‐10

0

5

10

15

20

25

30

35

r_D

TIME(ms)

FIG 4: SIMULATION RESPONSE OF PID USING CLZN FOR FAST, NORMAL AND SLOW PERFORMANCE

30 20 OC

r_T‐L

10

r_D

0 ‐5

‐10 0

5

10

15

20

25

30

35

TIME(ms)

FIG 5: SIMULATION RESPONSE OF PID USING T‐L METHOD

The Time domain specifications of responses with various tuning methods and the value of PID gains are shown in Table.2 TABLE 2: TIME DOMAIN SPECIFICATIONS OF DIFFERENT PID TUNING

Max Delay Rise Peak Settling Ti T d Overs Kp time time time time (min) (min) hoot (ms) (ms) (ms) (ms) (%) IMC 0.0320 0.0155 2.8E‐6 0.1 0.7 0.96 25 1.1 OL Z‐N 9.42 2.3E‐5 5.8E‐6 0.1 0.25 0.5 95.8 45.5 ‐FR OLZ‐N‐ 4.54 4.6E‐5 5.6E‐7 0.2 0.25 0.6 93.3 46 NR OLZ‐N‐ 2.74 4.6E‐5 5.6E‐7 0.25 0.3 0.8 93.3 47.5 SR CLZ‐N‐ 1.25E‐ 1.5 3E‐6 0.25 0.5 0.75 91.6 40 FR 5 CLZ‐N‐ 1.25E‐ 0.625 3E‐6 0.5 0.6 1.5 89.5 43 NR 5 CLZ‐N‐ 1.25E‐ 3E‐6 0.5 0.75 1.75 87.5 43 0.375 SR 5 T‐L 0.781 5.5e‐5 3.9E‐6 0.5 0.7 1.2 88.3 43 Tuning of method

From the above table it is cleared that IMC PID tuning has a very good response with less overshoot and very less settling time compared to other method which is desirable for the controlling of orthotic devices. After IMC, we can place Tyreus‐Luyben method for tuning.

But like Ziegler‐Nichols method, Tyreus‐Luyben method is also time consuming as trial and error method must be performed.

After analyzing above tuning methods, it is observed

48

that improvement of IMC method from the other methods is 42.18% in terms of settling time and 28.32% in terms of overshoot. Hence IMC tuning method is considered to be much more preferable in the case of ambulatory gait orthotic.

Discussion and Conclusion An orthotic device is a wearable device used by the user about their joints(McBean and Narendran 2008) [15].Hence it is recommended to have less overshoot in the response of actuation mechanism. Also to achieve a complete gait cycle in a prescribe time; settling time of the driver of the actuator should be less.

In this paper, we control the linear actuator of the ambulatory gait orthotic using PID. We analyze the response of the control algorithm by the application of different tuning methods of PID. Control algorithm is developed in LabVIEW and simulates it using control and simulation module of the LabVIEW. LabVIEW is a platform for visual programming language. LabVIEW control and simulation module provides an easy way to develop a mathematical model that describes physical system and can analyze the behavior of the dynamic characteristics of the system.

By the application of different tuning methods to our system, we can conclude that using of PID controller in an orthotic device with IMC method is the best controlling approach to obtain a good response.

Advances in Biomedical Engineering Research (ABER) Volume 2, 2014 www.seipub.org/aber

REFERENCES

step response data. Proceedings of the 6th International

Ang, K. H., G. Chong, et al. (2005). ʺPID control system analysis, design, and technology.ʺ Control Systems Technology, IEEE Transactions on 13(4): 559‐576.

Conference on Process Systems Engineering (PSE ASIA).

Kalaiselvan, E. and J. D. Tagore (2013). ʺA Comparative Novel Method of Tuning of Controller for Temperature

Dreinhoefer, L. H. (1988). ʺController tuning for a slow

Process.ʺ International Journal of Advanced Research in

nonlinear process.ʺ Control Systems Magazine, IEEE 8(2):

Electrical, Electronics and Instrumentation Engineering

56‐60.

2(11).

Drljevic, E., B. Perunicic, et al. (2007). A new closed‐loop identification method of a Hammerstein‐type system

McBean, J. M. and K. N. Narendran (2008). Powered orthotic device, Google Patents.

with a pure time delay. Control & Automation, 2007.

Morari, M. (1989). Robust process control, Morari.

MEDʹ07. Mediterranean Conference on, IEEE.

Rivera, D. E., M. Morari, et al. (1986). ʺInternal model control:

Fu, G., D. Shi, et al. (2009). An IMC‐PID controller tuning

PID controller design.ʺ Industrial & engineering

strategy based on the DE and NLJ hybrid algorithm. 2009

chemistry process design and development 25(1): 252‐265.

ISECS

International

Colloquium

on

Computing,

Communication, Control, and Management.

Gilbert, B. and D. Landry (2013). Joint actuation mechanism for a prosthetic and/or orthotic device having a compliant transmission, Google Patents.

Huidang, Z., T. Yubo, et al. (2010). PID Parameters Tuning Method by Particle Swarm Optimization with Chaotic Disturbance. Multimedia and Information Technology (MMIT), 2010 Second International Conference on, IEEE. Jeng, J.‐C., W.‐L. Tseng, et al. (2013). A direct method for PID controller tuning with desired system robustness using

Ruiz, A., A. Forner‐Cordero, et al. (2006). Exoskeletons for rehabilitation and motor control. Biomedical Robotics and Biomechatronics, 2006. BioRob 2006. The First IEEE/RAS‐EMBS International Conference on, IEEE. Shahrokhi, M. and A. Zomorrodi (2013). ʺComparison of PID Controller Tuning Methods.ʺ Department of Chemical & Petroleum Engineering Sharif University of Technology.

Weinberg, B., J. Nikitczuk, et al. (2007). Design, control and human testing of an active knee rehabilitation orthotic device.

Robotics

and

Automation,

2007

IEEE

International Conference on, IEEE.

49