 Open Access
 Total Downloads : 430
 Authors : Abhishek J Bedekar, Santosh Shinde
 Paper ID : IJERTV4IS050669
 Volume & Issue : Volume 04, Issue 05 (May 2015)
 DOI : http://dx.doi.org/10.17577/IJERTV4IS050669
 Published (First Online): 22052015
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Robust Deadbeat Control of Twin Rotor Multi Input Multi Output System
Abhishek J. Bedekar Department of Electrical Engg. Walchand College of Engineering, Sangli (Maharashtra), India.
Santosh Shinde
Department of Electrical Engg. Walchand College of Engineering, Sangli (Maharashtra), India.
AbstractThis paper deals with a deadbeat PID control of Nonlinear higher order system. The method used in this paper uses feedback arrangement which helps to improve system response. TheDeadbeat control method is applied to Nonlinear model of Twin Rotor MIMO Laboratory setup (Helicopter model).This helicopter model is first simulated in matlab with simple PID controller and then with deadbeat controller. Comparative study shows that Deadbeat PID controller is capable of providing robust performance.
Keywords MIMOsystem, TRMS, PID, Deadbeat control.

INTRODUCTION
The TRMS system is nonlinear system similar to helicopter as shown in Fig. 1.The conventional controller like PID is used to control such nonlinear system[14], as it has simple structure and easy to use. In recent years new methods like feedback linearization [5] and gain scheduling [6] have been applied with good outcomes. Intelligent control theories like Fuzzy control , Neural network and GA applied, but designing logic for such intelligent controller is not easy[7,8,9].
Many methods are tested in order to get an acceptable performance of the controller. This includes minimum settling time, rise time, zero steady state error, less oscillation, robustness against disturbances. TRMS system is very complex and it includes uncertainties thus finding gains of PID become difficult task. Also modeling of TRMs system is difficult [10, 11, and 12]. Even if we get system model, for entire input range it will not represent system exactly. In order to control TRMS system here, we use the method proposed in [13, 14] which include PID and Deadbeat controller. In [13] writer claims that response will remain unchanged when all parameters change by as much as 50%.
The main problem with TRMS is that of coupling effect between two rotors, to encounter this problem we are going to decouple [15] into two SISO system and effect is considered as disturbances to each of the SISO system. Then the Deadbeat control scheme is applied to the SISO system.
This paper is organized as follows. Section 1 introduction, Section 2 system model and its mathematical representation, section 3 Deadbeat control method and controller design, section 4 then system is simulated in MATLAB. Finally, comparative analysis between PID and Deadbeat PID controller and this study is summarized in conclusion.
Fig.1 Schematic diagram of TRMS control system

TWIN ROTOR SYSTEM
The TRMs is a laboratory platform designed for control experiment by Feedback Instruments Ltd [16]. It consists of a beam pivoted on its base in such way that it can rotate in both vertical and horizontal planes. Two DC motors are used for two rotors (main and tail rotor), at each end of the beam. In actual Helicopter, aerodynamic force is controlled by changing the angle of attack of the blades but TRMS model designed such that force is controlled by controlling speed of motors. The main rotor produces force, which allows the beam to raise vertically making rotation along pitch axis. While tail rotor produces horizontal force to make the beam turn left or right around the yaw axis.
Usually, phenomenological models tending to be nonlinear, this means that at least one of the states is an argument of a nonlinear function. So as to present such a model as a transfer function (a form of linear plant dynamics representing a control system), it has to be linearized. The following non linear model equations can be derived.
Mathematical equation in vertical plane is given as
1. = 1 (1) Where
1
1 = 1. 2 + 1. 1Nonlinear static characteristic(2)
= sin Gravity momentum (3) Friction forces momentum
= 1 . + 2 . sin( ) (4)
= . 1. . cos Gyroscopic momentum (5)
The motor and the electrical control circuit is approximated as a first order transfer function, thus the rotor momentum in Laplace domain is described as
1 1
= 1 (6)
11 +10
Mathematical equation in horizontal plane is given as
2. = 2 (7) Where
2
2 = 2. 2 + . 2 Nonlinear static characteristic (8)
Friction forces momentum
= 1 . + 2 sin (9)
Table 1 gives approximated values of parameters.
= 0+1
Cross reaction momentum (10)
Parameters
Value
1 moment of inertia of vertical rotor
6.8 102 2
2 moment of inertia of horizontal rotor
2 102 2
1static characteristic parameter
0.0135
1static characteristic parameter
0.0924
2static characteristic parameter
0.02
2static characteristic parameter
0.09
gravity momentum
0.32
1 friction momentum function
parameter
6 103 /
2 – friction momentum function
parameter
1 103 2 /
1 friction momentum function
parameter
1 101 /
2 – friction momentum function
parameter
1 102 2 /
– gyroscopic momentum
parameter
0.05 /
1motor 1 gain
1.1
2motor 2 gain
0.8
11motor 1 denominator parameter
1.1
10 motor 1 denominator parameter
1
21 motor 2 denominator parameter
1
20 motor 2 denominator parameter
1
11 cross reaction momentum parameter
2
11 cross reaction momentum parameter
3.5
1cross reaction momentum gain
0.2
+1 1
Rotor momentum in Laplace domain is given as
= (11)
+
The model parameters used in above (1)(11) equation are chosen experimentally, which makes the TRMS nonlinear model a semiphenomenological model.
The boundary for the control signal is set to [2.5 to +2.5].
Fig.2
Table 1
As we know there is cross coupling between main and tail rotor. With the help of model equation nonlinear Simulink model of TRMS is obtained as shown in Fig.3
Fig. 3 Nonlinear simulink model of TRMS

DEADBEAT CONTROLLER DESIGN METHODOLOGY
H1(s) =1 for = 2
H1(s) =1+ for = 3 4
H1(s) = 1 + + 2 for = 5
The main goal of control system is to reach the desired value6. select gain, using the coefficient from table 2 to achieve
with zero steady state error within specified settling time. A deadbeat response should have zero steady state error, minimum rise time, controllable settling time, % overshoot from 0 to 2%, % undershoot < 2% . Also have robustness against external disturbance and parameter uncertainty.Rfer following fig.4 for the basic structure of the controlled system design.
response with the following requirement: (a)set k=1
(b)set =
80%
(c)set C.E. of closed loop equal to:
+ 1 + 2 2+. . . +

The roots of H(s) must be real & negative

Smallest root of H(s) will set the desired

Fig.4 Basic structure

Use PID controller as ().
4
80%

Add cascade gain K before the PID controller.

Add state variable feedback gain Ka. This will make the system over specified by at least one variable

Determine for (), where equals the no of poles in ().

Add the feedback

Increase K until the response becomes deadbeat and the settling time is approximately equal to the desired value.
Order
2nd
1.82
–
–
–
–
4.82
3rd
1.90
2.20
–
–
–
4.04
4th
2.20
3.50
2.80
–
–
4.81
5th
2.70
4.90
5.40
3.40
–
5.43
6th
3.15
6.50
8.70
7.55
4.05
6.04
Table 2 Deadbeat coefficients and response time

CONTROLLER DESIGN
First using the decouple techniques we separate the system into two SISO ones as shown below
Vertical part (Tail Rotor)
This TF will be utilized throughout this work.

Tail rotor controller design
Fig.7 Tail rotor control
The close loop transfer function
() = 1 ()2 ()
()
1+2 2 +1 ()2 ()1 () (14)
Where 1 = and 2 =
Equals the no of poles in () = 4 Thus
1 = 1 + And2 =
Finally
Fig.5
()
15.02[3(2 + + )]
Horizontal part (Main Rotor)
() = 4 + 3.458 + 15.02 3 3 + 2.225 + 15.023 + 15.02 3 2 +
{15.02 + 15.023 + 15.02 3} + {15.023}
(15)
Then CE of above transfer function compared with Standard CE
4 + 3 + 2 2 + 3 + 4 (16)
From design procedure we get coefficient values from Table 2, also we get value of
Fig.6
=
=
80%
4.81
1.6
= 3.00625
TF of theTRMS in vertical and horizontal movement are given as
=
15.02 . Tail rotor (12)
3 +3.4582 +2.225
=
1.519 . Mainrotor (13)
3 +0.7482 +1.533+1.046
Therefore CE of deadbeat TF is:
4 + 6.6133 + 31.63142 + 76.07355 + 81.6771 (17)
Comparing characteristic equation (16) and (17) we have
3.485 + 15.02 3 = 6.6138
2.225 + 15.023 + 15.02 3 = 31.6314
15.02 + 15.023 + 15.02 3 = 76.0735
15.023 = 81.6771
Then cascade gain K is set equal to 1. After some trial and error we get values for 3 = 17
= 0.243 = 45.848
= 14.21 = 38.65
Select k until deadbeat response not reached.

Main rotor control
Similarly,
() = 1()2()
() 1 + 2 2 + 1()2()1()


SIMULATION AND RESULTS

For Step input
Fig. 8 PID response to main rotor(pitch)
Where 1 = and 2 =
Equals the no of poles in () = 4 Thus
1 = 1 + And2 =
()
[3(2 + + )]() = 4 + 0.748 + 1.519 3 3 + 1.533 + 0.15493 2 +
{1.046 + 1.519 + 0.1549 3} + {1.5193}
Then CE of above transfer function compared with Standard CE
4 + 3 + 2 2 + 3 + 4 (18)
Fig. 9 Deadbeat PID response to main rotor(pitch)
From design procedure we get coefficient values from Table 2, also we get value of
=
=
80%
4.81
1.6
= 3.00625
Therefore CE of deadbeat TF is:
4 + 6.6133 + 31.63142 + 76.07355 + 81.6771(19)
Comparing characteristic equation (18) and (19) we have
0.748 + 1.519 3 = 6.6138
1.533 + 0.15493 = 31.6314
1.046 + 1.519 + 0.1549 3 = 76.0735
1.5193 = 81.6771
Then cascade gain K is set equal to 1. After some trial and error we get values for 3 = 7.723
= 0.5 = 2.5453
= 3.131 = 6.963
Fig. 10 PID response to tail rotor
Fig.11 Deadbeat PID response to tail rotor

For sin wave input
Fig. 12 PID response to tail rotor (yaw)
Fig.13 Deadbeat PID response to tail rotor (yaw)

For square input
Fig. 14 PID response to main rotor(pitch)
Fig. 15 Deadbeat PID response to main rotor(pitch)
Above Figures shows the controller effect for different type of inputs. From results it is clear that traditional PID controller responses have overshoots and its settling time is more than designed Deadbeat controller. Here with Deadbeat control approach result shows remarkable improvement in system behavior.


CONCLUSION
In this study, we have successfully modeled TRMS system and successfully applied robust Deadbeat controller scheme. In system performance, the settling time has been reduced also overshoot has been decreased.Implemented scheme does not deal with much harder mathematics. it is easily understood method .
But as this method is model based, we require accurate system transfer function.
Fig. 16 simulation diagram of PID controller scheme
Fig. 17 simulation diagram of deadbeat controller scheme

REFERENCES


K. Turkoglu, U. Ozdemir, M. NIkbay, E. Jafarov, PID parameter otimization of UAV longitudinal Flight control system, World Academy of Science, Engineering and Technology 45, 2008.

S. Yang, K. Li and J. Shi, Design and Simulation of the Longitudnal Autopilot of UAV Based on SelfAdaptive Fuzzy PID Control, International Conference on Computational Intelligence and Security, 2009.

H. Takaaki, Y. Kou, A. Yoshinori, M. Wanori, A. Santoshi and M. Shun, A Design Method for Modified PID Control System for Multiple Input Multiple Output Plants to Attenuate Unknown Disturbances, World Automation Congress 2010 TSI Press.

F, Sajjad, G. Dawei, K. Naeem and P. Ian, Fault Detection, Isolation and Accommodation in a UAV Longitudinal Control System, Conference on Control and Fault Tolerent System, Nice, France, October 2010.

T. J. Koo, S. Sastry, Output Tracking Control Design of a Helicopter Model Based on Approximate Linearization, Decision and Control, 1998. Proceedings of the 37th IEEE

N. Wada, M. Minami, Y. Matsuo, M. Saeki, Tracking Control of a Twin Rotor Helicopter Model Under Thrust Constrains Using State Dependent Gain Schedulling and Reference Management , Mechatronics and Automation, 2008. ICMA 2008.

B. U. Islam, N. Ahmed, D. L. Bhatti and S. Khan, Controller Design Using Fuzzy Logic for a Twin Rotor MIMO System, pp.264268, 2003.

F. M. Aldebrez, M. S. Alam and M. O. TOkhi, Inputshaping with GA tuned PID for target tracking and vibration reduction, Limassol, Cyprus, pp.485490,2005.

Juang, J. G., Liu, T. K. Real Time Neural Network Control of Twin Rotor System,Adv. Mater. Res., 2011, 271273, pp. 616621

I. Z. Mat Darus, F. M. Aldebrez and M. O. Tokhi, Parametric modelling of a twin rotor system using genetic algorithms, Hammamet, Tunisia, pp.115118, 2004.

S. M. Ahmad, M. H. Shaheed, A. J. Chipperfield and M. O. Tokhi, Nonlinear modelling of a twin rotor MIMO system using radial basis function networks, pp.313320, 2000.

F. M. Aldebrez, I. Z. M. Darus and M. O. Tokhi, Dynamic modelling of a twin rotor system in hovering position, pp. 823826, 2004.

J Dawes, L. Ng, R. Dorf and C. Tam, Design of Deadbeat Robust System, Glasgow, UK, pp15971598, 1994

L. Chien, IMCPID Controller DesignAn Extension, IFAC Proceeding Series,6, pp.147152, 1988.

Stephanopoulos, Chemical Process Control.

Twin Rotor MIMO System Control Experiment 33949S User Manual, Feedback Instrument Ltd, UK
Abhishek Jayant Bedekar has obtained
B.E. in Electrical Engineering from Rajarambapu Institute of Tech. sakharale
, Islampur, Maharashtra, India in 2012. He is currently pursuing his M.Tech in Electrical Control System from Walchad College of Engg. Sangli under the guidence of Prof. Mr. N. V. Patel. His areas of interests are Controller Design, Control Systems.
Santosh Shinde has obtained B.E. in Electrical Engineering from Rajaram shinde college of engineering pedhambe chiplun Maharashtra, India in 2012. He is currently pursuing his M.Tech in Electrical Control System from Walchad College of Engg. Sangli under the guidence of Prof. Mr. N. V. Patel. His areas of interests are Controller Design, Control Systems.