1 IJISET - International Journal of Innovative Science, Engineering & Technology, Vol. 1 Issue 9, November 2014. ISSN 2348 7968 A NEW intelligent , ROBUST AND SELF TUNED CONTROLLER DESIGN (II). Farhan A. Salem Mechatronics engineering program, Department of Mechanical Engineering, College of Engineering, Taif University, 888, Taif, Saudi Arabia. Alpha center for Engineering Studies and Technology Researches, Amman, Jordan. Email: Abstract This paper proposes a new, simple, intelligent , robust and self-tuned controller design approach for getting a process under control, while achieving an important design compromise; acceptable stability, and medium fastness of response.
2 The proposed approach is based on analyzing plants step response to calculate it's parameters and based on calculated parameters, calculate controller's parameters, feed it to controller, and repeat process until achieving an acceptable stability, and medium fastness of response. The proposed approach was test using MATLAB and Simulink model for different systems Keywords: Controller design, Modeling/Simulation. 1. Introduction The term control system design refers to the process of selecting feedback gains (poles and zeros) that meet design specifications in a closed-loop control system.
3 Most design methods are iterative, combining parameter selection with analysis, simulation, and insight into the dynamics of the plant (Katsuhiko Ogata,1997),(Ahmad A. Mahfouz, et al,2013), An important compromise for control system design is to result in acceptable stability, and medium fastness of response, one definition of acceptable stability is when the undershoot that follows the first overshoot of the response is small, or barely observable(Farhan A. Salem,2013), Beside world wide known and applied controllers design method including Ziegler and Nichols known as the process reaction curve method (J.)
4 G. Ziegler, et al, 1943). and that of Cohen and Coon (G. H. Cohen, 1953) Chiein-Hrones-Reswick (CHR), Wang Juang Chan, many controllers design methods have been proposed and can be found in different texts including (Astrom K,J ,et al,1994)(R. Matousek, 2012)(Susmita Das, et al, 2012)(Saeed Tavakoli, et al, 2003)(Astrom K,J, et al, 1994)(Norman S. Nise,2011)(Gene F. Franklin, et ak, 2002)(Dale E. Seborg, et al, 2004), each method has its advantages, and limitations. This paper extend previous work (Farhan A. Salem,2013)(Farhan A. Salem,2014*)(J. G. Ziegler ,et al,1943)( G. H.
5 Cohen, et al,1953)(Astrom K,J, et al,1994), and proposes a new simple and intelligent controller design approach, that is based on relating controller(s)' parameters and plant's parameters to result in meeting an important design compromise; acceptable stability, and medium fastness of response in terms of minimum PO%, 5T, TS, and ESS. 2. Proposed approach (Farhan A. Salem,2013)(Farhan A. Salem,2014*) proposed (P-, PI-, PD- and PID-) controllers design methods with corresponding expressions for calculating controller's parameters (KP, KI, and KD), a long with soft tuning parameters ( , and ).
6 The proposed methods are based on relating and calculating controller's parameters from plant's parameters ( , n, T), to result in overall response with acceptable stability, medium fastness of response and minimum overshoot. For PID controller design, the proposed expressions derived by (Farhan A. Salem,2013)(Farhan A. Salem,2014*) are given in Table 1, where : parameter is responsible for speeding up response, and reducing Error, meanwhile, is responsible for tuning overshoot, where increasing will increase overshoot, and vise versa, finally parameter is responsible for reducing both overshoot and error.
7 As shown on block diagram representation (Figure 1) ,the proposed method is accomplished as follows; first by subjecting the closed loop system with only proportional controller with gain set to KP=1, where KI and KD are set to zero , to step input of R(s)=A/s, then feeding resulted step response to module with program, that will analyze response curve to calculate plant's parameters ( n,T), then use these parameters to assign values to controller s tuning parameters ( , and ) and calculate corresponding controller gains (KP, KI and KD) according to Table 1, and then feed calculated controller parameters to controller, to refine the resulted response, the program will subject the overall closed loop system with calculated gains, to the same step input, and feed resulted response to module with program and find corresponding closed loop system parameters and controller's gains, repeating this process to finally calculate controller's parameters, that will result in acceptable stability, medium fastness of response with minimum overshoot.
8 And maintain this response by continuously analyzing resulted response and maintaining it. In case of disturbance input, the proposed method will repeat the mention process, to return the closed loop response to previous state. For example for second order systems, the program will use system s step response to calculate system s damping ratio , undamped natural frequency n, and time constant T. for higher order systems, the program to use system s step response to analyze response and apply dominant poles approximation, and find corresponding plants approximated parameters, and proceed as mentioned.
9 30 IJISET - International Journal of Innovative Science, Engineering & Technology, Vol. 1 Issue 9, November 2014. ISSN 2348 7968 Table 1: Proposed expressions for PID parameters calculation Plant PID parameters KP KI KD TD TI N n 2n 12n 12n 2 n 2 20 Tuning limits 0:inf , 102n = 1 , = 2n 2 n 2 20 +PlantH(s)R(s)C(s)P- TermI- TermD- TermAnalyzing For Plants parameters : n,T Calculating gains(KP, KI,KD)Feeding gains(KP, KI,KD)Module & ProgramOutputD(s) Figure 1 Block diagram representation of the proposed approach 2. Testing proposed approach To clarify the operation of the proposed method, MATLAB/Simulink will be used to simulate the proposed method, write program for response analysis, calculating plant's parameters, calculating controller parameters, feeding calculated gains to controller, subjecting overall closed loop system with calculated gains to step input, and repeating the process until reaching, acceptable stability, medium fastness of response and minimum overshoot.
10 To test the proposed approach, Simulink model shown in Figure 2 is developed , this model is with four plants of different orders, including PMDC motor system as prime mover to be used for both, mobile robot speed control, and robot arm position control. Testing for mobile robot linear speed control The DC motor open loop transfer function without load attached relating the input voltage, Vin(s), to the motor shaft output angular speed is given by Eq.(1). To model, Simulate and analyze the open loop plant system, the total equivalent inertia, Jequiv and total equivalent damping, bequiv at the armature of the motor are given by Eq.
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