Parameter adjustment is usually applied for designing the proportional-integral-differential (PID) controllers. However, the ability to improve control performance by adjusting parameters is limited. Hence, with the goal to achieve ideal closed-loop response, this paper takes advantage of a structural optimization method for modifying the controller model. A symbolic adaptation algorithm for fractional order PID (FOPID) controller is employed to obtain precise nonlinear controller model. Firstly, a modeling comparison for nonlinear duffing system is carried out to highlight the efficiency of the symbolic adaptation algorithm. The case study indicates the proposed algorithm can establish compact dynamic models by amending the shortcomings of symbolic regression. Secondly, the proposed controller is restructured with the linear FOPID controller and its nonlinearity is increased by adjusting controllers’ components in symbolic form. The proposed controllers are simulated in an unstable second-order system, a time-delay system and a nonlinear VanderPol system. Compared with the IOPID and the FOPID controller, the symbolic adaptation algorithm improves the structural flexibility of these linear controllers. Meanwhile, the system response can better approximate the desired response and the structural integrity of the nonlinear controller model is guaranteed simultaneously. Finally, the nonlinear FOPD controllers for trajectory tracking experiments are carried out on a rotary inverted pendulum control system.
AlagozBBAtesAYerogluC, et al. (2014) An experimental investigation for error-cube PID control. Transactions of the Institute of Measurement and Control37(5): 652–660.
2.
AngelLViolaJ (2018) Fractional order PID for tracking control of a parallel robotic manipulator type delta. ISA Transactions79: 172–188.
3.
AteşAYerogluC. (2016) Optimal fractional order PID design via Tabu Search based algorithm. ISA Transactions60: 109–118.
4.
BarbosaRSMachadoJATJesusIS (2010) Effect of fractional orders in the velocity control of a servo system. Computers & Mathematics with Application59(5): 1679–1686.
5.
BoikoI (2013) Variable-structure PID controller for level process. Control Engineering Practice21(5): 700–707.
6.
ChenKTangRLiC (2016) Phase-constrained fractional order PI controller for second-order-plus dead time systems. Transactions of the Institute of Measurement and Control39(8): 1225–1235.
7.
DabiriAMoghaddamBPMachadoJAT (2018) Optimal variable-order fractional PID controllers for dynamical systems. Journal of Computational & Applied Mathematics339: 40–48.
8.
DasSPanIDasS, et al. (2012a) A novel fractional order fuzzy PID controller and its optimal time domain tuning based on integral performance indices. Engineering Applications of Artificial Intelligence25(2): 430–442.
9.
DasSPanIDasS, et al. (2012b) Improved model reduction and tuning of fractional-order PIλDμ controllers for analytical rule extraction with genetic programming. Isa Transactions51(2): 237–261.
10.
DeyCMudiRKSimhachalamD (2014) A simple nonlinear PD controller for integrating processes. ISA Transactions53(1): 162–172.
11.
EstakhrouiyehMRGharaveisiAMohammadaliV. (2017) Fractional order Proportional-Integral-Derivative controller parameter selection based on iterative feedback tuning. Case study: Ball Levitation system. Transactions of the Institute of Measurement and Control40(6): 1776–1787.
12.
GeorgeAGeorgeNStamatisM (2014) Advanced nonlinear PID Based antagonistic control for pneumatic muscle actuators. IEEE Transactions on Industrial Electronics61(12): 6926–6937.
13.
HanJQ (2009) From PID to Active Disturbance Rejection Control. IEEE Transactions on Industrial Electronics56(3): 900–906.
14.
HajiVHMonjeCA (2019) Fractional-order PID control of a MIMO distillation column process using improved bat algorithm. Soft Computing23(18): 8887–8906.
15.
JavidanRKhubanH (2018) Optimal non-integer PID controller for a class of nonlinear systems: multi-objective modified black hole optimization algorithm. Neural Computing & Applications30(1): 1–11.
16.
JengJCGeGP (2018) Data-based approach for feedback-feedforward controller design using closed-loop plant data. ISA Transactions80: 244–252.
17.
JinQBQiLFJiangBY, et al. (2014) Novel improved cuckoo search for PID controller design. Transactions of the Institute of Measurement and Control37(6): 721–731.
18.
KadlicBSekajIPerneckýD (2014) Design of continuous-time controllers using Cartesian genetic programming. IFAC Proceedings Volumes47(3): 6982–6987.
19.
KangJMengWAbrahamA, et al. (2014) An adaptive PID neural network for complex nonlinear system control. Neurocomputing135(C): 79–85.
20.
KangMCheongJDoH M, et al. (2017) A practical iterative PID tuning method for mechanical systems using parameter chart. International Journal of Systems Science48(13): 1–14.
21.
KhaledBKSoufieneBMounirA (2018) Design and co-simulation of a fuzzy gain-scheduled PID controller based on particle swarm optimization algorithms for a quad tilt wing unmanned aerial vehicle. Transactions of the Institute of Measurement and Control40(14): 3933–3952.
22.
KozaJR (1992) Genetic Programming: On the Programming of Computers by Means of Natural Selection. Cambridge, MA: MIT Press.
23.
KumarAKumarV (2017) A novel interval type-2 fractional order fuzzy PID controller: Design, performance evaluation, and its optimal time domain tuning. ISA Transactions68: 251–275.
24.
LaCavaWGDanaiK (2016) Gradient-based adaptation of continuous dynamic model structures. International Journal of Systems Science47(1): 249–263.
25.
LuoYChenYQWangCY, et al. (2010) Tuning fractional order proportional integral controllers for fractional order systems. Journal of Process Control20(7): 823–831.
26.
MaheswariCPriyankaEBMeenakshipriyaB (2017) Fractional-order PIλDµ controller tuned by coefficient diagram method and particle swarm optimization algorithms for SO2 emission control process. Proceedings of the Institution of Mechanical Engineers Part I Journal of Systems and Control Engineering231(8): 587–599.
27.
MehtaUVincentLSinghOP (2017) Simple FOPI tuning method for real-order time delay systems. Advances in Systems, Control and Automation. Lecture Notes in Electrical Engineering422: 459–468.
28.
Merrikh-BayatFMirebrahimiN (2011) Introduction to the nonlinear PIλDµ control. In: IEEE International Conference on Control System, Computing and Engineering, Penang, Malaysia, 25–27 November 2011, pp. 43–48. NJ, USA: IEEE.
29.
MuresanCCopotCBirsI, et al. (2018) Experimental validation of a novel auto-tuning method for a fractional order PI controller on an UR10 robot. Algorithms11(7): 95.
30.
MuresanCIDulfEHBothR (2016) Vector-based tuning and experimental validation of fractional-order PI/PD controllers. Nonlinear Dynamics84(1): 179–188.
31.
PerngJWChenGYHsuYW (2017) FOPID controller optimization based on SIWPSO-RBFNN algorithm for fractional-order time delay systems. Soft Computing21(14): 4005–4018.
32.
RadaidehSMHayajnehMT (2002) A modified PID controller . Journal of the Franklin Institute339(6): 543–553.
33.
Ramírez-NeriaMSira-RamírezHGarrido-MoctezumaR, et al. (2014) Linear active disturbance rejection control of underactuated systems: The case of the Furuta pendulum. ISA Transactions53(4): 920–928.
34.
RezaAHShahramJavadiRezaSN (2014) DC motor speed control by self-tuning fuzzy PID algorithm. Transactions of the Institute of Measurement and Control37(2): 164–176.
35.
SahibMA (2015) A novel optimal PID plus second order derivative controller for AVR system. Engineering Science and Technology: An International Journal18(2): 194–206.
36.
SearsonDPLeahyDEWillisMJ (2010) GPTIPS: An open source genetic programming toolbox for multigene symbolic regression. Lecture Notes in Engineering and Computer Science2180: 83–93.
37.
SekajIPerkaczJ (2007) Genetic programming-based controller design. In: IEEE Congress on Evolutionary Computation, Singapore, 25–28 September 2007, pp. 1339–1343. NJ, USA: IEEE.
38.
ShahPAgasheS (2016) Review of fractional PID controller. Mechatronics38: 29–41.
39.
ShuZTaftCWBentsmanJ, et al. (2012) Simultaneous gains tuning in boiler/turbine PID-based controller clusters using iterative feedback tuning methodology. ISA Transactions51(5): 609–621.
40.
SrivastavaSMisraAThakurSK, et al. (2016) An optimal PID controller via LQR for standard second order plus time delay systems. ISA Transactions60: 244–253.
41.
TepljakovAGonzalezEAPetlenkovE, et al. (2016) Incorporation of fractional-order dynamics into an existing PI/PID DC motor control loop. ISA Transactions60: 262–273.
42.
XieYTangXSongB, et al. (2018) Model-free tuning strategy of fractional-order PI controller for speed regulation of permanent magnet synchronous motor. Transactions of the Institute of Measurement and Control41(1): 23–35.
43.
ZamaniABarakatiSMYousofi-DarmianS (2016) Design of a fractional order PID controller using GBMO algorithm for load-frequency control with governor saturation consideration. ISA Transactions64: 56–66.
44.
ZhangBLiHWGuoLH, et al. (2010) Application of variable structure PID in velocity control for large telescope. Optics and Precision Engineering18(7): 1613–1619.
45.
ZhouDZhangKRaveyA, et al. (2016) Parameter sensitivity analysis for fractional-order modeling of lithium-ion batteries. Energies9: 123.
