Optimisation of Internal Model Control Performance Indices for Autonomous Vehicle Suspension

FUOYE Journal of Engineering and Technology, Volume 7, Issue 2, June 2022 ISSN: 2579-0617 (Paper), 2579-0625 (Online) Optimisation of Internal Model Control Performance Indices for Autonomous Vehicle Suspension *1Jibril A. Bala, 2Tologon Karataev, 3Sadiq Thomas, 1Taliha A. Folorunso, and 1Abiodun M. Aibinu 1Department of Mechatronics Engineering, Federal University of Technology, Minna, Nigeria. 2Department of Electrical and Electronics Engineering, Nile University of Nigeria, Abuja, Nigeria. 3Department of Computer Engineering, Nile University of Nigeria, Abuja, Nigeria. {jibril.bala|funso.taliha|abiodun.aibinu}@futminna.edu.ng|{tologun.karataev|sadiqthomas}@nileuniversity.edu.ng Received: 07-JAN-2022; Reviewed: 13-MAR-2022; Accepted: 21-APR-2022 https://doi.org/10.46792/fuoyejet.v7i2.770 ORIGINAL RESEARCH ARTICLE Abstract- Autonomous vehicles (AVs) have grown in popularity and acceptability due to their unique capacity to reduce pollution, road accidents, human error, and traffic congestion. Vehicle suspension is an important component of a car chassis since it affects the performance of vehicle dynamics. As a result, enhancing suspension performance and stability is critical in order to achieve a more pleasant and safer car. Although there are several suspension control methods, they all suffer from fixed gain characteristics that are prone to nonlinearities, disturbances, and the inability to be tuned online. This research provides a comparison of Internal Model Control (IMC) performance metrics for vehicle suspension control. The IMC approach was tuned using the Genetic Algorithm and the Particle Swarm Optimisation algorithms. The performance of each of these schemes was analysed and compared in order to determine the approach with the best performance in terms of AV suspension control. The performance of the system response was compared to that of the traditional IMC. According to the comparison analysis, the optimized IMC systems had lower IAE, ITAE, ISE, rising time, and settling time values than the traditional IMC. Furthermore, there were no overshoots in any of the controllers. Keywords- Autonomous Vehicles, Genetic Algorithm, Internal Model Control, Particle Swarm Optimisation, Vehicle Suspension —————————— ◆ —————————— Numerous control schemes have been proposed for suspension control (Djellal & Lakel (2018); Alexandru & he growth of robotics and intelligent systems has Alexandru (2010); Alvarez (2013); Ghandhi & accelerated the development of autonomous and selfRamaachandran (2017); Hanafi (2010)). However, the driving automobiles. The goal of these vehicles is to presence of uncertainties and nonlinearities affect the arrive at their destination safely and steadily (Park, Lee, fixed gain characteristics of these techniques. The & Han, 2015). Autonomous Vehicles (AVs) have gained feedback gains of these controllers are obtained offline widespread popularity and acceptance due to their based on the system model, and once deployed, the gains unique ability to minimise pollution, road accidents, cannot be changed (Fu, Li, Ning, & Xie, 2017). Thus, a human errors, and traffic congestion. AVs also more effective method for controller design is required for significantly contribute to saving energy, improving effective and efficient control performance. throughput, increasing efficiency, and enhancing safety (Bala, 2019). This study presents a comparative evaluation of IMC performance indices for suspension control in AVs. The Vehicle suspension is a vital component of a car chassis IMC technique was optimised using Genetic Algorithm because of its influence on vehicle dynamics performance. and Particle Swarm Optimisation algorithms. The The suspension is a collection of springs, linkages, and performance analysis of each of these schemes was shock absorbers that connects the vehicle to the wheels carried out and compared to determine the technique and supports motion between the two sections (Dishant, with better performance with respect to AV suspension Singh, & Sharma, 2017). The suspension establishes control. The rest of this paper is divided into four (4) contact between the vehicle tyres and the road surface. sections. Section 2 presents a review of existing literature This in turn has a direct implication on the ride, stability, while the research methodology is presented in Section 3. handling, and comfort of the vehicle (Meng, Chen, Wang, The results and analysis are presented in Section 4 and the Sun, & Li, 2021; Wang, 2018). Vehicles are complex and conclusion and future research directions are given in dynamic systems consisting of multiple inputs and Section 5. multiple outputs. As such, improving suspension performance and stability is vital in achieving a more comfortable and safer vehicle. 2 LITERATURE REVIEW 1 INTRODUCTION T *Corresponding Author Section C- MECHANICAL/MECHATRONICS ENGINEERING & RELATED SCIENCES Can be cited as: Bala J.A., Karataev T., Thomas S., Folorunso T.A., and Aibinu A.M. (2022): Optimisation of IMC Performance Indices for Autonomous Vehicle Suspension, FUOYE Journal of Engineering and Technology (FUOYEJET), 7(2), 193-199. http://doi.org/10.46792/fuoyejet.v7i2.770 Proportional Integral Derivative (PID) control is widely used in control engineering due to its simplicity, low cost, and ability to guarantee satisfactory performance. In the work of Hanafi, (2010), a PID control scheme was developed for semi-active car suspension. The suspension model was obtained from an intelligent system identification process. The results showed good performance in shock absorber control and road surface disturbance rejection. Similarly, Ignatius, Obinabo, & Evbogbai, (2016) designed a PID controller for an active © 2022 The Author(s). Published by Faculty of Engineering, Federal University Oye-Ekiti. 193 This is an open access article under the CC BY NC license. (https://creativecommons.org/licenses/by-nc/4.0/) http://doi.org/10.46792/fuoyejet.v7i2.770 http://journal.engineering.fuoye.edu.ng/ FUOYE Journal of Engineering and Technology, Volume 7, Issue 2, June 2022 suspension system using an automated tuning technique. The PID tuner in MATLAB was utilised for the automated selection of PID gains and a performance meeting the design requirements specified was shown by the results. Papkollu, Singru, & Manajrekar, (2014) carried out a comparative analysis between the performance of the Hinfinity controller and PID controller in a car suspension system. The PID was tuned using the root locus design technique and the results indicated that the PID outperformed the H-infinity control scheme in terms of passenger comfort although the H-infinity scheme provided better suspension deflection. A major limitation with these works is the employment of fixed gain parameters for PID controllers which limits performance in dynamic environments. Additionally, the utilisation of multiple gains in PID control leads to difficulty in tuning (selection of appropriate gains for effective performance) (Somefun, Akingbade &Dahunsi (2021)). Internal Model Control (IMC) provides an easier design method than PID due to the need for tuning one parameter instead of three parameters as in the case of PID (Folorunso, Bala, Adedigba &Aibinu (2021)). In the work conducted by Qiu, Sun, Jankovic, & Santillo, (2016), a nonlinear IMC was designed for regulation of a wastegate in a turbocharged gasoline engine. When compared with a PI controller, the IMC exhibited faster reference tracking with less overshoot or oscillation. Prakash & Sohom, (2018) developed an IMC-based fractional order control scheme for specific non-minimum phase systems. The developed controller provides a good control performance in reference tracking, disturbance rejection, and error minimisation. In addition, Roslan, Abd Karim, & Hamzah, (2018) carried out a performance analysis of different tuning techniques for an isothermal CSTR reactor. Although, the IMC showed better results than Direct Synthesis (DS) and Ziegler Nichols (ZN) methods in the aspect of overshoot and undershoot, the other techniques outperformed the IMC in error minimisation and settling times. IMC has also been implemented together with PID to provide an IMC-PID scheme or its variant. In the work of Cajo et al., (2018), an IMC-based PID technique was developed for a benchmark system. The suggested control scheme showed a better performance in disturbance rejection with lower control effort than the traditional PID scheme. Additionally, Babins & Pradeep, (2018) compared the performance of an IMC and an IMCPID in a low control system for a conservation tank. The IMC-PID scheme exhibited better dynamic performance in terms of parameters such as set-point tracking, disturbance rejection, and robustness. An IMC-based PID controller was designed for a coupled tank system in the study conducted by Prakash, Yadav, & Kumar, (2016). The performance of the controller was compared with a traditional PID tuned with Ziegler-Nichols, Cohen Coon, and Tyreus-Luyben methods. The IMC-PID showed better robustness and performance. Pathiran, (2019) improved the regulatory response of a PID controller using IMC principles. The results showed the proposed scheme gives improved response and servo-regulatory performance than Ziegler Nichols PI/PID control ISSN: 2579-0617 (Paper), 2579-0625 (Online) techniques. Despite the improved performance of IMC and IMC-PID schemes in the literature, a major limitation with IMC techniques is the reliance on the accurate representation of the plant model. Because of this, the robustness and performance of the IMC may be reduced due to model inaccuracies and uncertainties. Therefore, the need arises for an adaptive and optimised IMC scheme for improved control performance (Zhu, Xiong, Liu, & Zhu, 2016). 3 RESEARCH METHODOLOGY 3.1 PROBLEM FORMULATION The suspension of the vehicle is modelled centred on a quarter car, passive suspension (Alvarez-Sanchez (2013), Bala, (2019)). The free body diagram is shown in Figure 1. Fig. 1: Free Body Diagram of Car Suspension Where: Ms = Mass of Vehicle Mu = Mass of Suspension Ks = Spring Constant of Suspension Ku = Spring Constant of Wheel Bs = Damping Constant of Suspension The variables xs, xu, and u represent the displacement of the vehicle, displacement of the suspension, and road profile change respectively. Based on Figure 1, the following equations are obtained: (1) 𝑀𝑠 𝑥𝑠̈ = −𝐾𝑠 (𝑥𝑠 − 𝑥𝑢 ) − 𝐵𝑠 (𝑥𝑠̇ − 𝑥𝑢̇ ) (2) 𝑀𝑢 𝑥𝑢 = 𝐾𝑠 (𝑥𝑠 − 𝑥𝑢 ) + 𝐵𝑠 (𝑥𝑠̇ − 𝑥𝑢̇ ) − 𝐾𝑢 (𝑥𝑢 − 𝑢) Converting equations 1 and 2 to Laplace transforms and substituting the parameters selected in Table 1, we obtain the representation in equation 3. 𝑥 4𝑠+5 𝐺(𝑠) = 𝑠 = (3) 4 3 2 𝑢 0.06𝑠 + 0.092𝑠 + 20.01𝑠 +4𝑠+5 Equation 3 serves as the vehicle model transfer function. Table 1. Vehicle Suspension Parameters (Bala, 2019) Parameter Mass of Vehicle Mass of Suspension Spring Constant of Suspension Spring Constant of Wheel Damping Constant of Suspension Value 2000 kg 300 kg 50,000 N/m 100,000 N/m 1200 Ns/m © 2022 The Author(s). Published by Faculty of Engineering, Federal University Oye-Ekiti. 194 This is an open access article under the CC BY NC license. (https://creativecommons.org/licenses/by-nc/4.0/) http://doi.org/10.46792/fuoyejet.v7i2.770 http://journal.engineering.fuoye.edu.ng/ FUOYE Journal of Engineering and Technology, Volume 7, Issue 2, June 2022 3.2 INTERNAL MODEL CONTROLLER DESIGN The use of the Internal Model Controller in tuning the PID controllers has quickly gained popularity among researchers because of its simplicity, robustness, strong tracking performance, ease of disturbance abatement, and ease of tuning (due to single tuning parameter, ) (Yu, Karimi, & Zhu, 2014; Payne, 2014). A traditional IMC architecture is shown in Figure 2 (Folorunso, Bello, Olaniyi & Abdulwahab, 2013). ISSN: 2579-0617 (Paper), 2579-0625 (Online) 2016). The PSO algorithm is given in Figure 3. Fig. 3: PSO Algorithm From Figure 3, pbest and gbest respectively represent the particle’s best position and the global best position. U(0, ϕ) is a random vector generated for each particle. Table 2 shows the PSO parameters used for this study. Fig. 2: Internal Model Controller Architecture The variables r, u, d, and y respectively represent the input, control signal, disturbance, and output. Gp, and Ğp are the plant model, and process model respectively. GIMC represents the IMC, and this is obtained using equation 4. F(s) is the filter, which is given by equation 5. (4) 𝐺𝐼𝑀𝐶 (𝑠) = Ğp−1 (𝑠)𝐹(𝑠) 1 𝐹(𝑠) = (5) 𝑛 (1+ 𝜆𝑠) In equation 5, n represents the order of the plant model and λ is a tuning parameter responsible for speed of response and robustness. λ also deals with noise amplification and modelling errors. Thus,  needs to be appropriately selected for effective control performance. The IMC system is evaluated by taking the inverse of equation 3 and multiplying it by the filter in equation 5. Since the plant is a fourth order plant, the filter coefficient, n, will be equal to 4. Thus, we obtain the IMC equation as shown in equation 6. 𝐺𝐼𝑀𝐶 (𝑠) = 𝐺𝐼𝑀𝐶 (𝑠) = 0.06𝑠 4 + 0.092𝑠 3 + 20.01𝑠 2 +4𝑠+5 4𝑠+5 × 1 (1+ 𝑠)4 0.06𝑠 4 + 0.092𝑠 3 + 20.01𝑠 2 +4𝑠+5 44 𝑠 5 +(54 +163 )𝑠 4 +(203 +242 )𝑠 3 +(302 +16)𝑠 2 +(20+4)𝑠+5 (6) Table 2. PSO Parameters Parameter Swarm Size Number of Iterations Inertia Weight Upper Bound Lower Bound Value 100 200 0.7 10 1 3.4 GENETIC ALGORITHM Genetic Algorithm (GA) is an optimization algorithm introduced by John Holland in 1975 and solves problems using the principles of biological evolution (Haldurai, Madhubala, & Rajalakshmi, 2016; Obaid, Ahmad, Mostafa, & Mohammed, 2012). GA evaluates the problem space as a population of individuals and attempts to find the fittest individual by producing generations and applying concepts such as crossover, mutation and selection (Obaid et al., 2012). GA navigates a search area and attempts to find the optimum solution. Figure 4 shows a flowchart of the GA process. (7) The variable  will be selected using the optimisation algorithms to provide the optimum control performance. The IMC closed loop transfer function is given in equation 8. 𝐺𝐼𝑀𝐶 (𝑠) 𝐺𝑐 (𝑠) = (8) (𝑠)𝐺̃ 1− 𝐺𝐼𝑀𝐶 𝑝 (𝑠) 3.3 PARTICLE SWARM OPTIMISATION ALGORITHM Particle Swarm Optimisation (PSO) is an algorithm developed from Swarm Intelligence in 1995 by Kenndey and Eberhart. It is a global optimisation algorithm developed based on the behaviour of birds and fish. Just like these animal groups that eventually converge at a food source through communication between themselves, the algorithm attempts to converge at an optimum solution through imitation of the behaviours of these animals (Olaniyi, Folorunso, Kolo, Arulogun, & Bala, © 2022 The Author(s). Published by Faculty of Engineering, Federal University Oye-Ekiti. 195 This is an open access article under the CC BY NC license. (https://creativecommons.org/licenses/by-nc/4.0/) http://doi.org/10.46792/fuoyejet.v7i2.770 http://journal.engineering.fuoye.edu.ng/ FUOYE Journal of Engineering and Technology, Volume 7, Issue 2, June 2022 ISSN: 2579-0617 (Paper), 2579-0625 (Online) change in the objective function value. From Table 4 it is observed that the PSO algorithm ensures minimisation of the Best and Mean performance indices. However, in the instance of the mean ITAE, the minimisation value fluctuates around 3000. This can be attributed to the multiplication by the ‘time’ variable in the performance metric since the value increases as the algorithm progresses. Upon completion, the algorithm settles at the best objective value of 232.2, 168.8, and 2794 for the IAE, ISE and ITAE respectively. Fig. 4: GA Process The GA parameters used for this study are presented in Table 3. Table 3. GA Parameters Parameter Value Number of Generations 100 Population 50 Crossover Scattered (random) Mutation Gaussian Selection Type Stochastic Upper Bound 10 Lower Bound 1 3.5 OBJECTIVE FUNCTION DEVELOPMENT The objective functions implemented in this work are obtained based on common performance indices for control systems. These indices are the Integral Absolute Error (IAE), Integral Square Error (ISE), and the Integral of Time-weighted Absolute Error (ITAE). These are popular error performance indices with engineering practicality and selectivity (Li & Li, 2020). These indices will be adopted as the objective functions to be minimised by the optimisation algorithms. The functions are given in equations 9 to 11. ∞ 𝐽1 = 𝐼𝑇𝐴𝐸 = ∫0 𝑡|𝑒(𝑡)|𝑑𝑡 ∞ 𝐽2 = 𝐼𝑆𝐸 = ∫0 𝑒(𝑡)2 𝑑𝑡 ∞ 𝐽3 = 𝐼𝐴𝐸 = ∫0 |𝑒(𝑡)|𝑑𝑡 Table 4. The Iteration Performance of the PSO Best Best Mea Best Mea Mean f(x) Iteratio f(x) - n f(x) f(x) - n f(x) f(x) ITA n IAE - IAE ISE - ISE ITAE E 257. 172. 12000 0 1362 1030 3488 1 3 0 232. 168. 10330 1 876.7 689.3 2802 2 8 0 232. 168. 2 373.7 236.5 2796 26420 2 8 232. 168. 3 233.2 172.6 2796 4548 2 8 232. 168. 4 232.2 168.8 2795 2991 2 8 232. 168. 5 232.2 168.8 2795 3050 2 8 232. 168. 6 232.2 168.8 2795 3065 2 8 232. 168. 7 232.2 168.8 2795 3014 2 8 232. 168. 8 232.2 168.8 2794 3110 2 8 232. 168. 9 232.2 168.8 2794 2992 2 8 232. 168. 10 232.2 168.8 2794 3050 2 8 In Table 5, the results of the minimisation by GA are presented. Here, the algorithm ensure convergence to Best objective function values of 232.2, 168.8, and 4220 for the IAE, ISE, and ITAE respectively. Similar to the case of the PSO algorithm, the Mean ITAE hovers around 4500. However, this occurrence is also observed in the Mean ISE and Mean IAE values. (9) (10) (11) 4 RESULTS AND ANALYSIS The controller design and optimization algorithm were implemented using the MATLAB 2020 software. The iteration performance of the optimising algorithm is as presented in Table 4 and Table 5. In Table 4, the performance of the PSO is presented. The algorithm stops after 20 iterations due to the absence of any significant © 2022 The Author(s). Published by Faculty of Engineering, Federal University Oye-Ekiti. 196 This is an open access article under the CC BY NC license. (https://creativecommons.org/licenses/by-nc/4.0/) http://doi.org/10.46792/fuoyejet.v7i2.770 http://journal.engineering.fuoye.edu.ng/ FUOYE Journal of Engineering and Technology, Volume 7, Issue 2, June 2022 Table 5. The Generational Performance of the GA Mea Best Mea Best Mea Best n f(x) n f(x) n f(x) Generatio f(x) f(x) f(x) ITA n ITA IAE IAE ISE ISE E E 232. 168. 7592 1 1060 762.5 4323 2 8 0 232. 168. 4529 2 844.5 510.8 4323 2 8 0 232. 168. 2163 3 615.1 406.8 4323 2 8 0 232. 168. 1399 4 480.1 282.9 4323 2 8 0 232. 168. 5 415.6 227.6 4323 6328 2 8 232. 168. 6 317.8 226.8 4220 5104 2 8 232. 168. 7 272 200.1 4220 5036 2 8 232. 168. 8 265.3 203.2 4220 4380 2 8 232. 168. 9 244 196.6 4220 4404 2 8 232. 168. 10 237.2 189.2 4220 4373 2 8 The optimisation algorithms’ performance was also comparatively analysed in the aspect of the control system response of the performance metrics. Figures 4 to 6 show the step response of various controllers for the three performance indices. Fig. 4: Step Response of all Controllers (ITAE) ISSN: 2579-0617 (Paper), 2579-0625 (Online) Fig. 5: Step Response of all Controllers (IAE) Fig. 6: Step Response of all Controllers (ISE) In Table 6, the minimisation of the IAE resulted in a respective rise time and settling time of 4.94 seconds and 9.08 seconds for both the PSO and GA algorithms. The optimised IMC systems exhibited an IAE of 232.18 which is significantly lower than the value obtained by the traditional IMC which was 696.43. The  parametric value of the traditional IMC was selected manually and was chosen to be 3, while the optimisation algorithms selected  values of 1. All controllers exhibited an overshoot of 0% which is common with IMC systems. The results of the comparison of the various controllers with respect to the ITAE are presented in Table 7. The optimisation algorithms gave  values of approximately 1 and 1 for the PSO and GA-based IMCs respectively. The ITAE, rise times, and settling times of the optimised controllers are also significantly lower than that of their traditional counterparts. Table 8 shows the comparison of the various controllers with respect to the ISE. Similar to the IAE, the GA and PSO controllers exhibited similar response parameters and ISE values. The values gotten from the optimised controllers were significantly lower than the value gotten from the traditional controller. Similarly, all controllers gave no overshoots. © 2022 The Author(s). Published by Faculty of Engineering, Federal University Oye-Ekiti. 197 This is an open access article under the CC BY NC license. (https://creativecommons.org/licenses/by-nc/4.0/) http://doi.org/10.46792/fuoyejet.v7i2.770 http://journal.engineering.fuoye.edu.ng/ FUOYE Journal of Engineering and Technology, Volume 7, Issue 2, June 2022 ISSN: 2579-0617 (Paper), 2579-0625 (Online) 5 CONCLUSION Table 6. Controller Comparison (IAE & System Response) Controller IAE Rise Settling Overshoot  Time Time (%) (secs) (secs) Traditional 3 696.43 14.8 27.3 0 IMC PSO-IMC 1 232.18 4.94 9.08 0 GA-IMC 1 232.18 4.94 9.08 0 Table 7. Controller Comparison (ITAE & System Response) Controller  ITAE Rise Settlin Overshoo Tim g Time t (%) e (secs) (secs ) Traditiona 3 24675 14.8 27.3 0 l IMC PSO-IMC 1.013 2794. 5 9.21 0 4 3 GA-IMC 1.192 4219. 5.89 10.8 0 4 6 Table 8. Controller Comparison (ISE & System Response) Controller ISE Rise Settling Overshoot  Time Time (%) (secs) (secs) Traditional 3 506.43 14.8 27.3 0 IMC PSO-IMC 1 168.81 4.94 9.08 0 GA-IMC 1 168.81 4.94 9.08 0 The performance of the iteration performance of the PSO and GA algorithms, the optimal λ values of the have been selected based on tuning efficiency as depicted in Table 4 and Table 5. Based on this performance, an optimal λ value of 1 is selected. Hence, it is expected that the transient response of the IMC-PSO and IMC-GA would be the same. However, for the traditional IMC, a λ value of 3 was obtained based on the rule of thumb. Hence, it is expected that there would be a difference in the transient response and controller performance. Observe from Table 6-8, showing the transient response and controller performance based on the IAE, ITSE, and ISE. It can be seen that all 3 approaches depict a zero overshoot, this is expected based on the inherent characteristic of the IMC algorithm. However, there exists a difference in the settling time and the rise time. It can be observed that the PSO and GA approach has the same rise time and settling time of 4.98 sec and 9.08 sec. This is a result of the same λ value obtained from the tuning of the PSO and GA algorithm. However, there is a difference in the performance metrics in comparison with the traditional approach due to the varying values of λ. The PSO and GA have a faster rise time and settling time as compared to the traditional approach, these can be observed in the performance plot as depicted in Figures 4-6. This evaluation places PSO and GA approaches as better controllers as compared to the traditional approach. In this study, the optimisation of Internal Model Controller (IMC) performance indices was carried out for an Autonomous Vehicle (AV) suspension system. The suspension system was modelled based on a quarter car passive suspension. The IMC system was optimised using Particle Swarm Optimisation (PSO) and Genetic Algorithm (GA). These optimisation algorithms were designed to minimised error performance indices of control systems, namely: Integral Time-weighted Absolute Error (ITAE), Integral Absolute Error (IAE), and Integral Square Error (ISE). The obtained results indicated that the optimisation algorithms ensured minimisation of all the performance indices considered. Additionally, the system response performance was compared with the conventional IMC. The comparative analysis showed that the optimised IMC systems exhibited lower IAE, ITAE, ISE, rise time, and settling time values than the traditional IMC. Furthermore, all the controllers exhibited no overshoots. The results gotten from the study indicate that PSO and GA can be successfully implemented in optimising IMCbased systems for AV suspension control. The PSO and GA based IMC systems minimise the errors values, reduce the rise and settling times, and produce no overshoots. These characteristics are desirable in control systems since they minimise damage, inaccuracy, and instability. Future research directions will focus on implementation of optimisation on nonlinear control techniques for performance evaluation. ACKNOWLEDGMENT The authors wish to thank the National Information Technology Development Agency (NITDA) for their support through the 2020 NITDEF scholarship scheme. REFERENCES Alexandru, C., & Alexandru, P. (2010). The virtual prototype of a mechatronic suspension system with active force control. Wseas transactions on systems, 9(9), 927-936. Alvarez-Sánchez, E. (2013). A quarter-car suspension system: car body mass estimator and sliding mode control. Procedia Technology, 7, 208-214. Babins, P. J., & Pradeep, S. S. S. (2018). Comparison of IMC and IMCPID for Flow Control system in Conservation Tank. In Proceedings of 4th International Conference on Energy Efficient Technologies for Sustainability–ICEETS’18. St. Xavier’s Catholic College of Engineering, Nagercoil, TamilNadu, India, from 5th to 7th April, 2018. Bala, J. A. (2019). Development of Lane Keeping System for Autonomous Vehicle Platoons. Unpublished Masters’ Thesis, University of Salford, UK. Cajo, R., Zhao, S., Ionescu, C. M., De Keyser, R., Plaza, D., & Liu, S. (2018). IMC based PID Control Applied to the Benchmark PID18. In 3rd IFAC Conference on Advances in Proportional- IntegralDerivative Control, Ghent, Belgium, May 9-11, 2018 (pp. 728– 732). https://doi.org/10.1016/j.ifacol.2018.06.210 Dishant, Singh, E. P., & Sharma, E. M. (2017). Suspension Systems: A Review. International Research Journal of Engineering and Technology, 4(4), 1377–1382. Djellal, A., & Lakel, R. (2018). Adapted reference input to control PID-based active suspension system. European Journal of © 2022 The Author(s). Published by Faculty of Engineering, Federal University Oye-Ekiti. 198 This is an open access article under the CC BY NC license. (https://creativecommons.org/licenses/by-nc/4.0/) http://doi.org/10.46792/fuoyejet.v7i2.770 http://journal.engineering.fuoye.edu.ng/ FUOYE Journal of Engineering and Technology, Volume 7, Issue 2, June 2022 Automated Systems, 51(1-3), 7-23. Folorunso, T. A., Bala, J. A., Adedigba, A. P., & Aibinu, A. M. (2021, July). Genetic Algorithm Tuned IMC-PI Controller for Coupled Tank Based Systems. In 2021 1st International Conference on Multidisciplinary Engineering and Applied Science (ICMEAS) (pp. 72-77). IEEE. Folorunso, T. A., Bello-Salau, H., Olaniyi, O. M., & Abdulwahab, N. (2013). Control of a two layered coupled tank: Application of IMC, IMC-PI and pole-placement PI controllers. Fu, Z., Li, B., Ning, X., & Xie, W. (2017). Online Adaptive Optimal Control of Vehicle Active Suspension Systems Using SingleNetwork Approximate Dynamic Programming. Mathematical Problems in Engineering, 2017. Gandhi, P., Adarsh, S., & Ramachandran, K. I. (2017). Performance analysis of half car suspension model with 4 DOF using PID, LQR, FUZZY and ANFIS controllers. Procedia Computer Science, 115, 2-13. Haldurai, L., Madhubala, T., & Rajalakshmi, R. (2016). A Study on Genetic Algorithm and its Applications. International Journal of Computer Sciences and Engineering, 4(10), 139–143. Hanafi, D. (2010). PID Controller Design for Semi-Active Car Suspension Based on Model from Intelligent System Identification. In 2010 Second International Conference on Computer Engineering and Applications (pp. 60–63). https://doi.org/10.1109/ICCEA.2010.168 Ignatius, O. I., Obinabo, C. E., & Evbogbai, M. J. E. (2016). Modelling, Design and Simulation of Active Suspension System PID Controller using Automated Tuning Technique. Network and Complex Systems, 6(1), 11–15. Li, J., & Li, W. (2020). On-Line PID Parameters Optimization Control for Wind Power Generation System Based on Genetic Algorithm. IEEE Access, 8, 137094–137100. https://doi.org/10.1109/ACCESS.2020.3009240 Meng, Q., Chen, C., Wang, P., Sun, Z., & Li, B. (2021). Study on vehicle active suspension system control method based on homogeneous domination approach. Asian Journal of Control, 23, 561–571. https://doi.org/10.1002/asjc.2242 Obaid, O. I., Ahmad, M., Mostafa, S. A., & Mohammed, M. A. (2012). Comparing Performance of Genetic Algorithm with Varying Crossover in Solving Examination Timetabling Problem. Journal of Emerging Trends in Computing and Information Sciences, 3(10), 1427–1434. Olaniyi, O. M., Folorunso, T. A., Kolo, J. G., Arulogun, O. T., & Bala, J. A. (2016). Performance Evaluation of Mobile Intelligent Poultry Feed Dispensing System Using Internal Model Controller and Optimally Tuned PID Controllers Performance Evaluation of Mobile Intelligent Poultry Feed Dispensing System Using Internal Model Controller A. Advances in Multidisciplinary Research Journal, 2(2), 45–58. Papkollu, K., Singru, P. M., & Manajrekar, N. (2014). Comparing PID and H-infinity controllers on a 2-DoF nonlinear quarter car suspension system. Journal of Vibroengineering, 16(8), 3977– 3990. Park, M., Lee, S., & Han, W. (2015). Development of steering control system for autonomous vehicle using geometry-based path tracking algorithm. ETRI Journal, 37(3), 617–625. https://doi.org/10.4218/etrij.15.0114.0123 Pathiran, A. R. (2019). Improving the Regulatory Response of PID Controller Using Internal Model Control Principles. International Journal of Control Science and Engineering, 9(1), 9–14. https://doi.org/10.5923/j.control.20190901.02 Payne, L. (2014). Tuning PID control loops for fast response. Control Engineering, 61(7), 1-4. Prakash, A., Yadav, A. P., & Kumar, R. (2016). Design of IMC based PID Controller for Coupled Tank System. International Journal of Engineering Research & Technology (IJERT), 4(15), 1–8. Prakash, P. A., & Sohom, C. (2018). IMC based Fractional Order ISSN: 2579-0617 (Paper), 2579-0625 (Online) Controller Design for Specific Non-Minimum Phase Systems. In Preprints of the 3rd IFAC Conference on Advances in Proportional- Integral-Derivative Control, Ghent, Belgium, May 9-11, 2018 (pp. 847–852). Qiu, Z., Sun, J., Jankovic, M., & Santillo, M. (2016). Nonlinear internal model controller design for wastegate control of a turbocharged gasoline engine. Control Engineering Practice, 46, 105–114. https://doi.org/10.1016/j.conengprac.2015.10.012 Roslan, A. H., Abd Karim, S. F., & Hamzah, N. (2018). Performance analysis of different tuning rules for an isothermal CSTR using integrated EPC and SPC. IOP Conf. Series: Materials Science and Engineering, 334. https://doi.org/10.1088/1757899X/334/1/012019 Somefun, O. A., Akingbade, K., & Dahunsi, F. (2021). The dilemma of PID tuning. Annual Reviews in Control, 52, 65-74. Tan, W., Liu, J., Chen, T., & Marquez, H. J. (2006). Comparison of some well-known PID tuning formulas. Computers & chemical engineering, 30(9), 1416-1423. Wang, H. (2018). Enhancing vehicle suspension system control performance based on the improved extension control. Advances in Mechanical Engineering, 10(7), 1–13. https://doi.org/10.1177/1687814018773863 Yu, H., Karimi, H. R., & Zhu, X. (2014). Research of Smart Car’s Speed Control Based on the Internal Model Control. Abstract and Applied Analysis, 2014, 1–5. https://doi.org/10.1155/2014/274293 Zhu, Q., Xiong, L., Liu, H., & Zhu, Y. (2016). A New Robust Internal Model Controller and its Applications in PMSM Drive. Internal Journal of Innovative Computing, Information and Control, 12(4), 1257–1270. © 2022 The Author(s). Published by Faculty of Engineering, Federal University Oye-Ekiti. 199 This is an open access article under the CC BY NC license. (https://creativecommons.org/licenses/by-nc/4.0/) http://doi.org/10.46792/fuoyejet.v7i2.770 http://journal.engineering.fuoye.edu.ng/