Inverted Pendulum I

     A state-feedback fuzzy controller is designed to stabilise/regulate an inverted pendulum based on a 16-rule T-S fuzzy model.  The feedback gains is obtained by solving a feasible solution to a set of stability conditions in terms of linear matrix inequalities.  The following movie clips show the experiments of stabilisation/regulation of inverted pendulum using the fuzzy controller.


Regulation of inverted pendulum to different angles.

Stabilisation of inverted pendulum subject to disturbance.

Inverted Pendulum 2

     A state-feedback fuzzy controller is designed to stabilise/regulate an inverted pendulum on a cart based on 2-rule T-S fuzzy model with the consideration of system stability and performance.  The feedback gains is obtained by solving a feasible solution to a set of stability and performance conditions in terms of linear matrix inequalities.  The following movie clip shows a simulation result (the first 8 second is in slow motion (0.02x) and the rest is in normal speed).  The initial condition for all cart is the same: pendulum angle = 75 degrees, pendulum angular velocity = 0 degrees per second, cart displacement = 0 m eter and cart velocity = 0 meters per second.

Details can be found in the following paper:

  1. H.K. Lam and Mohammad Narimani, “Stability analysis and performance deign for fuzzy-model-based control system under imperfect premise matching,” IEEE Trans. Fuzzy Systems, vol. 17, no. 4, pp. 949-961, Aug. 2009.

     Three fuzzy controllers are designed to stabilise the inverted pendulum on a cart subject to different performance indices.  The performance index of the upper cart is to minimise the pendulum angle and cart displacement.  The fuzzy controller is able to drive the pendulum and the cart to the origin in the shortest time among the three carts.  The one in the bottom is to minimise the pendulum angle, cart displacement and the control energy. This fuzzy controller is still able drive the pendulum and the cart to the origin but a longer time is required and the control energy consumption is lower compared with the upper one.  The one in the middle puts a heavy weight on the minimisation of control energy.  It consumes the least control energy among the three fuzzy controllers.  However, it requires the longest time to return the cart to the origin (around 200 seconds but the movie only shows up to 38 seconds). 

Bolt Tigenting

     A 4-stage Mandani fuzzy logic control with error detection capability is implemented with a programmabl logic controller (PLC) which integrates MATLAB Simulink in real time in a Beckhoff TwinCAT 3 system for tightening process.  Linguistic rules representing the expert knowledge on the bolt tightening process are developed. The membership functions are designed heuristically to achieve a good bolt tightening performance in terms transient response, reliability and robustness.

Details can be found in the following paper:

  1.  Christian Deters, EmanueleLindoSecco, Helge Arne Wurdemann, Hak-Keung Lam, lakmalSeneviratne,KasparAlthoefer, “Model-free fuzzy tightening control for bolt/nut joint connections of wind turbine hubs,” inProc. of 2013 IEEE International Conference on Robotics and Automation, KongresszentrumKarlsruhe,Karlsruhe, Germany, May 6-10, 2013, pp. 270-276.

The above move clips (playing at 8x speed) shows a tightening tool (DSM BL/140 MDW) mounted on a robot arm (Fanuc M6iB) picking up a nut (M24), moving to the right position and tightening it to a bolt.


Mobile Robots

     A Mamdani-type fuzzy PI controller with 4 rules was employed to drive the mobile robot from the source position to the destination position (the position of the red ball in the video).  For comparison purposes, a traditional P controller was designed to achieve the same control objective.  It can be seen from the videos below that the fuzzy PI fuzzy controller performed better in terms of faster transient response and steady error.

Details can be found in the following paper:

  1. T.H. Lee, H.K. Lam, F.H.F. Leung, P.K.S. Tam, “A practical fuzzy logic controller for the path-tracking of wheeled mobile robots,” IEEE Control Systems Magazine, vol. 23, no. 2, pp. 60-65, April 2003.

Position control of mobile robot using a P controller.

Position control of mobile robot using a Mamdani-type fuzzy PI fuzzy controller.

Two robot soccer teams playing against each other using fuzzy control strategy and fuzzy logic decision maker.


Fuzzy PID control of anaesthesia

This work is about the automatic drug administration for the regulation of bispectral (BIS) index in the anesthesia process during the clinical surgery by controlling the concentration target of two drugs, namely, propofol and remifentanil. To realize the automatic drug administration, real clinical data are collected for 42 patients for the construction of patients' models consisting of pharmacokinetic and pharmacodynamic models describing the dynamics reacting to the input drugs. A nominal anesthesia model is obtained by taking the average of 42 patients' models for the design of control scheme. Three PID controllers are employed, namely linear PID controller, type-1 (T1) fuzzy PID controller and interval type-2 (IT2) fuzzy PID controller, to regulate the BIS index using the nominal patient's model. The PID gains and membership functions are obtained using genetic algorithm (GA) by minimizing a cost function measuring the control performance. The best trained PID controllers are tested under different scenarios and compared in terms of control performance. Simulation results show that the IT2 fuzzy PID controller offers the best control strategy regulating the BIS index while the T1 fuzzy PID controller comes the second.


The results were summarised in the following paper:


Hugo Araujo, Bo Xiao, Chuang Liu, Yanbin Zhao, and H.K. Lam, “Design of type-1 and interval type-2 fuzzy PID control for anesthesia using genetic algorithms,” Journal of Intelligent Learning Systems and Applications, vol. 6, no. 2, pp. 70-93, May 2014.


which can be downloaded from


The following video shows the regulation of BIS index using PID (red), T1 fuzzy PID (green) and IT2 fuzzy PID (blue) controllers.  The upper-left panel shows the transient response of the regulation of BIS index where the regions bounded by dash lines in magenta are an acceptable range the BIS index should stay.  The upper-right panel shows the firing strength of the rules corresponding to the membership functions N, Z and P.  The bottom-left panel shows the cost at time t. The smaller the cost, the better the performance is.  The bottom-right panel shows proportional, integral and derivative gains at time t.


Regulation of BIS index using PID, Fuzzy PID and Interval Type-2 Fuzzy PID Controllers.  GUI and video were prepared by Chuang Liu.