No abstract

The development and improvement of control techniques has attracted many researchers for many years.Especially in the controller design of complex and nonlinear systems, various methods have been proposed to determine the ideal control parameters. One of the most common and effective of these methods is determining the controller parameters with optimization algorithms.In this study, LQR controller design was implemented for position control of the double inverted pendulum system on a cart. First of all, the equations of motion of the inverted pendulum system were obtained by using Lagrange formulation. These equations were linearized by Taylor series expansion around the equilibrium position to obtain the state-space model of the system. The LQR controller parameters required to control the inverted pendulum system were determined by using a trial and error method. The determined parameters were optimized by using five different configurations of three different optimization algorithms (GA, PSO, and ABC). The LQR controller parameters obtained as a result of the optimization study with five different configurations of each algorithm were applied to the system and the obtained results were compared with each other. In addition, the configurations that yielded the best control results for each algorithm were compared with each other and the control results were evaluated in terms of response speed and response smoothness.

The inverted pendulum system is highly popular in control system applications and has the characteristics of unstable, nonlinear, and fast dynamics. A nonlinear controller is needed to control a system with these characteristics. In addition, there are disturbances and parameter uncertainty issues to be solved in the inverted pendulum system. Therefore, this study uses a nonlinear controller, which is the backstepping sliding mode control. The controller is robust to parameter uncertainty and disturbances so that it is suitable for controlling an inverted pendulum system. Based on testing with step and sine reference signals without interference, the controller can stabilize the system well and has a fast response. In testing with disturbances and mass uncertainty, the backstepping sliding mode controller is robust against these changes and able to make the system reach the reference value. Compared with sliding mode control, backstepping sliding mode control has a better and more robust response to disturbances and parameter uncertainty.

The use of DC motors is now common because of its advantages and has become an important necessity in helping human activities. Generally, motor control is designed with PID control. The main problem that is often discussed in PID is parameter tuning, namely determining the value of the Kp, Ki, and Kd parameters in order to obtain optimal system performance. In this study, one method for tuning PID parameters on a DC motor will be used, namely the Particle Swarm Optimization (PSO) method. Parameter optimization using the PSO method has stable results compared to other methods. The results of tuning the PID controller parameters using the PSO method on the MATLAB Simulink obtained optimal results where the value of Kp = 8.9099, K = 2.1469, and Kd = 0.31952 with the value of rise time of 0.0740, settling time of 0.1361 and overshoot of 0. Then the results of hardware testing by entering the PID value in the Arduino IDE software produce a stable motor speed response where Kp = 1.4551, Ki= 1.3079, and Kd = 0.80271 with a rise time value of 4.3296, settling time of 7.3333 and overshoot of 1.

This paper presents the trajectory tracking control of a two-link planar robot manipulator using MSC Adams and MATLAB co-simulation which enables the innovative virtual prototyping of the systems without any mathematical expressions. Firstly, the tracking control performance of the planar manipulator is investigated using the Sliding Mode Control (SMC) controller and the Proportional Integral Derivative (PID) controller in terms of the performance analysis. As a result, the SMC demonstrates effective control performances compared to the PID controller according to the required trajectory, settling time, and end position of the system. Then, the SMC controller parameters are determined using the different optimization methods offered as open source by MATLAB/Response Optimization Toolbox and compared to each other. In the virtual co-simulation, the trajectory tracking control performance is observed to be improved by optimizing the parameters of the SMC controller using Simplex Search (SS) method. All control results are examined and presented with graphics and international error standards.