Safe experimentation dynamics algorithm for data-driven PID controller of a class of underactuated systems - Nor Sakinah, Abdul Shukor (2019)
In recent decades, various control strategies for underactuated mechanical systems (UMS) have been widely reported which are derived from the systems’ model. Due to the problem of the unmodeled dynamics, there is a significant disparity between the theory of control and its actual applications, which makes the model-based controller difficult to apply. In recent years, control researchers have been switching to the method of data-driven control in order to eliminate this disparity. The control performance of this method is independent of the plant’s model accuracy to attain the control objective. This is because its controller’s design is founded only on the input-output (I/O) data measurement of the actual plants. In the industry, the proportional-integral-derivative (PID) controller is the control method that has been widely implemented because of its simplicity, the fact that it is more understandable and more reliable to be used for industrial purposes. So far, the tuning methods used for data-driven PID for the underactuated systems are mostly based on the multi-agent-based optimization, which means that the design requires substantial computation time and make it not practical for on-line tuning applications. Therefore, it is necessary to develop a tuning strategy that requires less computation time. Previously, a stochastic approximation based method such as the norm-limited simultaneous perturbation stochastic approximation (NL-SPSA) and global NL-SPSA (G-NL-SPSA) have shown successful results as tools for the data-driven PID tuning. Notably, the SPSA and GSPSA based methods only produced the optimal design parameter at the final iteration while it may keep a better design parameter during the tuning process if it has a memory feature. Hence, a memory-based optimization tool has good potential to retain the optimal design parameter during the PID tuning process. This can overcome the existing memory-based algorithms such as random search (RS) and simulated annealing (SA) which currently produce less control accuracy due to the local minimum problem. Motivated by the limitations of the current methods, there is an advantage to using safe experimentation dynamics (SED) as a tool for optimization. SED offers memory-based features and effectiveness to perform with lesser computation time to overcome a range of optimization problems, even for high-dimensional parameter tuning. Moreover, other than the memory-based feature, SED algorithm has fewer design parameters to be addressed and the independence of the gain sequence in the tuning process. Previously, SED algorithm has been applied in to control scheme of wind farm to optimize the total power production but has yet to be applied in PID tuning. Therefore, it is good to study the effectiveness of SED in PID tuning. In this study, the efficiency of the proposed approach is tested by applying the PID controller tuning to the slosh control system, double-pendulum-type overhead crane (DPTOC) control system and multi-input-multi-output (MIMO) crane control system. The performance was evaluated using numerical examples in terms of tracking performance and control input energy. Thirty trials have been performed to evaluate the SED, norm limited SPSA (NL-SPSA), global norm limited SPSA (G-NL-SPSA), and RS algorithms in each example. Next, when the pre-stated termination condition is fitted, each method is evaluated based on the statistical analysis involving the objective function, the total norm of the error and total norm of the input. Then, the rise time, settling time, and percentage of overshoot of the one best trial out of the 30 trials were observed for each method. In the DPTOC control system, we also present the examples with disturbance. The performance comparison was made only between the SED based method and G-NL-SPSA based method. In addition, the average percentage of the control objective improvement retrieved from the 30 trials for each method was also observed.