A neural network‐based design method of the fractional order PID controller for a class of motion control systems

In this paper, a finite‐time optimal tracking control scheme based on integral reinforcement learning is developed for partially unknown nonlinear systems. In order to realize the prescribed performance, the original system is transformed into an equivalent unconstrained system so as to a composite system is constructed. Subsequently, a modified nonlinear quadratic performance function containing the auxiliary tracking error is designed. Furthermore, the technique of experience replay is used to update the critic neural network, which eliminates the persistent of excitation condition in traditional optimal methods. By combining the prescribed performance control with the finite‐time optimization control technique, the tracking error is driven to a desired performance in finite time. Consequently, it has been shown that all signals in the partially unknown nonlinear system are semiglobally practical finite‐time stable by stability analysis. Finally, the provided comparative simulation results verify the effectiveness of the developed control scheme.

“…. By observing (13), we can see if the reinforcement interval T is small enough, Δ φ tends to 0. Define ℏ 0 as a small enough positive constant and one has…”

Section: Stability Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Finite‐time optimal tracking control for a class of nonlinear systems with prescribed performance

Wang

Liu

et al. 2023

“…Fractional-order proportional-integral-derivative (FOPID) controllers have gained a lot of interest in recent years, both academically and industrially [39][40][41][42][43][44][45][46][47][48]. The FOC was introduced in 1997 by Pdlubny et al [49].…”

Section: Introductionmentioning

confidence: 99%

Performance improvement of aircraft pitch angle control using a new reduced order fractionalized PID controller

Idir

Bensafia

Khettab

et al. 2022

In this paper, a new optimal reduced order fractionalized PID (ROFPID) controller based on the Harris Hawks Optimization Algorithm (HHOA) is proposed for aircraft pitch angle control. Statistical tests, analysis of the index of performance, and disturbance rejection, as well as transient and frequency responses, were all used to validate the effectiveness of the proposed approach. The performance of the proposed HHOA-ROFPID and HHOA-ROFPID controllers with Oustaloup and Matsuda approximations was then compared not only to the PID controller tuned by the original HHO algorithm but also to other controllers tuned by cutting-edge meta-heuristic algorithms such as the atom search optimization algorithm (ASOA), Salp Swarm Algorithm (SSA), sine-cosine algorithm (SCA), and Grey wolf optimization algorithm (GOA). Simulation results show that the proposed controller with the Matsuda approximation provides better and more robust performance compared to the proposed controller with the Oustaloup approximation and other existing controllers in terms of percentage overshoot, settling time, rise time, and disturbance rejection.

“…In recent years, fractional-order control (FOC) has attracted more and more attention from academic and industrial associations [31,32]. Due to the introduction of fractional-order calculus, the controller has additional parameters to tune, so more specifications can be met.…”

Section: Introductionmentioning

confidence: 99%

An optimal robust design method for fractional‐order reset controller

Wang

Sun

et al. 2022

In this paper, a novel design method for the reset controller structure (i.e., fractional‐order proportional and integral plus Clegg integrator (PI α$$ {}&#x0005E;{\alpha } $$ + CI α$$ {}&#x0005E;{\alpha } $$)), is proposed for a second‐order plus time delay plant. To this end, the designer can get an optimal fractional reset controller that gives the control system more phase margin over the base linear PI controller and robust to loop gain variation. The describing function method is used to investigate the capability of phase lead and the frequency domain properties of PI α$$ {}&#x0005E;{\alpha } $$ + CI α$$ {}&#x0005E;{\alpha } $$. The gain crossover frequency and phase margin specifications ensure the stability of the control system, and the flat phase constraint makes the control system robust to loop gain variations. Meanwhile, the integral of time and absolute error (ITAE) value is applied to achieve the optimal dynamic performance as the cost function. PI α$$ {}&#x0005E;{\alpha } $$ + CI α$$ {}&#x0005E;{\alpha } $$ is compared with its integer‐order counterpart (i.e., proportional and integral plus Clegg integrator (PI + CI) controller) and their base controllers (i.e., integer‐order PI and fractional‐order PI controllers) in terms of the step response and robustness to loop gain variations. The simulation results illustrate that the PI α$$ {}&#x0005E;{\alpha } $$ + CI α$$ {}&#x0005E;{\alpha } $$ control system obtains lower overshoot and oscillation and better robustness to loop gain variations than others. The experiments are performed on the speed control of an air bearing stage. Experimental results show that the designed PI α$$ {}&#x0005E;{\alpha } $$ + CI α$$ {}&#x0005E;{\alpha } $$ control system behaves better than others. The proposed PI α$$ {}&#x0005E;{\alpha } $$ + CI α$$ {}&#x0005E;{\alpha } $$ design method can be applied to other general control plants easily.