text: A multi-objective design approach for tuning LQR controllers is proposed.A new reinforced quantum-behaved PSO algorithm is introduced.Comparative studies among nine various techniques are conducted. A novel and generic multi-objective design paradigm is proposed which utilizes quantum-behaved PSO (QPSO) for deciding the optimal configuration of the LQR controller for a given problem considering a set of competing objectives. There are three main contributions introduced in this paper as follows. (1) The standard QPSO algorithm is reinforced with an informed initialization scheme based on the simulated annealing algorithm and Gaussian neighborhood selection mechanism. (2) It is also augmented with a local search strategy which integrates the advantages of memetic algorithm into conventional QPSO. (3) An aggregated dynamic weighting criterion is introduced that dynamically combines the soft and hard constraints with control objectives to provide the designer with a set of Pareto optimal solutions and lets her to decide the target solution based on practical preferences. The proposed method is compared against a gradient-based method, seven meta-heuristics, and the trial-and-error method on two control benchmarks using sensitivity analysis and full factorial parameter selection and the results are validated using one-tailed T-test. The experimental results suggest that the proposed method outperforms opponent methods in terms of controller effort, measures associated with transient response and criteria related to steady-state.
  @cite_55: This paper discusses design and performance issues of three design techniques for DSTATCOM controller with an aim to improve the robustness. The state feedback controller of DSTATCOM has been designed using Linear Quadratic Regulator (LQR), Linear Quadratic Regulator with prescribed degree of stability and Particle Swarm Optimization (PSO). Weak ac source and unbalanced nonlinear load are considered. The performance of the controller designed through the three methodologies has been compared under different operating conditions. Particle Swarm Optimization based controller is more robust and is suitable for a DSTATCOM working under uncertain parametric conditions like feeder impedance and load that are most common in a distribution system. This controller ensures stability under all possible operating conditions and has superior performance over the other two controller design techniques. The performance of the DSTATCOM controller designed through the three different methodologies is verified by detailed simulation studies.
  @cite_38: This paper presents the design of an active suspension control of a two-axle railway vehicle using an optimized linear quadratic regulator. The control objective is to minimize the lateral displacement and yaw angle of the wheelsets when the vehicle travels on straight and curved tracks with lateral irregularities. In choosing the optimum weighting matrices for the LQR, the Particle Swarm Optimization (PSO) method has been applied and the results of the controller performance with weighting matrices chosen using this method is compared with the commonly used, trial and error method. The performance of the passive and active suspension has also been compared. The results show that the active suspension system performs better than the passive suspension system. For the active suspension, the LQR employing the PSO method in choosing the weighting matrices provides a better control performance and a more systematic approach compared to the trial and error method.
  @cite_37: In this paper, considering some important indices such as closed-loop pole locations, speed of response and combining them into an objective function an optimization problem is defined in order to select the weighting matrices in Linear Quadratic Regulator (LQR) controller. To solve this optimization problem the Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) are utilized and compared. The proposed method is applied to rotational inverted pendulum. Simulation results show the relative superiority of PSO over GA.
  @cite_12: In this paper the method of Linear Quadratic Regulator (LQR) is employed for controlling accelerator PWM power supply, and improving its dynamic functioning. A method based on the Particle Swarm Optimization is proposed to optimize the weighting matrix Q and R. In order to control the dynamic behavior of the power supply, the fitness function of PSO is acquired considering the needs of the power properties. The results of simulation proved that the proposed method was much better than simple LQR method and LQR-GA method, and the performance of the power supply was improved dramatically.
summary: One of the most successful yet less applied techniques for optimal designing of LQR controllers is PSO. The superiority of PSO over GA in finding optimal weighting matrices has been experimentally shown in some studies @cite_37 @cite_12 . In @cite_38 PSO, GA and trial-and-error methods are utilized to adjust LQR weighting matrices which is applied to controlling an aircraft landing flare system. It is concluded that LQR design based on PSO is more efficient and robust compared to other methods. In @cite_55 authors compared the performance of the ordinary LQR, the LQR with prescribed degree of stability (LQRPDS) and the PSO-based LQR in controlling distribution static compensator and showed that PSO-based design results in best performance under different operating conditions.