Control Systems Anand Kumar Pdf Free 899

We study the problem of system identification and adaptive control in partially observable linear dynamical systems. Adaptive and closed-loop system identification is a challenging problem due to correlations introduced in data collection. In this paper, we present the first model estimation method with finite-time guarantees in both open and closed-loop system identification. Deploying this estimation method, we propose adaptive control online learning (AdapOn), an efficient reinforcement learning algorithm that adaptively learns the system dynamics and continuously updates its controller through online learning steps. AdapOn estimates the model dynamics by occasionally solving a linear regression problem through interactions with the environment. Using policy re-parameterization and the estimated model, AdapOn constructs counterfactual loss functions to be used for updating the controller through online gradient descent. Over time, AdapOn improves its model estimates and obtains more accurate gradient updates to improve the controller. We show that AdapOn achieves a regret upper bound of $\textpolylog\left(T\right)$, after $T$ time steps of agent-environment interaction. To the best of our knowledge, AdapOn is the first algorithm that achieves $\textpolylog\left(T\right)$ regret in adaptive control of \textitunknown partially observable linear dynamical systems which includes linear quadratic Gaussian (LQG) control.

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In this paper, a Sliding mode controller design method for frequency regulation in an interconnected power system is presented. A sliding surface having four parameters has been selected for the load frequency control (LFC) system model. In order to achieve an optimal result, the parameter of the controller is obtained by grey wolf optimization (GWO) and particle swarm optimization (PSO) techniques. The objective function for optimization has been considered as the integral of square of error of deviation in frequency and tie-line power exchange. The method has been validated through simulation of a single area as well as a multi-area power system. The performance of the Sliding mode controller has also been analyzed for parametric variation and random loading patterns. The performance of the proposed method is better than recently reported methods. The performance of the proposed Sliding mode controller via GWO has 88.91% improvement in peak value of frequency deviation over the method of Anwar and Pan in case study 1 and similar improvement has been observed over different case studies taken from the literature.

The main objective of LFC is to regulate the frequency and tie-line power flow within the control area. The main control challenges in LFC are system model parametric uncertainty, non-linearity present in a realistic power system, and load-disturbances [4,5,6].

In recent times, the SMC design technique has gained more attention for being robust to modeling error, parametric variation, and external disturbance. These properties make SMC quite effective in many applications such as automotive systems [21], robotics [22], electric drives [23], wind-energy conversion systems [24, 25], process control [26, 27], unmanned aerial vehicles [28], etc. Recently the SMC technique has been used by many researchers to address the control issues of LFC [29,30,31,32,33,34,35,36,37,38,39].

Decentralized SMC has been designed for frequency control in a multi-area power system (MAPS), considering unmatched uncertainty, by Mi et al. [29]. Qian et al. [30] have improved control performance by using neural network-based integral SMC for the LFC of a non-linear power system. The method has been extended by Qian and Fan [31] for frequency control of a power system with renewable energy. A non-linear Sliding mode controller with matched and unmatched uncertainty has been proposed by Prasad et al. [32] for LFC of a three-area interconnected power system. Further, Prasad et al. [33] have extended their SMC design method to control the frequency of wind-integrated power systems.

In this paper, a sliding mode controller is designed for a third-order system model. A sliding surface having four parameters is introduced and then the SMC control law is derived. This consists of two-parts: i.e., a continuous part UC(t) and a discontinuous part UD(t). The parameters of UC(t) and UD(t) have been obtained by optimizing the cost function as the integral of square error. To get the optimum value of the controller parameter, PSO and GWO optimization techniques have been used. The simulation results show that the proposed method outperforms recently reported methods.

This paper is organized as follows: the LFC model for a single-area as well as a multi-area power system along with the proposed controller design method is given in Section 2. The simulation results are shown in Section 3 and the paper is concluded in Section 4.

The SMC technique is a special type of variable structure control that was initially presented by Utkin and Vadim [12]. The SMC is a robust control technique that can effectively compensate for plant model mismatch and load-disturbances. The desired behavior is represented through sliding surface s(t) and the objective of the sliding mode controller is to drag the state of the system to the surface and keep it there.

Here, e(t) is the tracking error, and k1, k2, k3 and k4 are the tuning parameters that are selected by the designer. The control objective in this case will be to ensure that e(t) and its derivatives must be equal to zero at all times, once s(t) is reached. So, to maintain s(t) at a constant value, it is essential to make its derivative equal to zero which can be mathematically represented as

After selection of the sliding surface the control law U(t) is developed by considering the condition in Eqs. (1) and (2), the SMC control law U(t), consists of a continuous control part UC(t) and a discontinuous control part UD(t) as

Solving Eq. (7) for the third-order derivative of the controlled variable $ \overset\dddotx(t) $, in conjugation with Eq. (9) and replacing the expression into Eq. (8), the following equation is obtained:

The tuning parameters k1, k2, k3, k4, KD, and δ are obtained with the use of the metaheuristic optimization technique. Several researchers have used the metaheuristic optimization algorithm to determine the controller parameters in different control problems. The particle swarm optimization (PSO) technique is used by Mehta and Kaya [40] while the cuckoo search (CS) algorithm is adopted by Mehta and Rojas [41] to obtain the controller setting. The democratic joint operation algorithm [42], grouped grey wolf optimization [43], the dynamic leader-based collective intelligence algorithm [44] are some recently reported optimization techniques which have been successfully implemented in different control problems. Here, we have used PSO and GWO optimization techniques to obtain the controller parameters in Eq. (12).

The proposed controller design method is implemented for the LFC problem. The plant model for the LFC consists of governor, turbine, generator, and load. The schematic diagram of a single area power system (SAPS) is shown in Fig. 2.

The block diagram of a multi-area power system (MAPS) is shown in Fig. 3. The proposed controller design method can also be extended to MAPS where the goal of LFC is to regulate the frequency of each area and further to maintain the tie-line power flow exchange between the areas. With the variation of load in the power system the area frequency and tie-line power interchange vary. So, a combined parameter, area control error (ACE), is a linear combination of deviation in frequency response and tie-line power flow exchange, and is used in each LFC of MAPS.

To obtain the controller parameters (k1, k2, k3, k4, KD and δ) PSO and GWO techniques have been used. In the case of SAPS the ISE of the frequency deviation is taken as the objective function (Eq. 20) and in the case of MAPS, the ISE of the change in frequency in all the areas alongside the adjustment in tie-line power is taken as the objective function (Eq. 21).

To illustrate the proposed method, five cases are taken from K. Lu et al. [6]. Various cases are taken to analyze case study 5, which is given in Table 4. The block diagram of a two-area interconnected power system is shown in Fig. 9. The tuning parameters k1, k2, k3, k4, KD, and δ of the proposed method as obtained from GWO are 0.3554, 18.4423, 156.7927, 317.8682, 0.8789, and 3.3124 respectively. The tuning parameters k1, k2, k3, k4, KD, and δ of the proposed method as obtained from PSO are 0.086, 9.797, 47.4837, 113.97, 2.2183, and 0.5419 respectively. The controller parameters for both areas are the same.

Figure 16 shows the frequency regulation in area 1 and ACE in area 1 is shown in Fig. 17. Figures 16 and 17 show that the proposed1-GWO controller has much-improved performance over that of the proposed2-PSO, K. Lu et al. [6].

In this paper, the sliding mode controller has been designed for a third-order system and implemented for frequency regulation in single-area, two-area, and four-area power systems. The optimal value of SMC controller parameters is obtained via the GWO and PSO optimization techniques. The efficacy of the proposed method has been analyzed with consideration of GRC, parametric uncertainty, and a random loading pattern. The proposed SMC controller via GWO performs better than the proposed SMC controller via PSO and other recently reported methods. From the simulation study, it is seen that the proposed method via GWO has 88.91% improvement in peak value of frequency deviation with that of Anwar and Pan while the proposed method via PSO has 84.80% improvement in case study 1. Future work on the proposed method is to implement in LFC problem considering wind energy, hydro-energy, and photo-voltaic systems.

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