Shahab Tohidi

Stability analysis of flexibility function

Flexibility function as a nonlinear and stochastic dynamical system is introduced to represent the price-demand relationship in a price-responsive energy system. This dynamic function is going to become a core for decision-making at different levels of the hierarchy of controllers in the smart energy operating system (OS). Therefore, the widespread usage of this dynamic system pops up the need for a stability analysis.  

Adaptive model predictive control of building thermal dynamics

Model predictive controllers have been shown to be efficient for the control of energy and thermal systems. However, most existing approaches assume that the model is constant. In addition, the process of developing a precise model for MPC can be time-consuming and costly. This inspired us to propose an adaptive MPC that utilizes a simple linear nominal model of the thermal dynamics and is capable of identifying the changes in the system and accommodating the model for the MPC. Lyapunov’s stability theorem is provided to guarantee the convergence and stability of the identification and adaptive MPC, respectively. 

Optimal price signal generation

Finding an optimal price (penalty) signal for MPC for demand-side management is a requirement in many energy systems. Currently, this signal is prespecified based on a general pattern of electricity price changes in each region. However, employing the flexibility function provides the opportunity to connect different levels of control hierarchy such as the electricity market and aggregators. In this work, we investigate different optimization algorithms to provide a penalty signal using the reference demand provided by an aggregator. This approach can also be used for ancillary services in power systems.   

Adaptive flexibility function

The flexibility function is a nonlinear mapping between the energy price and demand. It can be employed in smart energy systems to generate price signals for MPCs for demand shifting and consumption scheduling. However, energy-flexible systems may change and consequently, a modified flexibility function is required. To this end, we proposed an adaptive flexibility function capable of identifying the changes and adapting the flexibility function. The proposed approach is based on the Lyapunov stability theorem and guarantees stability, boundedness, and convergence of the overall system.  

From white-box to grey-box modelling (stochastic system identification)

High quality models, which are able to predict the future evolutions are required for the advanced model-based control implementation. Although, white-box modelling is a common method to simulate and provide an in-detail description of dynamics, it is not a proper candidate for the controller design due to its complexity and high-dimensionality, and the requirement for various information about the systems. Grey-box models, on the other hand, consists of a set of stochastic differential equations (SDEs), describing the dynamics of the system, and allowing incorporation of prior physical knowledge and utilization of statistical methods for parameter estimation. We have introduced a procedure for finding grey-box models of thermal dynamics of a buildings from the white-box data.

Sliding mode controller for constraint systems with redundancy

Sliding mode controllers are well-known control approaches to provide robustness in nonlinear dynamical systems. However, considering actuator constraints in sliding mode controller design is not a simple task compare to the optimization-based control approaches. The design procedure gets more complicated in the presence of multi-inputs. This study proposes a time-varying sliding mode controller for over-actuated systems with constrained and uncertain actuators. By design, the initial point of the trajectories start on the proposed sliding surface. Also, the proposed controller keeps the trajectories on this surface.

Actuator constraints such as magnitude and rate limits play a prominent role in advanced control systems. These limits induce nonlinear behavior which may lead to performance degradation, occurrence of limit cycles, multiple equilibria, and even instability. In this research, we proposed a solution to handle actuator’s magnitude and rate constraints in uncertain over-actuated systems. This is done by introducing a modified projection algorithm. In addition, the properties of this new algorithm required for ensuring stability and boundedness of the signals are proved. This algorithm can also be employed for adaptive control systems.

Unique abilities of humans such as adaptive behavior in dynamic environments, social interaction, and moral judgment capabilities, make humans essential elements of many control loops, operating in close collaboration with autonomy. Investigation of human in the loop dynamics helps develop safe control mechanisms and provide a better realization and understanding of human control actions and limitations.

Most existing human models do not consider human adaptive behavior. Inspired by humans’ ability to adapt to changing environments, the proposed adaptive human model mimics this ability despite input bandwidth deviations and plant uncertainties. The proposed human pilot model structure is based on the model reference adaptive control, and the adaptive laws are obtained using the Lyapunov Krasovskii stability criteria. Experimental data show that the proposed model mimics human behavior in the presence of uncertainty.

Conventional control allocation methods distribute the total control effort among redundant actuators. These methods require identification techniques or persistent excitation assumption to handle actuator uncertainties. The proposed adaptive control allocation is able to distribute control signals among uncertain redundant actuators without any identification or assumptions on signals. Asymptotic stability of the proposed method is guaranteed.

Although optimization-based control allocation methods are able to handle the actuator constraints, their computational complexity is high, especially when the number of actuators increases. The proposed control allocation method uses the degrees of freedom provided by the null space of the control matrix and restricts the control signals in a fixed time slot.