Programmable Logic Controllers are widely used in industry. Reliable PLCs are vital to many critical applications. This paper presents a novel symbolic approach for analysis of PLC systems. The main components of the approach consists of: (1) calculating the uncertainty characterization of the PLC systems, (2) abstracting the PLC system as a Hidden Markov Model, (3) solving the Hidden Markov Model using domain knowledge, (4) integrating the solved Hidden Markov Model and the uncertainty characterization to form an integrated (regular) Markov Model, and (5) harnessing probabilistic model checking to analyze properties on the resultant Markov Model. The framework provides expected performance measures of the PLC systems by automated analytical means without expensive simulations. Case studies on an industrial automated system are performed to demonstrate the effectiveness of our approach.